Markets, Organizations and Incentives - Notes (31/30), Dispense di Economia Industriale

Scarica Markets, Organizations and Incentives - Notes (31/30) e più Dispense in PDF di Economia Industriale solo su Docsity! Lectures 1, 2, and 3 – Game Theory Normal Form Game For simplicity we consider only games with two players, but all the results can be extended to games with n>2 players. A game in normal form is a list Γ=({1 ,2 }, S1 , S2 , u1 ,u2) comprising the following objects: - A set of players {1 ,2 }. Given player i, we will write -i to denote the other player. - For each player i, a set of strategies Si. We defined S≔S1×S2. - For each player i, a payoff function ui :S→ R.  Note that the set of strategies is the cartesian product of each strategy. We say a game in normal form is finite if the set of strategies of each player is finite. A mixed strategy of player i is a probability distribution over Si. A pure strategy of player i is a degenerate mixed strategy of player i, that is, a mixed strategy that assigns probability one to a single element of Si. We let Σi denote the set of all mixed strategies of player i and we define Σ=Σ1× Σ2 . The utility function of each player i can be extended to Σ in the obvious way. Given (σ 1, σ 2) ϵΣ, Examples of a finite game: - {1,2} - S1 ={U,M,D} - S2 ={L,R} - S = S1 × S2 = {(U, L), (U, R), (M, L), (M, R), (D, L), (D, R)} - u1={u1(U,L) = 5, u1(U.R)= 4, u1(M,L) = 6, u1(M,R)=3,u1(D,L) = 6, u1(D,R) =4} - u2={u2(U,L)=1,u2(U,R)=0,u2(M,L)=0,u2(M,R)=1,u2(D,L)=4, u2(D,R)=4} Dominance and Best Response1 A rational player i cannot choose a strictly dominated strategy, nor can she believe player -i would, nor can she believe player -i believes that i would, and so on. How do we formalize this idea? - Starting from the game Γ, let us recursively delete all strictly dominated strategies of all players. - The strategies in Γ that survive iterated elimination of strictly dominated strategies are said to be rationalizable. - If every player has a unique rationalizable strategy, then we say the game Γ is dominance solvable. A basic assumption of game theory is that each player maximizes his payoff, given his belief about what the other players does. We say that a strategy si ∈Si is a best response to σ−i is ui (si , σ−i )≥u i (s i ' , σ−i ) for all si ' ∈Si. In some cases, a strategy of i does strictly better than another, regardless of what player -i will do . A strategy si ∈Si is strictly dominated if there exist σ i∈Σi such that ui (σ i , s−i ) ≥u i (s i , s−i ) for all s−i ∈S−i. In this case, we say σ i strictly dominates si. A strategy si ∈Si is weakly dominated if there exist σ i∈Σi such that ui (σ i , s−i ) ≥u i (s i , s−i ) for all s−i ∈S−i, with strictly inequality for some s−i. 1"s" is used when referring to specific actions or pure strategies, while "σ" is used when discussing probability distributions or mixed strategies. Here is another example. In a market there is a single firm (M). A potential competitor (E) must decide whether enter (e) or not (ne) in the market. If E enters, the monopolist must decide whether to accommodate (a) or fight (f). Both (ne, f) and (e, a) are Nash equilibria, but the first is unreasonable, because it prescribes f after e, which is irrational at the node following e. The idea of subgame perfect equilibrium is to rule these “not credible threats” by requiring that behaviour in part of the game can be regarded as games in themselves should agree with Nash equilibria of them. A subgame perfect equilibrium is a strategy such that, for every subgame, the continuation strategy profile from the initial node of the subgame is a Nash equilibrium of the subgame. A subgame is a subset of a game starting with an information set that contains a single decision node. - Every extensive form game is a subgame itself. In finite extensive games with perfect information subgame perfect Nash Equilibria can be found using the back ward induction method: - Solving first for optimal behaviour at the “end” of the game, - Then determining what optimal behaviour is earlier in the game given the anticipation of this later behaviour. Zermelo’s Theorem: Every finite game of perfect information has at least one pure strategy subgame perfect Nash equilibrium (that can be derived through backward induction). Repeated Games A repeated game consists in the repetition of a normal form game ({1, 2}, A1, A2, u1, u2), called the stage game. - We write Ai instead of Si to denote the stage game strategy set of player i. - This is because we reserve the symbol Si to denote i’s set of strategies in the repeat game. - A strategy of the stage fame is instead called an action. - We assume that A1, A2 are finite. - We also assume perfect monitoring, i.e. we assume that at each stage the two players choose their actions simultaneously and, once actions have been chosen, they are observed before the game moves to the following stage. A history is either the empty set of a finite sequence of action profiles, representing what has happened so far in the game. The empty set Ø is the initial history, i.e. nothing has happened yet. Thus, the set of initial histories is H 1≔ { Ø } and, for all t ≥2, the set of period t histories is H t≔ At−1. Let H denote the set of all histories, that is, H=H 1∪H 2∪H 3∪… A strategy for player is a function si :H → A i. In other words, a strategy for i specifies an action si ( Ø ) to take at the first stage and, for each t ≥2 and for each possible period t history H t, an action si ( H t ) to take in stage t . The set of all strategies for player i is denoted Si and as usual we define S≔S1× S2. A special kind of a repeated game is one where the same game in normal form is repeated a finite number of times. Consider the following: This game has two NE: (A, L) and (C, R). In the repeated version, it is a SPE to play (A, L) (or (C, R)) in the first stage, and then (A, L) (or (C, R)) in the second stage, regardless of what happened in the first stage. But there is also a SPE where at the first stage player 1 chooses B and player 2 plays M, and the second period behaviour prescribed by the equilibrium strategies depends in the following way on what happened in the first stage: - If in the first stage (B, M) was chosen, then in the second stage player 1 plays C and player 2 plays R. - If in the first stage (B, M) was not chosen, then in the second stage player 1 plays A and player 2 plays L. Example of stage game repeated twice: This combination of strategies suggests playing (B, M) in the first stage, that will lead to an immediate benefit since the payoff will be (4,4). Afterwards, players will play the “best NE” since they have no incentive to deviate from it.  They have no incentive to deviate from (B, M). Otherwise, they would always play (A, L) receiving a lower payoff.  Given that player 2 chooses M, for player 1 it would be optimal to choose A (with payoff (5,0)). However, this would lead to an immediate benefit but to a long-term loss. Infinitely repeated games Subscripts indicate players, superscripts indicate periods. When the game is repeated an infinite number of times an outcome is an infinite sequence (a1, a2 ,… ), so it is not obvious how to compute player i's payoff in the repeated game. For instance, since A is finite, if ui (at )>0 for all t , then just taking the sum ui (a1 )+u i ( a2 )+… will give +∞ regardless of what the sequence (a1 , a2 ,…) actually is. There are several possibilities to fix this problem, and one of the most commonly used in economics is discounting. It is assumed that both players evaluate streams of stage payoffs by taking the discounted sum according to a common discount factor δ ϵ (0,1 ). Thus, player i's payoff from the outcome (a1, a2 ,…) will be given by For any strategy profile s, we write U i (s ) to denote the utility to player i corresponding to the outcome induced by s. Using the discounting criterion to evaluate payoffs is convenient because it allows us to use the one-shot deviation principle to check whether a strategy profile is a subgame-perfect equilibrium. This principle says that a strategy profile is subgame if and only if, at each history, no player has an incentive to deviate choosing an action different from the one prescribed by the strategy profile at that stage and then follow the strategy profile in the continuation.  A first result that we establish is that, in an infinitely repeated game, the strategy profile where both players choose a stage-game NE in every period, regardless of history, is a SPE of the repeated game. Infinite repetition of the NE of the stage game: Suppose the stage game (N , ( Ai , ui )i ∈ N ) has a pure strategy Nash equilibrium a¿ϵ A. Then the strategy profile such that s (h )=a¿ for all h∈H is a subgame perfect equilibrium of the repeated game. However, in a repeated game there are many other SPE outcomes besides those consisting in the repetition of a stage game NE. Choose a Nash equilibrium a¿,i ∈ A of the stage game for every player i. There exists δ such that, for every δ ≥ δ and every a∈ A such that ui (a )>ui (a¿ ,i ) ∀ i, there exists a subgame perfect equilibrium s of the repeated game such that U i (s )=ui (a ) ∀ i. In general, it is hard to describe the set of SPE outcomes for a fixed value of δ. However, if the stage game has a unique NE and δ is very small, then the only SPE outcome in the repeated game is the infinite repetition of the stage game NE outcome: - The immediate gain from deviating (which some player must have, if players are not playing a stage game NE) cannot be compensate by the loss associated to future punishment. Bertrand Equilibrium with symmetric costs: 1. Consider (p1,p2) with p1=p2=p>c. Given that firm –i chooses p-i=p, by choosing pi’=p-e, firm i obtains πi ’=(p-e-c)Q(p-e)>(p-c)Q(p)/2= πi. There exists a profitable deviation! 2. Consider (p1,p2) with p1>p2>c. In the candidate equilibrium firm 1 obtains π1=(p1-c)0=0. Given that firm 2 chooses p2, by choosing c<p1’<p2, firm 1 obtains positive profits. π1 ’=(p1’ -c)Q(p1’)>0= π1. There exists a profitable deviation! 3. Consider (p1,p2) with p1>p2=c. Given that firm 1 chooses p1, by choosing c<p2’<p1, firm 2 obtains positive profits. π2 ’=(p2’ -c)Q(p2’)>0= π2. There exists a profitable deviation! 4. Consider (p1,p2) with p1¿p2≤c. Given that firm 2 chooses p2, by choosing p1’>p2, firm 1 makes zero profits π1 ’=(p1’ -c)0=0>π1. There exists a profitable deviation! 5. Similarly (p1,p2) with p1=p2=p<c. Given that firm -i chooses p-i=p, by choosing pi’>p, firm i makes zero profits πi ’=(pi’ -c)0=0>πi. There exists a profitable deviation! 6. Consider (p1,p2) with p1=p2=p=c. Given that firm -i chooses p-i=c, by choosing pi’>c, firm i does not sell and makes zero profits πi ’=(p1’ -c)0=0= pi . Given that firm -i chooses p-i=c, by choosing pi’<c, firm i makes negative profits πi ’=(pi’ -c)Q(pi’ )<0= πi.  Firm i cannot increase its profits by choosing a price different from c → pi=c is a best response to p-i=c. There is unique Nash Equilibrium in which ( p1¿=c , p2 ¿=c) which implies no market power. The Bertrand paradox exists especially because of all the assumptions we assumed to hold. Why do we obtain such a result? - As firms offer the same product (+ all other assumptions), slightly undercutting rival is hugely effective in stealing customers. - In equilibrium, no profitable deviation means undercutting must not be profitable; The end result is cut- throat competition! - In the Bertrand setting equilibrium prices must equal marginal cost, because this is the only profile of prices that makes stealing customers unprofitable. Market power is killed by the profitability of undercutting, which in turn is due to the fact that decreasing (slightly) the price attracts a lot of customers. Any factor that reduces the profitability of undercutting reduces the intensity of rivalry and creates market power (i.e. ability to sustain prices above marginal costs): - Cost asymmetries - Capacity constraints - Product differentiation - Search costs - Switching costs - Repeated interaction Asymmetric costs - Assumptions: as in the baseline model except MC1=c1>c2=MC2. - We also assume pm(c2)>c1 (see PS1 for the case in which this assumption is relaxed). Result: A Nash Equilibrium of this game is: ( p1¿=c , p2 ¿=c−ε ). However, all the pairs of prices expressed by p1 ¿=pwhere pϵ (c2 , c1 ) and p2 ¿= p−ε (where ε→0) are Nash equilibria as well. Remark: the more efficient firm captures all the demand. Considering ε→0, equilibrium profits are: π1=0 , π2=(c1−c2)Q (c1 )>0. Proof: No firm has the unilateral incentive to deviate from the candidate equilibrium. - Firm 1: if it sets a price lower than p1 ¿, he will get negative profits – since it will capture more demand, but with prices lower than its marginal cost. If p1’>p1 *, then π 1’=0= π 1. - Firm 2: if it sets a lower price than p2 ¿, it will get a profit lower than the equilibrium one p2’=(p2’- c2)Q(p2’)<(c1- c2)Q(c1)=p2. Even if demand captured will be higher, the profit will be lower by construction of the profit function. If p2’>p2 *, then π2’=0<π2. Cost asymmetries generate market power. - The less efficient firm has no incentive to undercut a price = c1 so as to steal customers. - The more efficient firm chooses a price above its marginal cost and gets a margin equal to its cost advantage relative to the rival firm. Market power is increasing in the cost difference between the two firms. However, in game theory is not convenient to have more than one NE, hence we have some ways to "exclude" some alternatives (it is a refinement of a Nash equilibrium): - Trembling hands: consider the second equilibrium. If some consumer at eq. should buy from firm 2, make a mistake and buy to firm 1. anticipating this, firm 1 won't choose that price since it would make a loss! The only equilibrium in which this holds with mistakes is the first one. - Pareto dominance: within all the possible equilibrium, firm 1 has always 0 profit. Firms 2 goes from 0 to the highest which is the difference between the two costs and the demand. In any case, firm 1 is indifferent, whereas firm 2 prefers, of course, the highest payoff. Kenneth Arrow: A more competitive environment may lead to stronger incentives to innovate (for instance in cost reduction technologies). Main intuition: innovation is driven by incremental profits. - A monopolist obtains high profits. Innovation (cost reduction) increases the monopolist’s profits, but since such profits are high even without innovation, the increase in profits caused by innovation is limited. - In a Bertrand environment where competition is extremely intense, without innovation (i.e. having the same marginal cost as rivals) profits are equal to zero. - The only way to make positive profits is to be more efficient than rivals. - Innovation increases profits significantly. Very strong incentive to innovate. Giving up the assumption that pm(c2)>c1, suppose now that pm(c2)<c1. - Now, ( p1¿=c , p2 ¿=c−ε ) is not a Nash equilibrium anymore.  This is because Firms 2 has an incentive to deviate by lowering its price to p2 ' =pm (c2 ) to increase profits, as pm (c2 ) isless than c1. - Same reasoning goes for any other pair of prices with p1 ϵ ( p2m ,c1 ] and p2=( p2m , c1 ]. Each pair of prices p1 ¿= p where pϵ (c2 , p2 m ) and p2 ¿= p−ε (where ε→0) are Nash equilibria.  At each of these equilibria, Firms 1 obtains zero profits, while Firm 2’s profit ranges from 0 to π2 m, increasing as the equilibrium price p rises. The Pareto Efficient equilibrium is (p1 ¿=p2 m and p2 ¿=p2 m−ε) (where ε→0). At this equilibrium, both firms maximize their profits given the constraint of their marginal costs. Capacity constraints In the baseline model each firm is always able to satisfy all the demand that addresses it. Increasing output beyond capacity limits is often prohibitively costly in the short run. With no capacity constraints price competition leads in equilibrium to prices being equal to marginal costs. Let us solve the following two-stage game: - Stage 1: firms choose capacities K1 and K2 simultaneously. - Stage 2: firms set prices simultaneously. Assumptions: - The marginal cost of capacity is c (incurred in stage 1) – cost to install one unit of capacity. - The marginal cost of production, incurred in stage 2, is 0 (for simplicity). Let us solve the game by backward induction. - Given K1 and K2, we find the NE of the second stage (price). - Then, anticipating the equilibrium outcome of the second stage, we solve for the NE capacity choice. To identify the Nash equilibrium, we need to specify the way customers are rationed. When one firm sets a lower price than the rival, but cannot satisfy all the demand: - We assume the efficient rationing rule: consumers with higher willingness to pay are served first. - They would obtain the product in a secondary market. Imagine p1<p2 and Q(p1)>K1. Among the rationed consumers, those whose willingness to pay is above p2, will buy from firm 2. When p1< p2 and K 1<Q (p2 ), firm 2’s residual demand is: Q2 r (p2 )={Q ( p2 )−K1 if Q ( p2)≥ K1 0otherwise Nash equilibrium in prices – For simplicity, let us assume that market demand is Q=a-p with a>c. Since capacity is costly, a firm would never choose a capacity level such that capacity costs are higher than the maximal period-2 profits:  The highest profit you can make is if you are a monopolist. We can exclude from the model every capacity that does not comply with the last equation. For simplicity we also assume that a< 4 3 c. Under the efficient rationing rule, the unique Nash equilibrium is (p1*, p2*) with p1*=p2*=p* such that: Q ( p¿)=K1+K 2 and p¿=a−K1−K2. At the NE equilibrium firms choose prices such that market demand is equal to total capacities. Cournot equilibrium – Properties: - Output per firm: q1 ¿=q2 ¿=a−c 3 - Price: p¿=a+2 c 3 >c - Profits: π¿=2( a−c 3 ) 2 Compared to a monopolist: Qm<q1 ¿+q2 ¿; pm> p¿; πm>π¿: - Total output under Cournot duopoly is higher than monopoly , but price and total profits are lower than under monopoly. - Even though firms choose capacity/output in such a way to limit the intensity of price competition, they do not manage to reproduce the monopoly outcome. When each duopolist chooses capacity/how much to produce it does not take into account the impact of its action on the other firms’ profits (negative externality). Firm 1 compares the benefit from a marginal increase in capacity/production (the margin P-c on the additional unit) with the loss from a marginal increase in capacity/production (the equilibrium price will decrease so as to make market demand equal to total production/capacity and such a price decrease is suffered on all of firm 1’s inframarginal units). However firm 1 does not take into account the loss that firm 2 suffers because of the price decrease. Instead, the monopolist evaluates the loss from a marginal increase in production on the entire production. Why can’t we just all get along? Another way to see the same issue is the following. Suppose that the two duopolists sit together and agree to each producing half of the monopoly output (only verbal agreement!). Will they behave according to the agreement? - The monopoly output is chosen in such a way that the benefit from a marginal increase in production is equal to the loss from a marginal increase in production: P (Qm )−c+Qm( ∂ P ∂Q )=0 (first order condition: what is the gain from an increase in production by one. P−c represents the profit margin). At Qm the profit function is flat: if quantity increases by a tiny amount, profit do not change. Under duopoly, if firm 1 expects its rival to choose q2= Qm 2 , would it optimally choose q1= Qm 2 ? - Total quantity would be Qm, so that the FOC of the duopolist is: P (Qm )−c+ Qm 2 ∂P ∂Q ∂Q ∂q1 >0 (where ∂Q ∂q1 =1) - By selling one more unit firm 1 needs to lower the price of all its units, which are only half of the monopoly output. It follows that firm 1’s marginal loss of selling one more unit is lower than the marginal loss to a monopolist and firm 1 will find it optimal to produce more than Q m 2 .  (Qm ,Qm ) is not a Nash Equilibrium, since there is incentive to deviate. Indeed, each player underestimates the detrimental effect of producing more, i.e. each player only considers its own profits and do not care about the effects it will have on the other player. Indeed, in our specific case in which P (Q )=a−q1−q2, the best reply of firm 1 is: Cournot equilibrium – many firms Suppose that in the same market with linear demand Q=a−P there are multiple firms. In particular there are N identical firms. Suppose that Firm 1 expects all the others to produce q2, q3, …qN. Then the optimal quantity of firm 1 is the one that solves the following maximization problem: max q1 [ (a−q1−q2−…qN ) q1 ]. The first order condition regarding firm 1 is given by: (a−q1−q2−…qN−c ) q1=0 There will be N first order condition, one for each firm: {( a−q1−q2−…qN−c )q1=0 ( a−q1−q2−…qN−c )q2=0 … (a−q1−q2−…qN−c ) qN=0 The Nash Equilibrium is given by the solution of the above system of equations. As a shortcut one can exploit symmetry (if we can – we assume that at eq. everyone produces the same quantity): q1 ¿=q2 ¿=q3 ¿=q¿. Therefore, substituting in one FOC: a−N q¿−c−q¿=0→a− (N+1 )q¿−c=0 ⇒ q¿= a−c N+1 Remark: the individual equilibrium production decreases as the number of competitors in the industry (N) increases. Once found the equilibrium production of each firm, one can find the equilibrium total production (Q¿=N q¿); then, substituting in the demand function, one obtains the equilibrium price (p*), the equilibrium individual profits (p*) and the equilibrium industry profits (P*): Q¿=N q¿= N ( a−c ) N+1 ; p¿=a+Nc N+1 ;π ¿=( a−c N+1 ) 2 ; Π ¿=N ( a−c N+1 ) 2  Two important insights: as the number of firms grows (N →∞), the equilibrium price tends to the competitive equilibrium (P →mc) and individual as well as industry profits tend to zero ( π→0 , Π →0)! Cournot equilibrium – general framework: - P (Q )→ market (inverse) demand. - Q=∑ 1 N q j→ total quantity produced. - C i (q i )=ci q i→ cost function of firm i. First order conditions Recalling that the elasticity of demand is given by ε= ∂Q ( P ) ∂P P Q  where Q ( P ) is the direct demand function. Therefore, 1 ε = 1 ∂Q ( P ) ∂P Q P =∂P (Q ) ∂Q Q P  where the last equality is due to the property the inverse of the derivative of the direct demand function is equal to the derivative of the inverse demand function. [ f ¿¿−1(x )] '= 1 f ' ( f−1 ( x ) ) ¿ Hence, it becomes: In the Cournot environment market power of firm i is higher: - the higher the market share of firm i. - the lower the elasticity of market demand.  Herfindhal-Hirshman Index (HHI): most used measure of concentration Therefore, we can write P−c P = HHI −ε .  In the Cournot environment, market power is correlated with concentration.  To the extent that the Cournot model is a reasonable description of the market functioning, based on HHI and an estimation of demand elasticity, one obtains a measure of market power. N.B. the Horizontal Merger Guidelines explicitly mention the HHI (before and after the merger). For homogenous products drastically different predictions. Cournot: - Competition erodes firm profits gradually. - Approach the socially efficient level of output as the number of competitors increases. Bertrand: - Cut-throat competition completely erodes firm profits even with only two firm. - “Any” number of competitors achieves the socially efficient level of output When products are not perfect substitutes, both frameworks predict prices above marginal cost.  Suitability depends on industry/technology studied.  Cournot: if firms have temporary built in-capacities, hard to adjust immediately to satisfy excess demand.  Bertrand: firm can easily adapt to changes in demand. Lecture 6 - Product Differentiation and Strategic positioning - Given p2, let us find the optimal price of firm 1: max p1 ( p1−c) N [ l2+l1 2 + p2−p1 2 t (l2−l1 ) ] - First order condition: In order to find the optimal price, firm 1 compares how much it gains and how much it loses changing the price at the margin. The price is optimal when the two are equalized. Otherwise, by changing the price firm 1 can increase its profits. From the FOC: p1 br ( p2 )= p2+c 2 + t (l2+l1 ) (l2−l1 ) 2 𝑁൤𝑙2 + 𝑙12 + 𝑝2 − 𝑝12𝑡ሺ𝑙2 − 𝑙1ሻ− 12𝑡ሺ𝑙2 − 𝑙1ሻሺ𝑝1 − 𝑐ሻ൨= 0 ↓ ↓ 𝐷1 (𝑝1 − 𝑐)𝜕𝐷1𝜕𝑝1 Given p1, let us find the optimal price of firm 2: max ( p2−c )N [ 2−l2−l1 2 + p1−p2 2 t (l2−l1 ) ] FOC: N [ 2−l2−l1 2 + p1−p2 2 t (l2−l1 ) − p2−c 2t (l2−l1 ) ]=0 p2= p1+c 2 + t (2−l1−l2 ) (l2−l1) 2 ≡ p2 r (p1 )  If firm 1 increases by one euro, it will sell everything at one euro more (benefit from increase in price). The derivative of the demand wrt the price tells how much the demand decreases by the increase in the price. Best reply curves are upward sloping: - If firm i increases pi, firm j responds by increasing its price. - This is an example of interaction in strategic complements. When your rival increases prices, it is optimal to increase price also for you. The FOC would become positive, hence you have to increase prices to go back to optimal level (FOC=0). The NE in prices is identified by the crossing of the best reply functions: p1 ¿=c+ t (l2−l1 ) (2+l2+l1 ) 3 ; p2 ¿=c+ t (l2−l1 ) (4−l2−l1 ) 3 Remarks: - The equilibrium prices tend to the marginal cost c as l2 approaches l1 or t tends to zero.  If l2=l1→ p=mc, it means that there is no differentiation between the products (either in terms of characteristics or in terms of geographical distance). Hence, this is basically a situation of baseline Bertrand competition.  If t=0→ p=mc, it means that consumer perceive the products as identical, or the geographical distance is not relevant. - The higher t and the higher (l2-l1) the higher equilibrium prices.  As t and (l2-l1) , products are more differentiated.  Decreasing price attracts fewer consumers (demand becomes less reactive ∂D1 ∂ p1 = −N 2 t (l2−l1 ) ). - Then, the profitability of undercutting decreases and the equilibrium prices must, as a result, be higher. Let us substitute the equilibrium prices (p1*, p2*) in the profit functions, so as to obtain second period profits as a function of locations choices: π1 ¿ (l1 , l2)=Nt (l2− l1 ) (2+l2+l1 )2 18 π2 ¿ (l1 , l2)=Nt (l2−l1 ) (4−l2+l1 )2 18 In period 1, firm 1 and firm 2 simultaneously choose their locations l1 and l2. Let us compute the best reply functions. Given l2, firm 1 solves: max l1 π1 ¿ ( l1 , l2 ) s . t . l1∈ [0 ,1 ] Note that ∂π1 ¿ ∂ l1 = Nt 18 (2+l2+l1 ) (−2−3 l1+ l2)<0 since the last term is negative. Hence, for any location choice of firm 2, the optimal choice of firm 1 is I 1 ¿=0. Similarly, given l1, firm 2 solves: max l2 π2 ¿ ( l1 , l2 ) s . t . l2∈ [0 ,1 ] Note that ∂π2 ¿ ∂ l2 = Nt 18 (4−l2−l1 ) (4−3 l2+l1 )>0. Hence for any location choice of firm 1, the optimal choice of firm 2 is I 2 ¿=1. Principles of Maximum Differentiation: at equilibrium, firms maximize distance between them locating at the extremes of the interval.  This is the principle of maximum differentiation. Firms choose to maximize the distance, softening the price competition. The main takeaway is that firm have incentive to create some differentiation in order to decrease price competition. Why do firms choose maximum differentiation? What are the different effects at play? Recall that the demand function is: D1 (p1, p2; l1 , l2)=N [ l1+l2 2 + p2−p1 2 t (l2−l1 ) ] and that p1 ¿=c+ t (l2−l1 ) (2+l2+l1 ) 3 ; p2 ¿=c+ t (l2−l1 ) (4−l2−l1 ) 3 . Therefore the profits of firm 1, once one substitutes the equilibrium prices, can be expressed as follows: π1 ¿ (l1 , l2)=[ p1¿ (l1, l2 )−c ]∗D1 [l1 , l2 , p1 ¿ (l1 , l2) , p2 ¿ ( l1, l2 ) ]. Differentiating with respect to l1: - d π1 ¿ d l1 the overall change in firm 1’s profit caused by a small change in its location. - ∂π1 ¿ ∂ l1 : (direct effect on firm 1’s profit due to a change in its own location) how firm 1’s profit changes directly as it moves its location without considering any adjustments in prices by itself or its competitors. - ∂π1 ¿ ∂ p1 ¿ ∂ p1 ¿ ∂ l1 : the first part measures how firm 1’s profit changes in response to a change in its own price, and the second part measures how firm 1’s price changes with respect to its own location. - ∂π1 ¿ ∂ p2 ¿ ∂ p2 ¿ ∂ l1 : (strategic effect) the first part measures how firm 1's profit changes in response to a change in its competitor's price, and the second part measures how firm 2's price changes with respect to firm 1's location.  Chain rule is used to decompose the total derivative into partial derivatives [ dy dx =dy du ∙ du dx ]. Two forces at play: ݀ ߨ ଵ כ ݈݀ ଵ ۛۛۛ ൌቈ߲ ߨ ଵ כ ߲݈ ଵ ۛۛۛ ȁ‰ ‹ ˜ ‡  ’ ଵ ’ȁכ ଶ כ ൤ ߨ߲ ଵ כ ߲൤ ଵ כ ۛۛۛ ߲൤ ଵ כ ߲݈ ଵ ۛۛۛ ൤ ߨ߲ ଵ כ ߲൤ ଶ כ ۛۛۛ ߲൤ ଶ כ ߲݈ ଵ ۛۛۛ൤ The presence of switching costs makes consumers less responsive to price decreases: - So far I have purchased product A. - The supplier of product B sets pB below pA. - In the base-line model I would buy from firm B. - If there exist switching costs I buy from firm B is the price cut is large enough to compensate for the switching costs. Otherwise I continue to buy from firm A, even though more expensive. The presence of switching costs makes undercutting less effective in attracting demand and thus less profitable. Switching costs are a source of market power. Precisely because switching costs are a source of market power, sometimes they are artificially created by firms: - Contracts offered by mobile phone operators with a certain minimum term. - Frequent flyers programs. - Retailers’ point collection programs. - Obstacles to number portability. - Costs to close bank accounts/to move mortgages. In the latter two cases, important role of regulatory intervention to make the market more competitive. The production and retail segment of energy markets (gas, electricity) has been liberalized and privatized in most of the European countries, in the 80’s and 90’s. - Previously vertically integrated state-owned monopoly. One company was involved in every step of the chain since one segment of this industry is a natural monopoly. Fixed costs are so high that competition is not profitable. - Only the network segments (the natural monopoly) remain a regulated monopoly. However, considerable market power still exists at the retail level. Consumers exhibit considerable inertia: they are reluctant to change supplier even though in the market there exists tariff plans much more favorable to them and despite the existence of websites that compare available plans. The combination of switching and search costs seems to be the source of consumers’ inertia and creates a lot of welfare loss. - Policy question: how can we reduce switching and search costs? Intensity of rivalry directly given by profitability of business stealing. Factors that decrease effectiveness and profitability of undercutting are sources of market power: - Product differentiation - Capacity constraints - Search costs - Switching costs Competition erodes profits as firms fail to internalize the externalities of their choices. Lecture 8 – Collusive Agreements So far we have analysed the functioning of an oligopolistic market in a static context . (Price) competition among firms is a repeated game, sometimes with high frequency (market of generation of electricity). The dynamic framework allows to explain that firms may abstain from taking actions that generate short-term benefit so as to obtain larger long-term profits. Collusion refers to a situation in which firms set prices (or quantities) which are higher (or lower) than the NE of the one-shot game. It has the goal to soften competition and allow firms to obtain a market power that they would not have otherwise. Collusion can be organised in different ways: - Cartels (a central office – instead of each firm independently – takes the main decisions).  Totally illegal to any anti-trust law. - Secret coordination: each firm takes its decision independently, but they communicate in order to agree on their behaviour. - Tacit collusion: no communication at all  The difference between tacit collusion and secret coordination may matter a lot for practical implementation. Collusion can concern: - Prices - Level of production - Market segmentation  Carlsberg and Heineken have been accused by the Commission to have agreed upon a market division. Each firm had agreed not to compete aggressively in the domestic market of the rival. Two factors matter for collusion: - Coordination: how do firms align on a collusive behaviour? How do they adjust their behaviour overtime (for example, after a demand shock)? - Self-enforcement: is the collusive agreement sustainable? Have participants an incentive to depart from the collusive behaviour? “Enforcing collusion”: - If firms set prices (quantities) that are higher (lower) than the NE of the one-shot game, there exists an intrinsic immediate benefit from a deviation [simply because it is not Nash]. How can such deviations avoided and therefore collusion be self-enforced? - Firms need to interact repeatedly. - Credible punishment of deviations (the more severe and the timelier the better for collusion). Infinite repetition of the (symmetric) Bertrand game – Let us consider n (symmetric) firms that produce homogeneous products and choose prices simultaneously in an infinite number of periods. - Demand function: Di ( p i )={ D ( p i )if pi< p j for any i≠ j D ( p ) n if p i=p j for any i , j Oif there∃onek suchthat pi> pk - Marginal cost=c - Discount factor=δ. We assume the same discount for all firms. - No capacity constraints. Let us consider the strategy profile in which each firm follows the strategy below as a candidate equilibrium: { at t=1 , pi=pm t >1 ,if p j ,t−1=pm , for every j , pi , t=pm ¿ if p j , t−1< pm for at least one j, pi ,t=pi ,t+i=…=c Consider any subgame following a price ≠ pm. Since prices = marginal costs is a NE of the one-shot game, for the one-shot deviation principle we can conclude that the proposed strategy is a SPE of the repeated game. But what about subgames that follow all prices = pm (or the whole game)? pm pm−ε t=1 π m n πm−ε t=2 δ πm n δ ∙0 t=3 δ 2 πm n δ 2∙0 Applying the one-shot deviation principles, the proposed strategy is a SPE if and only if: π m n +δ πm n +δ 2 π m n +δ 3 πm n +…≥πm+δ 0+δ 20+…  The above inequality is denoted as Incentive Compatibility Constraint (ICC). If we take for example firm A and firm B: - If π A CO>π B CO:  Ceteris paribus, the short-term benefit is smaller for firm B.  The long-term loss is smaller for firm B.  This means that the collusion is enforced more easily for firm A because firm B has less incentive to deviate from collusion. - If π A D>π B D:  Ceteris paribus, the short-term benefit is higher for firm A (it gains more from deviating from collusion compared to firm B).  It is easier to collude for firm B, since firm A has a stronger incentive to deviate. - If π A P >π B P:  Ceteris paribus, the long-term loss is smaller for firm A.  It is easier to collude for firm B. Structural factors that impact collusion: - Concentration: easier to satisfy ICC and to coordinate. In the base model: δ ¿=1−1 n ↓ if n↓. The lower the number of competitions, the higher the collusive profits πCO=πm n , the lower δ ¿. Also, the lower the number of competitors the easier to monitor each other and the easier to coordinate behaviour. - Entry barriers (see Problem Set 3) - Regularity and frequency of orders (see Problem Set 3) - Increasing demand: easier to satisfy ICC (when entry is not easy). Until now, we assumed demand constant in each period. We considered demand D(p). The monopoly price pm is the solution to max p ( p−c ) D ( p ) → ∂π ∂ p =D ( pm )+( pm−c ) D'=0 πm=( pm−c) D( pm) Assume now demand KD(p) where K is a constant max p ( p−c ) KD ( p )→ ∂π ∂ p =KD (pm )+( pm−c ) KD'=0 The price that satisfies the former FOC satisfies also the latter – the monopoly price is the same in the two cases. In the latter case, the monopoly profits are equal to K π m. For given number of competitors, collusion easier (more difficult) in growing (declining) markets than in stable markets:  In a growing (declining) market, the long-term cost of a deviation is larger (lower). To see this, assume that demand follows the following trend:  at t=1, demand = D( p)  at t=2, demand = (1+g)D( p)  at t=3, demand = (1+g )2 D(p)  … Then, if g>0 demand is increasing at the rate g, while if g<0 demand is decreasing. From the earlier technical remark, when demand is (1+g)D( p), monopoly profits are (1+g ) pm, when demand is (1+g )2 D(p) monopoly profits are (1+g )2 pm, and so on….. Then, the ICC in this case can be written as: π m n +δ πm (1+g ) n +δ2 πm (1+g )2 n +δ3 πm (1+g )3 n +…≥ πm πm− πm n ≤ δ π m (1+g ) n +δ 2 πm (1+g )2 n +δ 3 πm (1+g )3 n πm− πm n ≤ δ (1+g ) 1−δ (1+g ) πm n  When g=0, we are back to the initial model with stable demand.  When g>0, the long-term loss of a deviation is large than in the case of stable demand and collusion easier to be enforced.  When g<0, the long-term loss of a deviation is smaller than in the case of stable demand and collusion more difficult to be enforced. In practice, anti-trust authorities tend to consider growing demand as a factor that hinders collusion because growing demand facilitates entry and new entry makes collusion more difficult to enforce. It is very important to distinguish the direct effect of growing demand (for given number of competitors) and the indirect effect (new entry). Depending on which one dominates, growing demand may favour or hinder collusion. - Market opaqueness (difficult to observe price, quantity etc.) + unexpected shocks: difficult to monitor each other and detect deviations.  Green and Porter, Econometrica, (1984) ▪ Each firm only observes its own price and sales, but not aggregate demand (there is no profit monitoring). ▪ In each period, with some probability, demand vanishes: impossible to distinguish a deviation from a negative shock to demand.  Unobservability of rivals’ behavior + shocks make detection of deviations impossible. Despite the challenges of limited information and uncertainty, some collusion still exists:  Monopoly price as long as each firm maintains its market share.  Whenever a firm is unable to sell – its demand decreases, price war for T periods (afterwards, revert to monopoly price).  T long enough to deter potential cheaters.  Since punishment triggered by pure bad luck, T cannot be too long (T has to be long enough to discourage deviation, but not too long to discourage collusion). - Symmetry: the more similar firm are, the easier is collusion. First of all, it is easier to coordinate. Additionally, they have the same (or very similar ICC). Competition authorities and courts tend to see asymmetry among firms as a factor which hinders collusion. REMARK: when firms are asymmetric, each one has a different ICC. All of them need to be satisfied for collusion to be enforced. 1. Asymmetry in capacity  Compte, Jenny and Rey (1997): model where firms differ in their capacity. The large firm (not capacity constrained) has a stronger incentive to deviate: it benefits more from a deviation and its punishment profits are larger. Collusion is more difficult: a more equal distribution of capacities would help. Suppose K L>K S≥ Qm 2 (the two firms have different capacity, but both can sustain half of the monopoly quantity). The two firms have the same collusive profits, but πL D>π S D (by deviating the more efficient firm will have higher profits due to higher capacity). At the same time, πL P>π S P since in the one-shot Nash Equilibrium the more efficient firm will have higher profit due to higher capacity. Hence, looking at the ICC: πD−πCO≤ δ 1−δ ( πCO−π P ) : ▪ Agreements will be more difficult to find. ▪ The more efficient firm will have a higher short-term benefit than the less efficient firm. At the same time, the long-term benefit will be lower. 2. Cost asymmetries  More difficult to coordinate behaviour. Moreover, more difficult to sustain the agreement. The more efficient firm has a stronger incentive to deviate: ▪ Larger immediate gain (higher margin on the additional demand captured by deviating). ▪ Lower long-term cost (the punishment profits of the more efficient firm are larger). A model: ▪ 2 firms, one more efficient than the other: c H>cL; ▪ Rigid demand: D if p≤ v. Hence pm=v. Imagine the two firms share collusive demand evenly. Collusive profits: πH CO=( v−cH ) D 2 πL CO=(v−cL ) D 2 Deviation profits: πH D=(v−cH ) D πL D=(v−cL) D Punishment profits: πH P =0 πL P=(cH−cL)D ICC of the less efficient firm (H): (v−c H )D−(v−cH ) D 2 ≤ δ 1−δ [ (v−cH ) D 2 −0] ICC of the more efficient firm (L): (v−c L) D−(v−cL) D 2 ≤ δ 1−δ [ (v−cL ) D 2 −(cH−cL)D ] or rewriting (v−c L) D−(v−cL) D 2 ≤ δ 1−δ [ (v−cH ) D 2 −(cH−cL) D 2 ] ▪ The long-term loss is lower for the more efficient firm – the punishment will be softer. 3. Asymmetry in discount factors  The lower the discount factor (financial fragility), the stronger the incentive to deviate. Ex: airplane industry: the major reason why price wars start are financial difficulties of individual companies. Policy implications The prediction of the baseline model (with observable demand) is that when collusion can be enforced (i.e. when ICC is satisfied) one should observe high prices overtime. When, instead, demand is not observable and subject to shocks a successful collusive scheme (in which ICC is satisfied) involves periods of low prices, necessary for discipline. - Then the observation of periods in which prices are high that alternate with periods with low prices is not a signal of no collusion; rather it may be consistent with collusive behaviour. Collusion is more difficult when market is opaque (rivals’ behaviour is difficult to observe) and demand subject to shocks: it is either impossible or less profitable. Anti-trust agencies should pay special attention to practices that increase market transparency, helping firms monitor each other’s behaviour (ex. Exchange of information on past prices/sales). Facilitating practises Observability of firms’ actions facilitates enforcement: - Exchange of information on past prices/volumes to favor monitoring. The more disaggregate and recent the information, the stronger the pro-collusive effect due to facilitating monitoring. Ex.: Insurance companies (RCA) in Italy.  July 2000: most insurance companies accused of collusive agreement (fine amounting to €350 mil).  Dawn raids in the companies headquarters allowed to find documents proving an extensive exchange of information.  Such exchange was performed through a consultancy company (RC Log) that gathered, elaborated and disseminated detailed information on past prices (premia).  For instance, for each company it reported basic premium and all coefficients of personalization. More active policies can be used, ex ante and ex post. - Ex ante, make more difficult to coordinate or enforce collusion:  Administrative fines (+ private damages / collective actions – all the buyers of the product can start a legal action because they can require to be reimbursed of the extra paid under the collusive prices).  Blacklist of facilitating practices might deter collusion: ▪ Private announcements of future prices/outputs. ▪ Exchange of disaggregate current/past information. The more recent it is, the worse it is. ▪ Merger control (joint dominance).  Criminal sanctions? In the US and UK, collusion is a criminal violation. In EU, collusion is not, the worst that can happen is to pay a fine. - Ex post policies to fight collusion – to break an existing collusive agreement:  Dawn Raids  Leniency programmes – there exists whistle blowers. First introduced by the DoJ in 1978, revised in 1993. The EU Notice was introduced in 1996, revised in February 2002, last modification in December 2007. The main difference between the 1978 and 1996 versions and the 1993 and 2002 ones is the discretion v. automatism. Clearer criteria were introduced. These reforms seem to have been successful. ▪ In the US two applications for amnesty per month (a more than twenty-fold increase as compared to the rate of applications before the reform). In EU, from February 2002 to end-December 2006, 104 applications and granted immunity for 56 infringements. ▪ BUT at least in Europe, average per firm length of cartel investigations has not decreased. June 20, 2008 Settlement Procedures also in EU. More applications  more cartels are discovered. OR, more cartels are created due to immunity? Takeaways: Avoid direct contacts with your competitors concerning prices! Handle public pricing communication carefully Better if addressed directly to customers. If you adopt a facilitating practice (for instance, exchange of info) have a legitimate and convincing efficiency justification. Do not exchange recent and detailed info on past prices and quantities. Clear your pricing tactics with an attorney well-verse in antitrust law. Lecture 9 – Horizontal Mergers Horizontal mergers are mergers between former competitors (substitute goods) that, after the merger, become part of the same entity. The insiders are the merger firms, and the outsiders are the firms who are not merging. - They differ from vertical mergers (operating in different stages of the supply chain) and conglomerates mergers (different independent products or complements). Unilateral effects (absent efficiency gains) Considering the absence of efficiency gains (costs function is unchanged), by reducing the competitive pressure, a merger: - Benefits insiders . - Reduce the competitive pressure exerted by rivals. - Increases market power:  Allows the insiders to unilaterally increase prices (unilateral effect).  Increases market power overall (benefits both outsiders and insiders). - Benefits outsiders . - Hurts consumers and total welfare because it leads to price increases due to higher market power. The merger makes the merging parties partially internalize the externalities exerted by their decisions. - Bertrand Competition (→ strategic complements):  Direct effect : keeping the behaviour of the rivals fixed, insiders increase prices.  Strategic effect : prices of competitors are not fixed, competitors increase prices. Increase in prices by insiders triggers a reaction by the competitors. Because of strategic complementarity in price competition, they increase prices as well.  Under price competition, both the direct and the strategic effects are beneficial to the merging parties: the merger is profitable. - Cournot Competition (→ strategic substitutes):  Direct effect : keeping the behaviour of the rivals fixed, insiders reduce production for equal prices (they internalise more).  Strategic effect : prices of competitors are not fixed, competitors expand production and decrease prices. Decrease in production by insiders triggers a reaction by competitors. Because of strategic substitutability in Cournot competition, they increase production, which decreases prices.  The expansion of outsiders is dominated by the reduction in prices by insiders (because we take into account the additional detrimental effect). Hence, quantity decrease, and prices increase.  The strategic effect is detrimental to the merging parties: Merger Paradox. The merger may turn out to be unprofitable for the firms that undertake it (if the strategic effect is higher than the direct effect). In both cases: - The merger is beneficial to the outsiders (the other competitors in the market). - The merger is detrimental to consumers and total welfare. A formalization under price competition: Consider an industry with three firms. They produce differentiated substituted product (each firm produces one variety and compete in prices). Each firm faces demand q i(p i , p j , pz) with i , j , z=1 ,2 ,3 and i≠ j≠ z has marginal cost c i and fixed cost F i. Pre-merger situation: firm i chooses pi in order to max its profits max pi ( pi−c i )qi ( p i , p j , pz )−F i. The FOC is given by ∂π i ∂ p i =qi ( p i , p j , pz )+( pi−ci ) ∂q i ∂ p i =0. From the FOC one obtains the best reply function of firm i that in increasing in the rivals’ prices. The pre-merger Nash equilibrium is given by the vector of price ( pi b , p j b , pz b) that satisfy the three FOCs (i.e. intersection of the best replies). Firm 1 and firm 2 merge: The merged firm chooses p1 and p2 in order to max its total profits. max p1 , p2 [( p1−c1 )¿q1 ( p1 , p2 , p3 )−F1+( p2−c2 )q2 ( p1 , p2 , p3 )−F2]¿ The FOCs are given by: ∂π M ∂ p1 =q1 ( p1 , p2 , p3 )+( p1−c1 ) ∂q1 ∂ p1 +( p2−c2) ∂q2 ∂ p1 =0 ∂π M ∂ p2 =q2 ( p1 , p2 , p3 )+( p2−c2 ) ∂q2 ∂ p2 +( p1−c1) ∂q1 ∂ p2 =0 The third term in the FOCs captures the internalization effect: the merged entity, when choosing pi (with i=1,2) takes into account the effect that a change in pi exerts on the sales of the other variety ( j, with j ≠1 ), now owned by the merged entity. However, it does not internalize the effects of firms 3: the outcome will not be monopolistic. More in detail, a unit increase in the price of variety 1 leads to (on the first FOC): - An unit of earnings more on each quantity sold of variety one. - A decrease on the quantity sold of variety one, hence to a loss of profit margin. - An increase on the quantity of variety two and to gain the margin on those units.  The merged entity has incentive to increase prices, given fixed the behaviour of the outsiders. This is called the unilateral effect. Of course, this will trigger a response of the outsiders. Evaluated at ( p1b , p2 b , p3 b ) the FOCs of the merged entity: ∂π M ∂ p1 =q1 ( p1 , p2 , p3 )+( p1−c1 ) ∂q1 ∂ p1 +( p2−c2 ) ∂q2 ∂ p1 >0 ∂π M ∂ p2 =q2 ( p1 , p2 , p3 )+( p2−c2 ) ∂q2 ∂ p2 +( p1−c1 ) ∂q1 ∂ p2 >0 Because of the internalization effect, the merged entity will optimally choose higher prices. Its best reply functions are shifted upward. Nothing changes for the outsider: its FOC and best reply remain the same. The new NE ( p1M ,P2 M , p3 M ) involves higher prices (higher market power) of the insiders and the outsiders. - The merger harms consumers. - The merger increases the profits of the insiders and the outsiders. - The merger decreases total welfare. Efficiency gains: A merger, by combining the merging firms’ assets, can produce costs savings (exploitation of scale economies, stronger bargaining power, limited duplication of fixed costs). Efficiency gains can concern fixed and variable costs. max p1 , p2 [( p1−ec1 )¿q1 ( p1 , p2 , p3 )−F1+( p1−ec2 ) q2 ( p1 , p2 , p3 )−F2]with e≤1∧a≤1¿ ∂π M ∂ p1 =q1 ( p1 , p2 , p3 )+( p1−ec1 ) ∂q1 ∂ p1 +( p2−ec2 ) ∂q2 ∂ p1 =0 ∂π M ∂ p2 =q2 ( p1 , p2 , p3 )+( p2−ec2 ) ∂q2 ∂ p2 +( p1−c1 ) ∂q1 ∂ p2 =0 Given that p1−ec1=p1−c1+(1−e ) c1, the FOC can also written as ∂π M ∂ p1 =q1 ( p1 , p2 , p3 )+( p1−c1 ) ∂q1 ∂ p1 +(1−e ) c1 ∂q1 ∂ p1 +( p2−c2 ) ∂q2 ∂ p1 +(1−e ) c2 ∂q2 ∂ p1 =0 Efficiency gains concerning fixed costs: - Consider e=1 and a<1. - The price increase produced by the merger is the same as in the case in which there are no efficiency gains (fixed costs do not appear in the FOC, they do not affect the decision of price and are not relevant in the maximization process – they only affect profits). - This type of efficiency gains does not benefit consumers (whose surplus decreases as a consequence of the merger). - However, such efficiency gains are beneficial to firms and possibly to total welfare. - In EU and US, efficiency gains concerning fixed costs cannot be proposed by the merging parties as a rebuttal of harm (Consumer Surplus standard). Efficiency gains concerning variable costs The merger decreases marginal costs of the insiders. The change in mc changes the price of the merger (it appears in the FOC). Evaluated at ( p1M ,P2 M , p3 M ) the FOCs of the merged entity: ∂π M ∂ p1 =q1 ( p1 , p2 , p3 )+( p1−ec1 ) ∂q1 ∂ p1 +( p2−ec2 ) ∂q2 ∂ p1 <0 New US Merger Guidelines (December 2023) - More stringent again - Expansion of presumption area:  back to the 1982 one: HHI >1800 and Delta >100  New category: merged entity market share >30% and Delta HHI >100 EU Merger Policy: - One-stop shop for mergers [subsidiarity principle – there are threshold criteria (based on turnover) - that determine which mergers are assessed by the Commission and which ones by National Competition Authorities] - Reasonably quick and effective, with certain time horizon.  Within seven days from offer, notification to DG Comp, who in turn has 30 d- ays for authorization – autonomous decision of the Competition Commissioner.  If there are doubts, Phase II, four months investigation. Economic analysis for mergers: - Analysis of unilateral effects :  (Product and Geographical) Market definition.  Qualitative assessment of increase in market power (absent efficiency gains).  Quantitative assessment of increase in market power (absent efficiency gains): ▪ UPP (Upward Pricing Pressure) Indexes. ▪ Simulations and econometric analysis (if data rich enough). - A nalysis of efficiency gains :  The larger the insiders' market power, the larger must be the cost savings needed to outweigh the price effects. Two possible outcomes: 1. The merger is likely to increase (unilaterally) market power of the involved firms: Prohibition or remedies. 2. No likely unilateral effects. Does the merger make collusion easier to enforce? Analysis of pro-collusive effects. Merger control has become a hot topic recently. Report of US Council Economic Advisors in 2016 (Obama administration) documented increase in concentration in the US economy, followed by several empirical studies (De Loecker and Eeckhout, 2018). Is merger control too weak? - Kwoka (2013): “meta-study” of US merger retrospectives. 76% anticompetitive; remedies were inadequate. - FTC: 4 out of 5 hospital mergers price increases: even non-profit organisations raise prices. Even ex post assessment of some mergers (e.g. S-PVC, mobile) by EC and National Agencies points to price rises…(!) Not representative samples! - Event studies: Duso et al. (2013) find unconditional approval of anticompetitive mergers in 2/3 of the sample (and intervention in procompetitive mergers in 1/3 of it) Sketchy, but suggestive of under-enforcement… M&As in digital markets: Hundreds of acquisitions by Amazon, Apple, Facebook, Google, Microsoft in the last few years. Targets typically very young firms (≤4 years old in 60% of cases). Significant volume of transactions, with 5, 6 and 15 companies per year acquired on average. Only a handful were investigated by Antitrust Authorities (turnover thresholds typically not met), none was prohibited. Facebook/Instagram, Facebook/Whatsapp, Google/Waze examples of particularly controversial mergers. - Difficult to predict the evolution of the acquired firms  risk of systematic elimination of possible future rivals. - Digital Market Act is not paying sufficient attention to this issue. Lecture 10 – The determinants of concentration: the free entry model Entry and exit dynamics change competitive landscape. - Entry of new firms increases competition. - Competition drives out least efficient firms, who exit. Entry and exit dynamics determine market structure in equilibrium. - The same sector can exhibit different degrees of concentration across different countries. However, different sectors exhibit the same ordering in terms of concentration across different countries – e.g. generation of electricity more concentrated than production of trucks which is more concentrated than manufacturing of shoes in every country. - In some sectors the degree of concentration is inversely related to market size. However, in other sectors the level of concentration seems to be independent of market size. Exogenous Sunk Cost Industries Assumptions: - M potential entrants (reservation profits normalized to 0). - All firms use the same technology C i (q i )=F+c qi  F fixed set-up cost. - Market demand: Q ( P )=(a−P)S  S measures market size. Two-stage game:  t 0: M firms simultaneously decide whether to enter or not. Entry requires to pay the fixed set- up cost F.  t 1: n≤ M entrants compete. Solving by backward induction: - Stage 2 (we assume that at stage 1 n firms entered) : Given n number of entrants, equilibrium profits are given by (with the inverse demand being P=a−Q S ) π i P (Q ) qi−cq i=[a−∑ j=1 n q j S −c ]q i→0= ∂ π i ∂qi =a− ∑ j=1 n q j S −c− qi S Symmetric equilibrium, hence q1 ¿=q2 ¿=…=q¿→a−nq¿ S −q¿ S −c=0→q¿=a−c n+1 S P=a−nq¿=a−n ( a−c ) S (n+1 ) S =a−n ( a−c ) (n+1 ) =a+nc n+1 Post-entry profits are π¿¿  They are decreasing in the number of entrants: the more intense competition when more firms compete in the market.  They are increasing in market size. - Stage 1 (entry decision) : Imagine M=5. Each firm has two possible strategies Si= (¿ ,Out ) . A Nash Equilibrium in the first stage is a strategy profile (s¿¿1 , s2 , s3 , s4 , s5)¿ - for instance (¿ ,∈,Out ,Out ,∈,Out) or equivalently ¿ since what matters is how many enters not who – such that: 1. Firms that decide to enter do not make losses (otherwise incentive to deviate and stay out). 2. Firms that decide to stay out would make losses by entering the market (otherwise, incentive to deviate and enter). Hence, a Nash Equilibrium is summarised by the number of firms that decide to enter n¿, which has to satisfy the following properties:  Enter: π i ¿ (n¿ )−F ≥0 Keeping fixed the decisions of the others, staying out o the market is not more profitable than entering. This is because post-entry profits are enough to cover the entry cost.  Stays out: π i ¿ (n¿+1 )−F<0 Keeping fixed the decisions of the others, entering is less profitable than staying out. This is because post-entry profits with n¿+1 active firms are short of entry cost F. We can determine the equilibrium number of firms as π i ¿ (n¿ )−F=0→S (a−c )2 (n+1 )2 −F=0→n¿=[ (a−c )√ S F −1] Predictions – Market size and entry costs are crucial determinants of market structure:  Markets characterised by higher entry costs are more concentrated (n is lower).  Larger markets are less concentrated .  No lower limit to concentration . Increasing market size eventually leads to concentration converging to zero. Remark: in a symmetric model where α i ¿= q¿ Q¿ = q¿ nq¿= 1 n then HHI=∑ j=1 n ( 1n ) 2 =n( 1n ) 2 = 1 n and we proxy concentration with 1/n. In a more general model concentration (HHI) is affected by the number of competitors but also by the distribution of market shares. These results can be brought to a more general scenario. It is enough that post entry equilibrium profits are π¿¿ - If S'>S →π¿ (n¿ , S ' )>F  π¿¿ with n¿∗¿>n¿ ¿ - If F '>F → π¿ (n¿ , S )<F '  π¿¿ with n¿∗¿<n¿ ¿ Competition is more intense in markets where products are less differentiated, irrespective of the mode of competition (price, quantity): π¿ (n¿ , S , γ ) is decreasing in γ  Where γ measures the degree of substitutability among products. We expect to find higher concentration in markets where products are more homogeneous (less differentiated). Ex-post competition dissuades ex-ante entry: the intensity of post-entry rivalry determines ex-ante entry incentive. Tougher ex-post competition invites less firms (leads to higher concentration). Softer ex-post competition invites more firms (leads to lower concentration). - If S'>S →π¿ (n¿ , S ' )>F  π¿¿ with n¿∗¿>n¿ ¿ An extreme case is Bertrand competition with homogenous product. - π¿ (n ,S )=0 for any n>1. - Then, n¿=1 for any F (as long as π¿ (1 , S )≥ F).  Cut-throat competition scares off ex-ante entrants (leading to very high concentration levels). Summing up, the exogenous fixed cost model π¿¿: - Higher market size → less concentration (↑n¿). - Higher fixed cost → more concentration (↓n¿). - Stronger rivalry → more concentration (↓n¿). Endogenous Sunk Cost Industries Sutton (1991) observes that some large markets remain highly concentrated: increasing market size does not lead to net entry. For instance, beer market in the US is at least 30 times as larger as the Portuguese market, but the degree of concentration is similar across them. These markets are characterized by However, x¿>πm(B+C>B) For the Incumbent it is not profitable to offer the ED contact the buyer will accept: the necessary compensation is larger than the Incumbent’s increase in profits due to exclusivity. The incumbent cannot (profitably) use ED to deter entry. ED will be signed only if mutually beneficial. Efficiency considerations explain the use of ED, not anti-competitive goals. Anti-trust agencies should not be concerned by ED. The Chicago School argument relies on a number of simplifying assumptions. In particular, consider several (un-coordinated) buyers instead of a single one. In this setting ED can profitability allow the incumbent to secure key buyers, thereby depriving the entrant of the scale it needs to operate successfully. Main idea: multiple (uncoordinated) buyers. - Key assumption: individual demand insufficient to cover F. If the entrant sells to a high number of buyers, it will be able to cover the entry costs (F). If a buyer accepts the ED contract, a negative externality is exerted on the other buyer: also, the free buyer cannot purchase from Entrant because its demand alone is insufficient to make entry profitable. By exploiting these externalities, the incumbent can profitably use ED to exclude. Timing: Incumbent offers to B1 and B2 to sign an ED (x ). Buyers decide. Entry decision. Price decisions. Assumption: - (c I−c E )q (c I )<F<2 ( cI−cE ) q ( cI )  fixed costs are higher than monopoly profits but lower than the post entry profits πm<F<π post entry. - CS (cI )−CS ( pm )=x¿>πm, butx¿<2 πm. Backward induction: - Last stage: price decisions  If no entry: Incumbents is a monopoly and sets pm both to free and exclusive buyers.  If entry: ▪ Incumbents pm to exclusive buyers (which receive also the compensation) ▪ Free buyer buys from Entrants at p¿=cI (c I>cE since the Entrant is more efficient). - Entry decision  Entrant enters only if both buyers reject the ED offer: 2 (cI−cE )q (cI )−F>0. ▪ Entrant knows that at the price p=cI it would make positive post entry profits which cover fixed costs.  If a single buyer rejects or none, entry is not profitable: (c I−c E )q (c I )−F<0 ;0−F<0. ▪ If only one buyer is free, the post entry profits of the entrant are lower than F, because the individual demand of a single buyer is not enough to make entry profitable and cover for the F. 1. Case I: Simultaneous + non-discriminatory offers The incumbent makes simultaneous offers to all buyers. Buyers simultaneously decide. The compensation x must be the same across all buyers. - Buyers’s decisions  If the Incumbent offers x≥ x¿: dominant strategy for each buyer to accept the contract (A, A). ▪ Both accept because irrespective of the other, since accepting ensures they pay the monopoly price, but they receive compensation that makes them indifferent or better off.  If the Incumbent offers x<x¿: multiple equilibria (A, A) and (R, R). B1{B ¿2 Accept Reject Accept CS ( pm )+x ;CS ( pm )+x CS ( pm )+x ;CS ( pm ) Reject CS ( pm ) ;CS ( pm )+x CS (cI );CS (cI ) ▪ If a buyer expects the other buyer to accept, then she is worse off by deviating and rejecting exclusivity because she would pay the same price and not receive the compensation. Coordination failure: (Accept, Accept). ▪ If a buyer expects the other buyer to reject, then she is worse off by accepting exclusivity because she would pay a higher price and x is not high enough to compensate for that. CS ( pm )+x<CS(cI ) since x<x¿: (Reject, Reject). - Incumbent’s decision (1st mover advantage) For the Incumbent:  It not (strictly) profitable to offer x≥ x¿: they both accept, but 2π m−2 x<0.  It not (strictly) profitable to offer x∈ [πm , x¿ ]: even if both buyers accept 2π m−2 x≤0.  If is profitable to offer x∈ [0 , π m ]. Following these offers: ▪ (A, A)  no entry Both buyers accept exclusivity  entry does not follow  exclusion equilibria. ▪ (R, R)  entry Both buyers reject exclusivity  entry follows  entry equilibria.  Incumbent exploits coordination failures to exclude. A necessary condition for exclusion is that buyers suffer from coordination failures. 2. Case II: Simultaneous + discriminatory offers - Buyer’s Decisions  If at least one offer is such that x i≥ x¿, unique equilibrium such that both buyers accept the contract. ▪ For buyer i accept is a dominant strategy. ▪ Given that buyer i accepts, for buyer j accepting is a best reply.  If both x i< x¿ and x j<x¿: multiple equilibria (A, A) (R, R)  coordination failures. - Incumbent’s Decision Only exclusion equilibria exist where the incumbent makes an offer than one or both buyers accept. Entry equilibria cannot exist: it is impossible to have an equilibrium in which both buyers reject and entry occurs.  Consider a situation in which following the incumbent’s offer, both buyers reject, and entry follows.  Can it be an equilibrium? No, the incumbent has an incentive to deviate and offer x¿+ε to one buyer and 0 to the other.  For the former, it is a dominant strategy to accept. The other buyer is indifferent between accepting and rejecting. ▪ In both cases, entry does not follow, and she pays pm.  Incumbent would set monopoly price for both buers, it will collect twice the monopoly profits and has to pay compensation only once. The deviation makes the Incumbent earn 2π m−x¿>0 and is profitable. There exist multiple exclusion equilibria in which incumbent offers (x i , x j) such that x i+ x j≤ x¿.  Discriminatory offers facilitate exclusion (divide and conquer: by bribing few buyers the incumbent can secure ALL of them).  The incumbent does not need to rely on buyer’s coordination failure to exclude.  Coordination failure may still help the incumbent to exclude more cheaply, hence it is more profitable. 3. Case III: Sequential offers Most powerful instrument to exclude by exploiting buyers’ externalities. Unique exclusion equilibrium where both buyers accept (or one buyer accepts) with the incumbent offering almost zero compensations. Intuition:  If B1 accepts, B2 is indifferent between accepting (for free) and rejecting: CS ( pm )=CS( pm). In both cases entry does not follow, and she pays pm.  If B1 rejects B2, requires at least x¿ to sign. Offering slightly more than x¿ profitable for the incumbent 2π m−x¿−0.1>0. Entry does not follow.  Anticipating that she will pay pm irrespective of her acceptance decision, B1 is willing to accept in return for a negligible compensation. Exclusion is the only outcome: even when paying a very low compensation it is very profitable for the incumbent if there are sequential games. Exclusion does not even entail lower profits. Buyer power: if market demand less fragmented so that each buyer sufficient to attract entry and make it profitable  no exclusion. There is no externality that the buyer exerts on the others. Asymmetric buyers: - Nothing changes as long as buyers are asymmetric, but no buyer is large enough to attract entry. - If, instead a large buyer alone attracts entry (it makes entry profitable):  Exclusion based on coordination failures becomes unfeasible.  Exclusion based on ‘divide-and-conquer’ strategies still possible.  Exclusion, when profitable, more costly for the incumbent because crucial buyers will be compensated fully. - When exclusion is possible, crucial buyers (more generally those that contribute more to the entrant’s success) will be compensated fully. Consider same setting as before, with B2 twice as large (now her demand makes entry profitable). 1. Simultaneous and non-discriminatory offers  If the incumbent offers x<x2 ¿, B2 will always reject (even if she expects B1 to accept): CS (c I )>CS (pm )+x2.  Coordination failures do not arise any longer!  In order to have both contracts accepted, the incumbent should offer x1=x2=x2 ¿, but this is not profitable.  Exclusion equilibria do not exist (E will always decide to enter). 2. Simultaneous and discriminatory offers Unique exclusion equilibrium where the incumbent offers x1=0 and x2=x2 ¿=24+ε obtaining π1 m=π2 m=27−ε.  A sort of divide and conquer, where there is only one equilibrium, and the identity of the buyer is critical. 3. Sequential offers Unique exclusion equilibrium where B2 receives x2=24+ε. B1 B2 x¿=12 π1 m=9 x2 ¿=24 π2 m=18