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More Game Theory Rob Seamans & Richard Wang MBA 299: Strategy April 18 th , 2008
More game theory ,[object Object],[object Object],[object Object],[object Object]
Application of Prisoner’s Dilemma: Oil Production $70M,$60M $180M,$50M $160M,$100M $60M,$120M Increase  Production Restrict Output Increase Production  Restrict Output Saudi Arabia Iran Nash Equilibrium:  Given what the other player is doing, you can’t do better by deviating
More game theory ,[object Object],[object Object],[object Object],[object Object]
What about repeated games? ,[object Object],0,0 4,-3 1,1 -3,4 Fight Accommodate Fight  Accommodate Coke Pepsi What happens if Coke and Pepsi play a price war again and again?
Thinking about price wars ,[object Object],[object Object],[object Object],[object Object],[object Object]
Equilibrium in repeated play ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Infinitely repeated game with discounting ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Folk Theorem Result ,[object Object],[object Object],[object Object]
Finitely repeated game ,[object Object],[object Object],[object Object],[object Object],[object Object]
More game theory ,[object Object],[object Object],[object Object],[object Object]
Sequential games ,[object Object],[object Object],[object Object]
Example: Capacity Expansion and Entry ,[object Object],[object Object],[object Object],[object Object]
Incumbent decides to expand or not, then rival decides whether to enter I R R 1,1 3,2 2,4 4,2 Expand Do not expand Enter Don’t Enter Enter Don’t Enter
Game is solved using Backward Induction ,[object Object],[object Object],[object Object]
What will rival do? I R R 1,1 3,2 2,4 4,2 Expand Do not expand Enter Don’t Enter Enter Don’t Enter
Rival’s Choice I R R 1,1 3,2 2,4 4,2 Expand Do not expand Enter Don’t Enter Enter Don’t Enter
What will the Incumbent do? I R R 1,1 3,2 2,4 4,2 Expand Do not expand Enter Don’t Enter Enter Don’t Enter
Incumbent’s Choice I R R 1,1 3,2 2,4 4,2 Expand Do not expand Enter Don’t Enter Enter Don’t Enter
Equilibrium Prediction ,[object Object],[object Object],[object Object]
Sequence of Play is Important ,[object Object],[object Object],[object Object]
Game Tree – Rival moves first, same payoffs R I I 1,1 4,2 2,3 2,4 Enter Don’t Enter Expand Not expand Expand Not expand
Game Tree – Rival moves first, same payoffs R I I 1,1 4,2 2,3 2,4 Enter Don’t Enter Expand Not expand Expand Not expand
Equilibrium Prediction ,[object Object],[object Object],[object Object]
More game theory ,[object Object],[object Object],[object Object],[object Object]
Signaling game set-up ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Slide 1

  • 1. More Game Theory Rob Seamans & Richard Wang MBA 299: Strategy April 18 th , 2008
  • 2.
  • 3. Application of Prisoner’s Dilemma: Oil Production $70M,$60M $180M,$50M $160M,$100M $60M,$120M Increase Production Restrict Output Increase Production Restrict Output Saudi Arabia Iran Nash Equilibrium: Given what the other player is doing, you can’t do better by deviating
  • 4.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14. Incumbent decides to expand or not, then rival decides whether to enter I R R 1,1 3,2 2,4 4,2 Expand Do not expand Enter Don’t Enter Enter Don’t Enter
  • 15.
  • 16. What will rival do? I R R 1,1 3,2 2,4 4,2 Expand Do not expand Enter Don’t Enter Enter Don’t Enter
  • 17. Rival’s Choice I R R 1,1 3,2 2,4 4,2 Expand Do not expand Enter Don’t Enter Enter Don’t Enter
  • 18. What will the Incumbent do? I R R 1,1 3,2 2,4 4,2 Expand Do not expand Enter Don’t Enter Enter Don’t Enter
  • 19. Incumbent’s Choice I R R 1,1 3,2 2,4 4,2 Expand Do not expand Enter Don’t Enter Enter Don’t Enter
  • 20.
  • 21.
  • 22. Game Tree – Rival moves first, same payoffs R I I 1,1 4,2 2,3 2,4 Enter Don’t Enter Expand Not expand Expand Not expand
  • 23. Game Tree – Rival moves first, same payoffs R I I 1,1 4,2 2,3 2,4 Enter Don’t Enter Expand Not expand Expand Not expand
  • 24.
  • 25.
  • 26.
  • 27.
  • 28.
  • 29.
  • 30. Signaling game 0,0 0,0 Business people Artists B School No B School B School No B School 3,2 3,1 -1,0 -2,0 2,2 1,1 50% 50% Nature H N H N H N H N
  • 31. Signaling game - Equilibrium 0,0 0,0 Business people Artists B School No B School B School No B School 3,2 3,1 -1,0 -2,0 2,2 1,1 50% 50% Nature H N H N H N H N
  • 32. Signaling game – No incentive to deviate by the business people 0,0 0,0 Business people Artists B School No B School B School No B School 3,2 3,1 -1,0 -2,0 2,2 1,1 50% 50% Nature H N H N H N H N EV=(3+0)/2=1.5
  • 33. Signaling game – No incentive to deviate by the artists 0,0 0,0 Business people Artists B School No B School B School No B School 3,2 3,1 -1,0 -2,0 2,2 1,1 50% 50% Nature H N H N H N H N EV = (1-2)/2 = -0.5
  • 34.
  • 35.
  • 36.
  • 37.