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

2. 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 ©
Adapted from Baye © 2002

3. 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 ©
Adapted from Baye © 2002

4. 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 ©
Adapted from Baye © 2002

5. 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 ©
Adapted from Baye © 2002

6. 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 ©
Adapted from Baye © 2002

7. “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 ©
Adapted from Baye © 2002

8. 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 ©
Adapted from Baye © 2002

9. 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 ©
Adapted from Baye © 2002

10. Step 1: Management’s Move10 5 M 1
David Bryce ©
Adapted from Baye © 2002

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

12. 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 ©
Adapted from Baye © 2002

13. 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 ©
Adapted from Baye © 2002

14. 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 ©
Adapted from Baye © 2002

15. 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 ©
Adapted from Baye © 2002

16. 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 ©
Adapted from Baye © 2002

17. 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 ©
Adapted from Baye © 2002

18. 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 ©
Adapted from Baye © 2002

19. 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 ©
Adapted from Baye © 2002

20. 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 ©
Adapted from Baye © 2002

21. 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 ©
Adapted from Baye © 2002

22. 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 ©
Adapted from Baye © 2002

23. 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 ©
Adapted from Baye © 2002

24. 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 ©
Adapted from Baye © 2002

25. 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 ©
Adapted from Baye © 2002