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  • 1. More Game Theory Rob Seamans & Richard Wang MBA 299: Strategy April 18 th , 2008
  • 2. More game theory
    • Warm Up
    • Repeated games
    • Sequential Games
    • Signaling games
  • 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. More game theory
    • Warm Up
    • Repeated games
    • Sequential Games
    • Signaling games
  • 5. What about repeated games?
    • What happens if Coke and Pepsi play a price war, given the payoffs below?
    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?
  • 6. Thinking about price wars
    • Why do price wars start?
      • How do you credibly signal commitment to fight forever?
    • Why do price wars stop?
        • PV (nice payoffs) > PV (bitter competition)
    • What role will the future play in determining the outcome?
  • 7. Equilibrium in repeated play
    • Consider the strategy: If you fought in the previous round I will fight forever . . . If you accommodated in the previous round I will accommodate until you fight
    • Assume no discounting for simplicity, then you get:
      • 4+0+0+0+0 . . . . =4 if choose “fight” (call this “strategy f”, or S f )
      • 1+1+1+1+1 . . . . =n if choose “accommodate” (call this “strategy a”, or S a )
    • What would you do if there were three periods?
    • What would you do if there were five periods? (keep this answer in mind…)
  • 8. Infinitely repeated game with discounting
    • Assumptions:
      • Receive x each period
      • Discount factor is  = 1/[1+r] < 1
    • Solve for NPV in terms of x and delta:
      • NPV=x+  x+  2 x+  3 x+…=S
      •  S=  x+  2 x+  3 x+  4 x+…
      • S-  S=x  S=x/(1-  )
    • Compare payoffs between two strategies:
      • For example, from last slide, x=1:
      • Let S a =1/(1-  ) and S f =4
      • When is S a >S f ? When is S a <S f ?
      • When does S a= S f ? Set 1/(1-  ) =4   =3/4
      •  >3/4  Accommodate;  <3/4  Fight
  • 9. The Folk Theorem Result
    • As long as delta is big enough (players are sufficiently patient) any outcome can be supported.
    • This is a nice result because it tells us we can support cooperation with trigger strategies in long-period repeated games where players are patient as long as neither player knows when the game will end.
    • Doesn’t rely exclusively on “doom triggers” but punishments must be “big”.
  • 10. Finitely repeated game
    • What happens if it’s not an infinite game? Would you ever cooperate?
      • What if you do know when the game will end?
      • What if you don’t know when the game will end?
    • We can use backward induction to solve the outcome for finitely repeated games.
    • So why might you not want to announce you intend to exit after a certain point?
  • 11. More game theory
    • Warm Up
    • Repeated games
    • Sequential Games
    • Signaling games
  • 12. Sequential games
    • In sequential games, players move in a pre-determined order, and might observe moves of other players that happen before they move
    • This type of game is useful in developing predictions in situations where one firm moves first and others follow
      • RyanAir vs. BA/AL on pricing
  • 13. Example: Capacity Expansion and Entry
    • An established manufacturer is facing possible competition from a rival
    • The established manufacturer can try to stave off entry by engaging in costly capacity expansion, which increases supply and lowers price charged to customers
    • Rival can observe whether incumbent expands capacity or not before deciding on entry
      • Example: Nutrasweet vs. HSC on capacities
  • 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. Game is solved using Backward Induction
    • Look to the end of the game tree and prune back (similar to working backwards through a decision tree)
    • Rationality assumption implies that players choose the strategy at each node that yields highest expected payoff
    • There’s no incomplete information in this game, so there’s no uncertainty in the prediction
  • 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. Equilibrium Prediction
    • The prediction from this model is that the incumbent will expand capacity and this will effectively forestall entry
    • Notice that even in absence of actual entry, the potential competition from the rival eats into the incumbent’s profits.
    • By thinking dynamically, game theory allows a refinement of the typical economics monopoly prediction of production quantity at MR=MC
  • 21. Sequence of Play is Important
    • The preceding game assumed rival could move at the last moment, after seeing incumbent’s decision
    • Suppose that the rival must commit to enter or not before the capacity expansion decision of the incumbent
    • How would this affect the outcome of the game?
  • 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. Equilibrium Prediction
    • Game sequence can affect decision outcomes and payoffs!
    • This game has a first-mover advantage
    • Is it always true in sequential move games that there is a first-mover advantage?
  • 25. More game theory
    • Warm Up
    • Repeated games
    • Sequential Games
    • Signaling games
  • 26. Signaling game set-up
    • Imagine there are two types of people in the world, but that type is private information know only to the individual:
      • people who are good at business but not at art (business people)
      • people who are good at art but not at business (artists)
    • Employers want to hire business people not artists
    • Employers pay very well such that artists would like to have business jobs
    • How should employers find business people?
  • 27. How do employers find business people?
    • One solution is to ask people, “are you a business person or an artist?”
      • What will business people say?
      • What will artists say?
    • Is there a signal business people can send?
      • What if wearing a suit signals that one is a business person? What will artists do?
      • Is there a credible signal business people can send that businesses will believe?
  • 28. Credible signals
    • A signal is credible if it is costly enough such that artists will not want to invest in signaling
    • One potential credible signal is going to business school
    • Interestingly the signal works even if business school does not affect business people’s productivity
  • 29. Signaling game set-up
    • Assumptions:
    • ½ the people in the world are business people and ½ are artists
    • Business people are worth $5 to employers, while artists are worth $4*
    • Only enough business jobs for ½ the people in the world
    • Employers pay $3 to anyone hired, regardless of type (since unobservable)
    • Business school is free. However, it costs $1 of effort from business people and $2 of effort from artists (artists dislike business school)
    • School does not change the productive capacity of the people
    • *Feel free to multiply these numbers by 100K to make more realistic!
  • 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. Equilibrium
    • Business people go to business school, artists do not and employers only hire business school graduates
      • This is the only equilibrium in this game, no one can do better by changing their strategy given what other players do
      • Note that if everyone goes to school the expected value for artists is -½.
    • Note the role of business school in this game
      • Business people don’t learn anything useful in business school in this set up.
      • However business school is still a socially useful institution since it allows business people to send credible signals to potential employers.
  • 35. A few comments
    • A signal is only valuable if it is credible
    • Credible signals must be costly to send
    • This game is actually more complicated than what has been laid out here . . . If you want more take John Morgan’s game theory class
  • 36. Application of Game Theory
    • In a prisoner’s dilemma set up, everyone loses. How can firms get away from this bad outcome?
    • How might the following game theory concepts help your team in the CSG?
      • Repeated play
      • Sequential moves
      • Signaling
  • 37. Next week
    • Oligopoly Games
    • Value Net
    • Transaction Cost Economics