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UNIT III: COMPETITIVE STRATEGY

UNIT III: COMPETITIVE STRATEGY. Monopoly Oligopoly Strategic Behavior. 7/19. Market Structure. Perfect Comp Oligopoly Monopoly No. of Firms infinite (>)2 1 Output MR = MC = P ??? MR = MC < P Profit No ? Yes

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UNIT III: COMPETITIVE STRATEGY

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  1. UNIT III: COMPETITIVE STRATEGY • Monopoly • Oligopoly • Strategic Behavior 7/19

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

  3. 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

  4. Duopoly Models • Cournot Duopoly • Nash Equilibrium • Leader/Follower Model • Price Competition

  5. Duopoly Models • Cournot Duopoly • Nash Equilibrium • Stackelberg Duopoly • Bertrand Duopoly

  6. 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

  7. 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 MC = 8 MR D Q* = 66 180 Q

  8. 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 Will Megacorp enter the market? What is its profit maximizing level of output?

  9. 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

  10. 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* = $13.50P2 = 141.5 Before entry, P* = 19; P1 = 686 Now, P1’ = 323ow, PC‘ = 297 $ 30 19 13.5 q2 = 0 MC2 = 8 q1*+q2* = 99 180 Q

  11. 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?

  12. 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

  13. Cournot Duopoly To find R1, set MR = MC. Now, MR is a (-) function not only of q1but 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 66 132 q2

  14. 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 q2* = 44 q2

  15. 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 q2* = 44 q2

  16. 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

  17. 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

  18. 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. q2* q2

  19. 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 = ? p1 = ? R2 q2

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

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

  28. 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 What would you do?

  29. 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 decisiontobuythe ticket. Buy Don’t Buy (1000) (-1) (0) (0) Chance

  30. 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

  31. 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

  32. 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

  33. Matrix Games A D A D Firm 1 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

  34. 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.

  35. 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

  36. 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.

  37. 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?

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

  39. 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 Nash Equilibrium: aset 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) 0,44,0 5,3 4,0 0,45,3 3,5 3,5 6,6 -3 0 -10 -1 5 2 -2 -4 0 S1 S2 S3 S1 S2 S3

  40. Nash Equilibrium T1 T2 T3 Nash equilibrium need not be Efficient. 4,4 2,3 1,5 3,2 1,1 0,0 5,1 0,0 3,3 -3 0 -10 -1 5 2 -2 -4 0 S1 S2 S3 S1 S2 S3

  41. Nash Equilibrium T1 T2 T3 Nash equilibrium need not be unique. A COORDINATION PROBLEM 1,1 0,0 0,0 0,0 1,1 0,0 0,0 0,0 1,1 -3 0 -10 -1 5 2 -2 -4 0 S1 S2 S3 S1 S2 S3

  42. Nash Equilibrium T1 T2 T3 Multiple and Inefficient Nash Equilibria. 1,1 0,0 0,0 0,0 1,1 0,0 0,0 0,0 3,3 -3 0 -10 -1 5 2 -2 -4 0 S1 S2 S3 S1 S2 S3

  43. 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? 1,1 0,0 0,-100 0,0 1,1 0,0 -100,0 0,0 3,3 -3 0 -10 -1 5 2 -2 -4 0 S1 S2 S3 S1 S2 S3

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

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