1. 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

2. 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”

3. David Bryce © 1996-2002 Adapted from Baye © 2002 Competitor Response Concepts from Game Theory Sequential move games in normal form –Simultaneous vs. sequential move games – hypothetical Boeing v. McDonnell-Douglas game (bullying brothers) Sequential move games in extensive form –Backward induction –Subgame-perfect equilibria Sequential move games in normal form –Simultaneous vs. sequential move games – hypothetical Boeing v. McDonnell-Douglas game (bullying brothers) Sequential move games in extensive form –Backward induction –Subgame-perfect equilibria

4. 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

5. David Bryce © 1996-2002 Adapted from Baye © 2002 Simultaneous-Move Bargaining Management and a union are negotiating a wage increase Strategies are wage offers & wage demands Successful negotiations lead to $600 million in surplus, which must be split among the parties Failure to reach an agreement results in a loss to the firm of $100 million and a union loss of $3 million Simultaneous moves, and time permits only one-shot at making a deal. Management and a union are negotiating a wage increase Strategies are wage offers & wage demands Successful negotiations lead to $600 million in surplus, which must be split among the parties Failure to reach an agreement results in a loss to the firm of $100 million and a union loss of $3 million Simultaneous moves, and time permits only one-shot at making a deal.

6. David Bryce © 1996-2002 Adapted from Baye © 2002 The Bargaining Game in Normal Form Union Management 500-3 100-100 -3300-3 -100 300-100 -3 100 -100 500 W=$10 W=$5 W=$1 W=$10 W=$5 W=$1 * * * * * *

7. David Bryce © 1996-2002 Adapted from Baye © 2002 “Fairness” – the Natural Focal Point Union Management 500-3 100-100 -3300-3 -100 300-100 -3 100 -100 500 W=$10 W=$5 W=$1 W=$10 W=$5 W=$1 * * * * * *

8. David Bryce © 1996-2002 Adapted from Baye © 2002 Lessons in Simultaneous-Move Bargaining Simultaneous-move bargaining results in a coordination problem Experiments suggests that, in the absence of any “history,” real players typically coordinate on the “fair outcome” When there is a “bargaining history,” other outcomes may prevail Simultaneous-move bargaining results in a coordination problem Experiments suggests that, in the absence of any “history,” real players typically coordinate on the “fair outcome” When there is a “bargaining history,” other outcomes may prevail

9. David Bryce © 1996-2002 Adapted from Baye © 2002 A Sequential Game - Single Offer Bargaining Now suppose the game is sequential in nature, and management gets to make the union a “take-it-or-leave-it” offer Write the game in extensive form –Summarize the players –Their potential actions –Their information at each decision point –The sequence of moves and –Each player’s payoff Now suppose the game is sequential in nature, and management gets to make the union a “take-it-or-leave-it” offer Write the game in extensive form –Summarize the players –Their potential actions –Their information at each decision point –The sequence of moves and –Each player’s payoff

10. David Bryce © 1996-2002 Adapted from Baye © 2002 M M 10 5 5 1 1 Step 1: Management’s Move

11. David Bryce © 1996-2002 Adapted from Baye © 2002 Accept Reject Step 2: Append the Union’s Move M M 10 5 5 1 1 Accept Reject U U U U Accept Reject U U

12. David Bryce © 1996-2002 Adapted from Baye © 2002 100, 500 -100, -3 300, 300 -100, -3 500, 100 -100, -3 Step 3: Append the Payoffs Accept Reject M M 10 5 5 1 1 Accept Reject U U U U Accept Reject U U

13. David Bryce © 1996-2002 Adapted from Baye © 2002 100, 500 -100, -3 300, 300 -100, -3 500, 100 -100, -3 Multiple Nash Equilibria Accept Reject 10 5 5 1 1 Accept Reject Accept Reject * * M M U U U U U U * * * *

14. David Bryce © 1996-2002 Adapted from Baye © 2002 Step 7: Find the Subgame Perfect Nash Equilibrium Outcomes Outcomes where no player has an incentive to change its strategy at any stage of the game, given the strategy of the rival, and The outcomes are based on “credible actions;” that is, they are not the result of “empty threats” by the rival. Outcomes where no player has an incentive to change its strategy at any stage of the game, given the strategy of the rival, and The outcomes are based on “credible actions;” that is, they are not the result of “empty threats” by the rival.

15. David Bryce © 1996-2002 Adapted from Baye © 2002 Final player chooses the option that maximizes her payoff The previous player chooses the option that maximizes his payoff conditional on the expected choice of the final player, and so on This is backward induction – work backward from the end “sub-game,” each player makes optimal choices assuming that each subsequent rival chooses rationally The equilibrium is called sub-game perfect Final player chooses the option that maximizes her payoff The previous player chooses the option that maximizes his payoff conditional on the expected choice of the final player, and so on This is backward induction – work backward from the end “sub-game,” each player makes optimal choices assuming that each subsequent rival chooses rationally The equilibrium is called sub-game perfect Sequential Strategies in the Game Tree

16. David Bryce © 1996-2002 Adapted from Baye © 2002 Only One Subgame-Perfect Nash Equilibrium Outcome 100, 500 -100, -3 300, 300 -100, -3 500, 100 -100, -3 Accept Reject 10 5 5 1 1 Accept Reject Accept Reject M M U U U U U U * *

17. David Bryce © 1996-2002 Adapted from Baye © 2002 Re-Cap In take-it-or-leave-it bargaining, there is a first-mover advantage. Management can gain by making a take-it or leave-it offer to the union. Management should be careful, however; real world evidence suggests that people sometimes reject offers on the the basis of “principle” instead of cash considerations. In take-it-or-leave-it bargaining, there is a first-mover advantage. Management can gain by making a take-it or leave-it offer to the union. Management should be careful, however; real world evidence suggests that people sometimes reject offers on the the basis of “principle” instead of cash considerations.

18. David Bryce © 1996-2002 Adapted from Baye © 2002 Moroni, Zarahemna and Credible Threats M M Spare Attack -200 -50 200 -150 M M Spare 100 -100 0 0 -200 Z Z Deliver/Oath Don’t Deliver Payoffs Attack * * See Alma 44, Book of Mormon (or Bush, Saddam and those pesky WMDs)

19. David Bryce © 1996-2002 Adapted from Baye © 2002 Moroni – Zarahemna and Credible Threats M M Spare Attack -200 -50 200 -150 M M Spare 100 -100 0 0 -200 Z Z Take Oath Don’t Deliver Payoffs Attack * * Z Z Don’t Take M M Spare Attack Deliver ? ? 100 -175 -100 See Alma 44, Book of Mormon

20. David Bryce © 1996-2002 Adapted from Baye © 2002 Summary and Takeaways The reasoning of game theory supplies a useful way to predict the outcome of competitive interactions By diagramming a game, players can identify their best potential strategies Threats of retaliation must be credible Incumbents may be able to deter entrants by making major strategic commitments (credible threats) The reasoning of game theory supplies a useful way to predict the outcome of competitive interactions By diagramming a game, players can identify their best potential strategies Threats of retaliation must be credible Incumbents may be able to deter entrants by making major strategic commitments (credible threats)