UNIT III: COMPETITIVE STRATEGY 4/17/2017 UNIT III: COMPETITIVE STRATEGY Monopoly Oligopoly Strategic Behavior 7/19

Market Structure Perfect Comp Oligopoly Monopoly 4/17/2017 Market Structure Perfect Comp Oligopoly Monopoly No. of Firms infinite (>)2 1 Output MR = MC = P ??? MR = MC < P Profit No ? Yes Efficiency Yes ? ???

4/17/2017 Oligopoly We have no general theory of oligopoly. Rather, there are a variety of models, differing in assumptions about strategic behavior and information conditions. All the models feature a tension between: Collusion: maximize joint profits Competition: capture a larger share of the pie Firms have an interest to get together and discuss their profit maximizing decisions with one another, to collude; or even to form a cartel e.g., OPEC and set prices or production quotas.

Duopoly Models Cournot Duopoly Nash Equilibrium Leader/Follower Model 4/17/2017 Duopoly Models Cournot Duopoly Nash Equilibrium Leader/Follower Model Price Competition

Duopoly Models Cournot Duopoly Nash Equilibrium Stackelberg Duopoly 4/17/2017 Duopoly Models Cournot Duopoly Nash Equilibrium Stackelberg Duopoly Bertrand Duopoly

4/17/2017 Monopoly Cyberstax is the only supplier of Vidiot, a hot new computer game. The market for Vidiot is characterized by the following demand and cost conditions:   P = 30 - 1/6Q TC = 40 + 8Q a) Find the equilibrium level of output, price and profits and draw a graph of your answer. What levels of consumer and total surplus would result?

Monopoly P = 30 - 1/6Q TC = 40 + 8Q P = TR – TC 4/17/2017 Monopoly P = 30 - 1/6Q TC = 40 + 8Q MR = 30 - 1/3Q MC = 8 => Q* = 66 P* = 19 P = TR – TC = PQ – (40 + 8Q) = (19)(66) – 40 -(8)(66) P = 686 $ 30 P* = 19 So here’s a monopolist that looks at its cost conditions and its demand conditions, calculates its profit maximizing output and expects to earn profits of $686. Now what happens when another firm arrives on the scene? MC = 8 MR D Q* = 66 180 Q

4/17/2017 Duopoly Megacorp is thinking of moving into the Vidiot business with a clone which is indistinguishable from the original. It has access to the same production technology, reflected in the following total cost function:   TC2 = 40 + 8q2 Notation: I will use small q to refer to a firm’s output and capital Q for the industry output. Will Megacorp enter the market for Vidiot? If it assumes Cyberstax’s output is given, how much will it produce and what will be the new market price? What level of profits will the two firms earn? Does this maximize their profits?   Will Megacorp enter the market? What is its profit maximizing level of output?

4/17/2017 Duopoly If Megacorp (Firm 2) takes Cyberstax’s (Firm 1) output as given, its residual demand curve is P = 30 - 1/6Q Q = q1+ q2; q1 = 66 P = 30 - 1/6(q1+ q2) P = 19 - 1/6q2 $ 30 19 q2 = 0 q1 = 66 180 Q

4/17/2017 Duopoly P = 19 - 1/6q2 TC2 = 40 + 8q2 MR2 = 19 - 1/3q2 = MC2 = 8 => q2* = 33 q1* = 66 P = 30 – 1/6(q1 + q2) P* = $13.50 P2 = 141.5 Before entry, P* = 19; P1 = 686 Now, P1’ = 323 ow, PC‘ = 297 $ 30 19 13.5 q2 = 0 MC2 = 8 q1*+q2* = 99 180 Q

4/17/2017 Duopoly What will happen now that Cyberstax knows there is a competitor? Will it change its level of output? How will Megacorp respond? Where will this process end? We need to specify some behavioral or strategic assumption about how each firm will respond to the actions of the other. What if Cyberstax were to reoptimize given qMega? The Cournot model is based on the simplest strategic assumption.

4/17/2017 Cournot Duopoly Reaction curves (or best response curves) show each firm’s profit maximizing level of output as a function of the other firm’s output. q1 qm R1: q1* = f(q2) q2 q2

Cournot Duopoly P = 30 - 1/6(q1+q2) MR1 = 30 -1/3q1 - 1/6q2 = MC = 8 4/17/2017 Cournot Duopoly To find R1, set MR = MC. Now, MR is a (-) function not only of q1 but also of q2: P = 30 - 1/6(q1+q2) TR1 = Pq1 = [30 - 1/6(q1+q2)]q1 = 30q1 - 1/6q12 - 1/6q2q1 MR1 = 30 -1/3q1 - 1/6q2 = MC = 8 R1: q1* = 66 – 1/2q2 q1 66 q1* Firm 1’s profit maximizing output as a function of Firm 2’s output. 132 q2

4/17/2017 Cournot Duopoly The outcome (q1*, q2*) is an equilibrium in the following sense: neither firm can increase its profits by changing its behavior unilaterally. R2: q2* = 66 - 1/2q1 R1: q1* = 66 - 1/2q2 q1 q1* = 44 For the case of identical firms q1*, q2*: Each firm’s profit maximizing level of output, given the other’s profit maximizing output. A Nash Equilibrium exists in an oligopolistic market, if each firm is basing its pmax output on a correct assumption (consistent) about the rivals’ behavior. On Dynamics: We arrive at the NE in logical time not historical time. Convergence to the NE is not the result of a series of actions but a series of conjectures, or beliefs. I think-that you think-that I think … [I]f game theory is to provide a unique solution to a game-theoretic problem then the solution must be a Nash equilibrium in the following sense. Suppose that game theory makes a unique prediction about the strategy each player will choose. In order for this prediction to be correct, it is necessary that each player be willing to choose the strategy predicted by the theory. Thus each player’s predicted strategy must be that player’s best response to the predicted strategies of the other players. Such a prediction could be called strategically stable or self-enforcing, because no single player wants to deviate from his or her predicted strategy (Gibbons: 8). q2* = 44 q2

4/17/2017 Nash Equilibrium A Nash Equilibrium is a pair of “best responses,” such that q1* is a best response to q2* and q2* is a best response to q1*. R2: q2* = 66 - 1/2q1 R1: q1* = 66 - 1/2q2 q1 q1* = 44 For the case of identical firms A Nash Equilibrium exists in an oligopolistic market, if each firm is basing its pmax output on a correct assumption (consistent) about the rivals’ behavior. On Dynamics: We arrive at the NE in logical time not historical time. Convergence to the NE is not the result of a series of actions but a series of conjectures, or beliefs. I think-that you think-that I think … [I]f game theory is to provide a unique solution to a game-theoretic problem then the solution must be a Nash equilibrium in the following sense. Suppose that game theory makes a unique prediction about the strategy each player will choose. In order for this prediction to be correct, it is necessary that each player be willing to choose the strategy predicted by the theory. Thus each player’s predicted strategy must be that player’s best response to the predicted strategies of the other players. Such a prediction could be called strategically stable or self-enforcing, because no single player wants to deviate from his or her predicted strategy (Gibbons: 8). q2* = 44 q2

4/17/2017 Nash Equilibrium A Nash Equilibrium is a pair of “best responses,” such that q1* is a best response to q2* and q2* is a best response to q1*. q1 q1* Is this the best they can do? If Firm 1 reduces its output while Firm 2 continues to produce q2*, the price rises and Firm 2’s profits increase. q2* q2

4/17/2017 Nash Equilibrium A Nash Equilibrium is a pair of “best responses,” such that q1* is a best response to q2* and q2* is a best response to q1*. q1 q1* Is this the best they can do? If Firm 2 reduces its output while Firm 1 continues to produce q1*, the price rises and Firm 1’s profits increase. q2* q2

4/17/2017 Nash Equilibrium A Nash Equilibrium is a pair of “best responses,” such that q1* is a best response to q2* and q2* is a best response to q1*. q1 q1* Is this the best they can do? If they can agree to restrict output, there are a range of outcomes to the SW that make both firms better off. The duopolists have an incentive to collude: to restrict their output – below the NE level – and increase their profits. What is socially optimal q2* q2

4/17/2017 Stackelberg Duopoly Firm 1 is the dominant firm, or Leader, (e.g., GM) and moves first. Firm 2 is the subordinate firm, or Follower. q1 Firm 1 gets to search along Firm 2’s reaction curve to find the point that maximizes Firm 1’s profits. p1 = ? 1934 Firm 1 knows Firm 2’s cost structure and hence can calculate its reaction curve R2. p1 = ? R2 q2

4/17/2017 Stackelberg Duopoly Firm 1 is the dominant firm, or Leader, (e.g., GM) and moves first. Firm 2 is the subordinate firm, or Follower. MR1 = MC1 TR1 = Pq1 = [30-1/6(q1+q2*)]q1 Find q2* from R2: q2* = 66 - 1/2q1 = [30-1/6(q1+66-1/2q1)]q1 = 30q1-1/6q12 -11q1+1/12q12 MR1 = 19 -1/6q1 = MC1 = 8 q1* = 66; q2* = 33 q1 q1* = 66 R2 q2* = 33 q2

4/17/2017 Stackelberg Duopoly Firm 1 is the dominant firm, or Leader, (e.g., GM) and moves first. Firm 2 is the subordinate firm, or Follower. Firm 1 has a first mover advantage: by committing itself to produce q1, it constraints Firm 2’s output decision. Firm 1 can employ excess capacity to deter entry by a potential rival. q1 q1* = 66 R2 q2* = 33 q2

4/17/2017 Bertrand Duopoly Under Bertrand duopoly, firms compete on the basis of price, not quantity (as in Cournot and Stackelberg). If P1 > P2 => q1 = 0 If P1 = P2 => q1 = q2 = ½ Q If P1 < P2 => q2 = 0 P P2 d1 q1

4/17/2017 Bertrand Duopoly Under Bertrand duopoly, firms compete on the basis of price, not quantity (as in Cournot and Stackelberg). Eventually, price will be competed down to the perfect competition level. Not very interesting model (so far). P P2 d1 q1

4/17/2017 Duopoly Models If we compare these results, we see that qualitatively different outcomes arise out of the finer-grained assumptions of the models: P 15.3 13.5 8 c P = 30 - 1/6Q TC = 40 + 8q Cournot Stackelberg Bertrand 88 99 132 Q

4/17/2017 Duopoly Models If we compare these results, we see that qualitatively different outcomes arise out of the finer-grained assumptions of the models: P Pc Ps Pb=Ppc c Qc < Qs < Qb Pc > Ps > Pb p1s > p1c >p1b p2c > p2s >p2b Cournot Stackelberg Bertrand Qc Qs Qb = Qpc Q

Duopoly Models Summary 4/17/2017 Duopoly Models Summary Oligopolistic markets are underdetermined by theory. Outcomes depend upon specific assumptions about strategic behavior. Nash Equilibrium is strategically stable or self-enforcing, b/c no single firm can increase its profits by deviating. In general, we observe a tension between Collusion: maximize joint profits Competition: capture a larger share of the pie Examples of Collusion

Game Theory Game Trees and Matrices Games of Chance v. Strategy 4/17/2017 Game Theory Game Trees and Matrices Games of Chance v. Strategy The Prisoner’s Dilemma Dominance Reasoning Best Response and Nash Equilibrium Mixed Strategies

4/17/2017 Games of Chance Player 1 You are offered a fair gamble to purchase a lottery ticket that pays $1000, if your number is drawn. The ticket costs $1. Buy Don’t Buy (1000) (-1) (0) (0) Chance E.g., Lottery, roulette. What would you do?

4/17/2017 Games of Chance Player 1 You are offered a fair gamble to purchase a lottery ticket that pays $1000, if your number is drawn. The ticket costs $1. The chance of your number being chosen is independent of your decision to buy the ticket. Buy Don’t Buy (1000) (-1) (0) (0) Chance E.g., Lottery, roulette.

Games of Strategy Player 2 chooses the winning number. 4/17/2017 Games of Strategy Player 1 Player 2 chooses the winning number. What are Player 2’s payoffs? Buy Don’t Buy (1000,-1000) (-1,1) (0,0) (0,0) Player 2 E.g., Lottery, roulette.

4/17/2017 Games of Strategy Firm 1 Duopolists deciding to advertise. Firm 1 moves first. Firm 2 observes Firm 1’s choice and then makes its own choice. How should the game be played? Advertise Don’t Advertise A D A D (10,5) (15,0) (6,8) (20,2) Firm 2 Backwards-induction

4/17/2017 Games of Strategy Firm 1 Duopolists deciding to advertise. The 2 firms move simultaneously. (Firm 2 does not see Firm 1’s choice.) Imperfect Information. Advertise Don’t Advertise A D A D (10,5) (15,0) (6,8) (20,2) Information set Firm 2 Extensive Form Games

Matrix Games 10, 5 15, 0 6, 8 20, 2 A D A D Firm 1 Advertise Don’t 4/17/2017 Matrix Games Firm 1 A D A D 10, 5 15, 0 6, 8 20, 2 Advertise Don’t Advertise A D A D (10,5) (15,0) (6,8) (20,2) Firm 2

Games of Strategy Games of strategy require at least two players. 4/17/2017 Games of Strategy Games of strategy require at least two players. Players choose strategies and get payoffs. Chance is not a player! In games of chance, uncertainty is probabilistic, random, subject to statistical regularities. In games of strategy, uncertainty is not random; rather it results from the choice of another strategic actor. Thus, game theory is to games of strategy as probability theory is to games of chance.

A Brief History of Game Theory 4/17/2017 A Brief History of Game Theory Minimax Theorem 1928 Theory of Games & Economic Behavior 1944 Nash Equilibrium 1950 Prisoner’s Dilemma 1950 The Evolution of Cooperation 1984 Nobel Prize: Harsanyi, Selten & Nash 1994

The Prisoner’s Dilemma 4/17/2017 The Prisoner’s Dilemma The pair of dominant strategies (Confess, Confess) is a Nash Eq. In years in jail Player 2 Confess Don’t Confess Player 1 Don’t -10, -10 0, -20 -20, 0 -1, -1 GAME 1.

The Prisoner’s Dilemma 4/17/2017 The Prisoner’s Dilemma Each player has a dominant strategy. Yet the outcome (-10, -10) is pareto inefficient. Is this a result of imperfect information? What would happen if the players could communicate? What would happen if the game were repeated? A finite number of times? An infinite or unknown number of times? What would happen if rather than 2, there were many players?

Dominance S1 S1 S2 S2 S3 S3 0,2 4,3 3,3 0,2 4,3 3,3 (S2,T2) (S2,T3) 4/17/2017 Dominance Definition Dominant Strategy: a strategy that is best no matter what the opponent(s) choose(s). T1 T2 T3 T1 T2 T3 S1 S2 S3 0,2 4,3 3,3 4,0 5,4 5,3 3,5 3,5 2,3 S1 S2 S3 0,2 4,3 3,3 4,0 5,4 5,6 3,5 3,5 2,3 (S2,T2) (S2,T3) Sure Thing Principle: If you have a dominant strategy, use it!

Nash Equilibrium S1 S1 S2 S2 S3 S3 (S3,T3) T1 T2 T3 0,4 4,0 5,3 4/17/2017 Nash Equilibrium Definitions Best Response Strategy: a strategy, s*, is a best response strategy, iff the payoff to (s*,t) is at least as great as the payoff to (s,t) for all s. T1 T2 T3 S1 S2 S3 0,4 4,0 5,3 4,0 0,4 5,3 3,5 3,5 6,6 Nash Equilibrium: a set of best response strategies (one for each player), (s*, t*) such that s* is a best response to t* and t* is a b.r. to s*. (S3,T3) S1 S2 S3 -3 0 -10 -1 5 2 -2 -4 0 Now let me pause and see if there are any questions.

Nash Equilibrium S1 S1 S2 S2 S3 S3 T1 T2 T3 4/17/2017 Nash Equilibrium T1 T2 T3 Nash equilibrium need not be Efficient. S1 S2 S3 4,4 2,3 1,5 3,2 1,1 0,0 5,1 0,0 3,3 S1 S2 S3 -3 0 -10 -1 5 2 -2 -4 0 This is similar to the PD, but w/o dominant strategies.

Nash Equilibrium S1 S1 S2 S2 S3 S3 T1 T2 T3 4/17/2017 Nash Equilibrium T1 T2 T3 Nash equilibrium need not be unique. A COORDINATION PROBLEM S1 S2 S3 1,1 0,0 0,0 0,0 1,1 0,0 0,0 0,0 1,1 S1 S2 S3 -3 0 -10 -1 5 2 -2 -4 0 GC PS TS A relatively simple problem to solve, if the players can communicate.

Nash Equilibrium S1 S1 S2 S2 S3 S3 T1 T2 T3 Multiple and Inefficient 4/17/2017 Nash Equilibrium T1 T2 T3 Multiple and Inefficient Nash Equilibria. S1 S2 S3 1,1 0,0 0,0 0,0 1,1 0,0 0,0 0,0 3,3 S1 S2 S3 -3 0 -10 -1 5 2 -2 -4 0 (S1,T1) and (S2,T2) remain NE, despite the appeal (salience) pf (S3,T3)

Nash Equilibrium S1 S1 S2 S2 S3 S3 T1 T2 T3 Multiple and Inefficient 4/17/2017 Nash Equilibrium T1 T2 T3 Multiple and Inefficient Nash Equilibria. Is it always advisable to play a NE strategy? What do we need to know about the other player? S1 S2 S3 1,1 0,0 0,-100 0,0 1,1 0,0 -100,0 0,0 3,3 S1 S2 S3 -3 0 -10 -1 5 2 -2 -4 0 We need to assume the other player is rational. Let’s pause for questions. Nash Equilibrium has an important property (strategic stability) but it is not necessarily unique nor efficient. Indeed, other solution concepts have been proposed, but Nash wins out for generality. In 1950, Nash proved that every finite game has an equilibrium point. For along time it was thought that these sort of I-think that you think – t hat I think … chains of reasoning led to infinite regress, but (first von Neumann for zerosum games and then …) In 1950, Nash proved that every finite game has an equilibrium point, a way to truncate the infinite regress and arrive at a course of action that should be chosen by rational decision-makers.

Next Time 7/21 Strategic Competition Pindyck and Rubenfeld, Ch 13. 4/17/2017 Next Time 7/21 Strategic Competition Pindyck and Rubenfeld, Ch 13. Besanko, Ch. 14.