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

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

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

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

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

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 David Bryce © 1996-2002 Adapted from Baye © 2002

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

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

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

Step 4: Identify the Firm’s Feasible Strategies Management has one information set and thus three feasible strategies: Offer $10 Offer $5 Offer $1 David Bryce © 1996-2002 Adapted from Baye © 2002

Step 5: Identify the Union’s Feasible Strategies Accept $10, Accept $5, Accept $1 Accept $10, Accept $5, Reject $1 Accept $10, Reject $5, Accept $1 Reject $10, Accept $5, Accept $1 Accept $10, Reject $5, Reject $1 Reject $10, Accept $5, Reject $1 Reject $10, Reject $5, Accept $1 Reject $10, Reject $5, Reject $1 David Bryce © 1996-2002 Adapted from Baye © 2002

Step 6: Identify Nash Equilibrium Outcomes Firm's Best Mutual Best Union's Strategy Response Response? $1 Yes Accept $10, Accept $5, Accept $1 $5 Yes Accept $10, Accept $5, Reject $1 Accept $10, Reject $5, Accept $1 $1 Yes $1 Reject $10, Accept $5, Accept $1 Yes $10 Yes Accept $10, Reject $5, Reject $1 $5 Yes Reject $10, Accept $5, Reject $1 Reject $10, Reject $5, Accept $1 $1 Yes Reject $10, Reject $5, Reject $1 $10, 5, 1 No David Bryce © 1996-2002 Adapted from Baye © 2002

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

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

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

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

Checking for Credible Actions Are actions credible? Union's Strategy Yes Accept $10, Accept $5, Accept $1 No Accept $10, Accept $5, Reject $1 Accept $10, Reject $5, Accept $1 No No Reject $10, Accept $5, Accept $1 No Accept $10, Reject $5, Reject $1 No Reject $10, Accept $5, Reject $1 Reject $10, Reject $5, Accept $1 No Reject $10, Reject $5, Reject $1 No David Bryce © 1996-2002 Adapted from Baye © 2002

The “Credible” Union Strategy Are actions credible? Union's Strategy Yes Accept $10, Accept $5, Accept $1 No Accept $10, Accept $5, Reject $1 Accept $10, Reject $5, Accept $1 No No Reject $10, Accept $5, Accept $1 No Accept $10, Reject $5, Reject $1 No Reject $10, Accept $5, Reject $1 Reject $10, Reject $5, Accept $1 No Reject $10, Reject $5, Reject $1 No David Bryce © 1996-2002 Adapted from Baye © 2002

Sequential Strategies in the Game Tree 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 David Bryce © 1996-2002 Adapted from Baye © 2002

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