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Managerial Economics & Business Strategy Chapter 10 Game Theory: Inside Oligopoly

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A Market-Share Game Two managers want to maximize market share. Strategies are pricing decisions. Simultaneous moves. One-shot game.

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The Market-Share Game in Normal Form Manager 2 Manager 1 What is the Nash Equilibrium???

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Market-Share Game Equilibrium Manager 2 Manager 1 Nash Equilibrium

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What do we see? Game theory can be used to analyze situations where “payoffs” are non monetary! n Here we were looking at market shares Typically we will focus on environments where businesses want to maximize profits. n Typical payoffs are measured in monetary units.

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Is the Nash Equilibrium always best? What is the Nash equilibrium? n Low Price – Low Price Is it the best? n Could collude and both charge high prices What if we “agree” to charge high prices, but then firm A cheats? n Firm A will increase profits (can’t rat them out because collusion is illegal) Everyone fears cheating…we don’t agree. Firm A Firm B

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Examples of Coordination Games Coordination games should we produce things to coordinate with our rivals, or do something completely different Laser disks vs. DVDs Industry standards n size of floppy disks. n size of CDs. National standards n electric current. n traffic laws.

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A Coordination Game in Normal Form Player 2 Player 1

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A Coordination Problem: Three Nash Equilibria! Player 2 Player 1 More than one Nash equilibrium!! Anytime we do the same…we maximize our profits.

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Key Insights: Not all games are games of conflict. Communication can help solve coordination problems. Sequential moves can help solve coordination problems.

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An Advertising Game Two firms (Kellogg’s & General Mills) managers want to maximize profits. Strategies consist of advertising campaigns. Simultaneous moves. n One-shot interaction. n Repeated interaction.

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Infinitely Repeated Games It appears that Collusion is not possible in a one-shot game, but what if we can build trust??? Need to look at the STREAM of payoffs when they make their current decision n Cheat or not cheat What was the formula for PV??

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If profits are the same in every period

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Can collusion work if firms play the game each year, forever? Consider the following “trigger strategy” by each firm: n “Don’t advertise, provided the rival has not advertised in the past. If the rival ever advertises, “punish” it by engaging in a high level of advertising forever after.” In effect, each firm agrees to “cooperate” so long as the rival hasn’t “cheated” in the past. “Cheating” triggers punishment in all future periods. n Trigger causes a FUTURE cost of cheating Remember the deal is Don’t advertise!!

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Suppose General Mills adopts this trigger strategy. Kellogg’s profits? Cooperate = 12 +12/(1+i) + 12/(1+i) 2 + 12/(1+i) 3 + … = 12 + 12/i General Mills Kellogg’s Value of a perpetuity of $12 paid at the end of every year Cheat = 20 +2/(1+i) + 2/(1+i) 2 + 2/(1+i) 3 + … = 20 + 2/I Gain 20 the first period but 2 after cheating episode

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Kellogg’s Gain to Cheating: Cheat - Cooperate = 20 + 2/i - (12 + 12/i) = 8 - 10/i n Suppose i =.05 Cheat - Cooperate = 8 - 10/.05 = 8 - 200 = -192 It doesn’t pay to deviate. n Collusion is a Nash equilibrium in the infinitely repeated game! If Immediate Benefit - PV of Future Cost > 0 n Pays to “cheat”. If Immediate Benefit - PV of Future Cost 0 n Doesn’t pay to “cheat”.

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Key Insight Collusion can be sustained as a Nash equilibrium when there is no certain “end” to a game. Doing so requires: n Ability to monitor actions of rivals. n Ability (and reputation for) punishing defectors. n Low interest rate. n High probability of future interaction.

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Real World Examples of Collusion Garbage Collection Industry OPEC NASDAQ Airlines

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Can we do it? (demonstration problem 10-6) Suppose firm A and firm B repeatedly face the situation presented below and the interest rate is 40 percent. The firms agree to charge a high price each period provided neither firm has cheated on this agreement in the past. n What are firm A’s profits if it cheats on the collusive agreement? n What are firm A’s profits if it does not cheat on the collusive agreement? n Does an equilibrium result where the firms charge the high price each period? Price Firm B LowHigh Firm A Low0,00,050,-40 High-40,5010,10

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Cheat get 50 now and zero after that Not Cheat get 10 forever Since 50 (cheat) > 35 (not cheat we would end up CHEAT

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Factors affecting collusion Collusion is easier when firms know… n Who their rivals are (so then they know who to punish) n Who their rivals’ customers are (so they can steal them by charging lower prices if they have to punish the rival) n When their rivals deviate from the agreement n Be able to punish successfully for deviations from agreement n The end of the game is not known If there is no tomorrow there is no punishment everyone will cheat

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Chapter 10 Homework Numbers 2, 4, and 14

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