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David Bryce © 1996-2002 Adapted from Baye © 2002 Game Theory: The Competitive Dynamics of Strategy MANEC 387 Economics of Strategy MANEC 387 Economics of Strategy David J. Bryce

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David Bryce © 1996-2002 Adapted from Baye © 2002 The Structure of Industries Competitive Rivalry Threat of new Entrants Bargaining Power of Customers Threat of Substitutes Bargaining Power of Suppliers From M. Porter, 1979, “How Competitive Forces Shape Strategy”

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David Bryce © 1996-2002 Adapted from Baye © 2002 Competitor Response Concepts from Game Theory Simultaneous move games in normal form: Dominant strategies equilibria –prisoner’s dilemma games –repeated games Nash equilibria –Dominant strategy “loses” – bullying brothers –Dominant strategy “wins” – rational pigs –Conditional strategies – battle of sexes (coordination game) Simultaneous move games in normal form: Dominant strategies equilibria –prisoner’s dilemma games –repeated games Nash equilibria –Dominant strategy “loses” – bullying brothers –Dominant strategy “wins” – rational pigs –Conditional strategies – battle of sexes (coordination game)

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David Bryce © 1996-2002 Adapted from Baye © 2002 Fundamentals of Game Theory 1. 1.Identify the players 2. 2.Identify their possible actions 3. 3.Identify their conditional payoffs from their actions 4. 4.Determine the players’ strategies – My strategy is my set of best responses to all possible rival actions 5. 5.Determine the equilibrium outcome(s) – equilibrium exists when all players are playing their best response to all other players 1. 1.Identify the players 2. 2.Identify their possible actions 3. 3.Identify their conditional payoffs from their actions 4. 4.Determine the players’ strategies – My strategy is my set of best responses to all possible rival actions 5. 5.Determine the equilibrium outcome(s) – equilibrium exists when all players are playing their best response to all other players

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David Bryce © 1996-2002 Adapted from Baye © 2002 Prisoner’s Dilemma Games of Dominant Strategies Two thieves are caught after their getaway (they hide the loot) They are being held in separate interrogation rooms Evidence against them is not strong so the DA needs one to testify against the other – or they go free and get the loot If one rats against his partner, he gets leniency; if one is ratted against by his partner, the evidence convicts him Should they rat or not rat? Two thieves are caught after their getaway (they hide the loot) They are being held in separate interrogation rooms Evidence against them is not strong so the DA needs one to testify against the other – or they go free and get the loot If one rats against his partner, he gets leniency; if one is ratted against by his partner, the evidence convicts him Should they rat or not rat?

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David Bryce © 1996-2002 Adapted from Baye © 2002 The Prisoner’s Dilemma Games of Dominant Strategies -2 2 21 -21 Prisoner B Rat Not Rat Rat Not Rat Prisoner A * *

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David Bryce © 1996-2002 Adapted from Baye © 2002 Pricing for Market Share A Prisoner’s Dilemma Two managers want to maximize market share Strategies are pricing decisions Simultaneous moves One-shot game Two managers want to maximize market share Strategies are pricing decisions Simultaneous moves One-shot game

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David Bryce © 1996-2002 Adapted from Baye © 2002 Pricing for Market Share A Prisoner’s Dilemma 0.50.80.9 0.50.20.1 0.20.50.8 0.50.2 0.10.20.5 0.90.80.5 P=10 P=5 P=1 P=10 P=5 P=1 Manager B Manager A * *

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David Bryce © 1996-2002 Adapted from Baye © 2002 An Advertising Game Two firms (Kellogg & General Mills) managers want to maximize profits Strategies consist of advertising campaigns Simultaneous moves One-shot interaction Repeated interaction Two firms (Kellogg & General Mills) managers want to maximize profits Strategies consist of advertising campaigns Simultaneous moves One-shot interaction Repeated interaction

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David Bryce © 1996-2002 Adapted from Baye © 2002 A One-Shot Advertising Game General Mills Kellogg 122015 12 1 169 20 6 0 02 15 9 2 None Moderate High None Mod High * *

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David Bryce © 1996-2002 Adapted from Baye © 2002 Can collusion work if the game is repeated 2 times? General Mills Kellogg 122015 12 1 169 20 6 0 02 15 9 2 None Moderate High None Mod High * *

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David Bryce © 1996-2002 Adapted from Baye © 2002 No (by backward induction) In period 2, the game is a one-shot game, so equilibrium entails High Advertising in the last period. This means period 1 is “really” the last period, since everyone knows what will happen in period 2. Equilibrium entails High Advertising by each firm in both periods. The same holds true if we repeat the game any known, finite number of times. In period 2, the game is a one-shot game, so equilibrium entails High Advertising in the last period. This means period 1 is “really” the last period, since everyone knows what will happen in period 2. Equilibrium entails High Advertising by each firm in both periods. The same holds true if we repeat the game any known, finite number of times.

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David Bryce © 1996-2002 Adapted from Baye © 2002 Can collusion work if firms play the game each year, forever? Consider the following “tit-for-tat” strategy by each firm: –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. Consider the following “tit-for-tat” strategy by each firm: –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.

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David Bryce © 1996-2002 Adapted from Baye © 2002 General Mills Adopts Tit-for-Tat Strategy – Kellogg’s Profits? Cooperate = 12 +12/(1+i) + 12/(1+i) 2 + 12/(1+i) 3 + … = 12 + 12/i Cooperate = 12 +12/(1+i) + 12/(1+i) 2 + 12/(1+i) 3 + … = 12 + 12/i Value of a perpetuity Cheat = 20 +2/(1+i) + 2/(1+i) 2 + 2/(1+i) 3 + … = 20 + 2/i Cheat = 20 +2/(1+i) + 2/(1+i) 2 + 2/(1+i) 3 + … = 20 + 2/i General Mills Kellogg 122015 12 1 169 20 6 0 02 15 9 2 None Mod High None Mod High * *

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David Bryce © 1996-2002 Adapted from Baye © 2002 Kellogg’s Gain to Cheating? General Mills Kellogg 122015 12 1 169 20 6 0 02 15 9 2 None Mod High None Mod High * * Cheat - Cooperate = 20 + 2/i -(12+12/i) = 8 - 10/i Suppose i =.05 Cheat - Cooperate = 8 - 10/.05 = 8 - 200 = -192 It doesn’t pay to deviate – collusion is a Nash equilibrium in the infinitely repeated game Cheat - Cooperate = 20 + 2/i -(12+12/i) = 8 - 10/i Suppose i =.05 Cheat - Cooperate = 8 - 10/.05 = 8 - 200 = -192 It doesn’t pay to deviate – collusion is a Nash equilibrium in the infinitely repeated game

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David Bryce © 1996-2002 Adapted from Baye © 2002 Benefits & Costs of Cheating Cheat - Cooperate = 8 - 10/i 8 = immediate benefit (20 - 12 today) 10/i = PV of future cost (12 - 2 forever after) If immediate benefit > PV of future cost*, it pays to “cheat” If immediate benefit PV of future cost*, it doesn’t pay to “cheat” Cheat - Cooperate = 8 - 10/i 8 = immediate benefit (20 - 12 today) 10/i = PV of future cost (12 - 2 forever after) If immediate benefit > PV of future cost*, it pays to “cheat” If immediate benefit PV of future cost*, it doesn’t pay to “cheat” General Mills Kellogg 122015 12 1 169 20 6 0 02 15 9 2 None Mod High None Mod High * * *Remember: Future cost also may include your foregone celestial reward!

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David Bryce © 1996-2002 Adapted from Baye © 2002 Key Insight to Repeated Games Collusion can be sustained as a Nash equilibrium when there is no certain “end” to a game. Doing so requires: –Ability to monitor actions of rivals –Ability (and reputation for) punishing defectors –Low interest rate –High probability of future interaction Collusion can be sustained as a Nash equilibrium when there is no certain “end” to a game. Doing so requires: –Ability to monitor actions of rivals –Ability (and reputation for) punishing defectors –Low interest rate –High probability of future interaction

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David Bryce © 1996-2002 Adapted from Baye © 2002 Bullying Brothers An older brother and a younger brother sell lemonade on opposite ends of the block Both brothers are considering adding sugar to their lemonade Older brother earns more with better inputs, location, and knowledge Younger brother has inferior location and spills sugar An older brother and a younger brother sell lemonade on opposite ends of the block Both brothers are considering adding sugar to their lemonade Older brother earns more with better inputs, location, and knowledge Younger brother has inferior location and spills sugar

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David Bryce © 1996-2002 Adapted from Baye © 2002 Bullying Brothers 68 4 3 54 3 2 Older Brother No Sugar Sugar No Sugar Sugar Younger Brother * *

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David Bryce © 1996-2002 Adapted from Baye © 2002 Rational Pigs One dominant and one subordinate pig in a pen Lever at one end dispenses 6 units of food in a trough at the other end While pig that presses lever runs to trough, other pig is eating from trough –Costs ½ food unit to run to trough –Big pig can eat all 6 units with or without the small pig at the trough –If both press lever, small pig beats big pig and eats 2 units before big pig gets there One dominant and one subordinate pig in a pen Lever at one end dispenses 6 units of food in a trough at the other end While pig that presses lever runs to trough, other pig is eating from trough –Costs ½ food unit to run to trough –Big pig can eat all 6 units with or without the small pig at the trough –If both press lever, small pig beats big pig and eats 2 units before big pig gets there

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David Bryce © 1996-2002 Adapted from Baye © 2002 Rational Pigs 3.56 1.5-0.5 0.50 5.0 0 Big Pig Press Lever Don’t Press Press Don’t Press Small Pig * *

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David Bryce © 1996-2002 Adapted from Baye © 2002 Battle of the Sexes Games of Coordination A husband and wife are planning a night out Husband prefers to attend a boxing match Wife prefers to attend the theater For both, the strongest preference is to spend time together rather than apart What should they do? A husband and wife are planning a night out Husband prefers to attend a boxing match Wife prefers to attend the theater For both, the strongest preference is to spend time together rather than apart What should they do?

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David Bryce © 1996-2002 Adapted from Baye © 2002 Battle of the Sexes Games of Coordination 5 3 13 1 5 Husband Attend Boxing Attend Theater Boxing Theater Wife * * * *

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David Bryce © 1996-2002 Adapted from Baye © 2002 Competitive Dynamics Influence Strategic Cash Flow Analysis Game theory incorporates competitor response into expected payoffs of strategic decisions. Time Cash Flow Even Break

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David Bryce © 1996-2002 Adapted from Baye © 2002 On Game Theory and Strategy When you influence your rival and vice versa, correct strategic decisions must be informed by game theoryWhen you influence your rival and vice versa, correct strategic decisions must be informed by game theory Formal games can be hard to model and are sometimes difficult to solveFormal games can be hard to model and are sometimes difficult to solve Formal games can be constructed through NPV analysis where payoffs are conditioned on the actions of rivalsFormal games can be constructed through NPV analysis where payoffs are conditioned on the actions of rivals When you influence your rival and vice versa, correct strategic decisions must be informed by game theoryWhen you influence your rival and vice versa, correct strategic decisions must be informed by game theory Formal games can be hard to model and are sometimes difficult to solveFormal games can be hard to model and are sometimes difficult to solve Formal games can be constructed through NPV analysis where payoffs are conditioned on the actions of rivalsFormal games can be constructed through NPV analysis where payoffs are conditioned on the actions of rivals

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David Bryce © 1996-2002 Adapted from Baye © 2002 Summary and Takeaways Strategy and economics aid in choosing paths in unstable, dynamic environments Firms with market power typically have some influence on market structure Firms must not only react to changing environment, but must understand their impact on the environment and rivals –Interdependent cash flows can be assembled to help in understanding these relationships –Let game theory shape your intuition Strategy and economics aid in choosing paths in unstable, dynamic environments Firms with market power typically have some influence on market structure Firms must not only react to changing environment, but must understand their impact on the environment and rivals –Interdependent cash flows can be assembled to help in understanding these relationships –Let game theory shape your intuition

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