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Game Theory

Game Theory. “Life must be understood backward, but … it must be lived forward.” - Soren Kierkegaard Mike Shor Lecture 4. Review. Recognize dominant and dominated strategies Dominant strategies are always played Dominated strategies are never played

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Game Theory

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  1. Game Theory “Life must be understood backward, but … it must be lived forward.” - Soren Kierkegaard Mike Shor Lecture 4

  2. Review • Recognize dominant and dominated strategies • Dominant strategies are always played • Dominated strategies are never played • Your opponent recognizes this, too • Common knowledge • Equilibrium: likely outcome of a game • Dominance solvable • Iterated deletion of dominated strategies Game Theory - Mike Shor

  3. Cell-by-Cell Inspection • Games of Assurance • The “good” equilibrium is risky • Need assurances • Games of Coordination • Failure to agree leads to no profits • Can’t agree on “what to agree on” • Games of Chicken Game Theory - Mike Shor

  4. Games of Chicken • A monopolist faces a potential entrant • Monopolist can accommodate or fight • Potential entrant can enter or stay out Monopolist Potential Entrant Game Theory - Mike Shor

  5. Equilibrium • Use best reply method to find equilibria Monopolist Potential Entrant Game Theory - Mike Shor

  6. Importance of Order • Two equilibria exist • ( In, Accommodate ) • ( Out, Fight ) • Only one makes temporal sense • Fight is a threat, but not credible • Not sequentially rational • Simultaneous outcomes may not make sense for sequential games Game Theory - Mike Shor

  7. out 0 , 100 E in -50 , -50 fight M acc 50 , 50 Sequential Games The Extensive Form Game Theory - Mike Shor

  8. -50 , -50 fight M acc 50 , 50 Looking Forward… • Entrant makes the first move: • Must consider how monopolist will respond • If enter: • Monopolist accommodates Game Theory - Mike Shor

  9. out 0 , 100 E in M acc 50 , 50 … And Reasoning Back • Now consider entrant’s move • Only ( In, Accommodate ) is sequentially rational Game Theory - Mike Shor

  10. Sequential Rationality COMMANDMENT Look forward and reason back. Anticipate what your rivals will do tomorrow in response to your actions today Game Theory - Mike Shor

  11. Solving Sequential Games • Start with the last move in the game • Determine what that player will do • Trim the tree • Eliminate the dominated strategies • This results in a simpler game • Repeat the procedure Game Theory - Mike Shor

  12. Voting Revisited • Majority rule results: • M beats E ; E beats R ; R beats M • If you set the agenda: • M vs. R then winner vs. E  E • Problem: • You are the engineering director: M vs. R, then winner versus E? Good Luck! • Better chance: M vs. E, then winner versus R Game Theory - Mike Shor

  13. Extensive Form M M M vs. R R M M vs. E R E E E E vs. R R R Game Theory - Mike Shor

  14. Looking Forward M M M vs. R A majority prefers R to M R R E E A majority prefers E to R E vs. R R R Game Theory - Mike Shor

  15. Trim The Tree M vs. R R M M vs. E R E E E E vs. R Game Theory - Mike Shor

  16. Reasoning Back • First stage, in effect vote between R & E • E beats R, so in first stage, vote for E M vs. R R M M vs. E R E E E E vs. R Game Theory - Mike Shor

  17. What Happened? • Director of marketing has preferences • Marketing > Engineering > R&D • In first round, vote between M and E • Director of Marketing prefers M But vote for M is in effect a vote for R • So Director of Marketing votes E Guarantees herself second best choice Game Theory - Mike Shor

  18. Rollback in Voting and “Being Political” • Not necessarily good to vote your true preferences • Amendments to make bad bills worse • Crossing over in open primaries • “Centrist” voting in primaries • Supporting your second-best option • STILL – Outcome predetermined • AGENDA SETTING! Game Theory - Mike Shor

  19. Predatory Pricing • An incumbent firm operates in three markets, and faces entry in each • Market 1 in year 1, Market 2 in year 2, etc. • Each time, I can slash prices, or accommodate the new entry • What should I do the first year? Game Theory - Mike Shor

  20. Predatory Pricing E3 E2 out out E1 fight fight M in in M acc acc Game Theory - Mike Shor

  21. 0 , 100 + previous out E3 -50 , -50 + previous fight M in acc 50 , 50 + previous Predatory Pricing • The end of the tree: year 3 • In year 3: ( In, Accommodate ) Game Theory - Mike Shor

  22. E3 M in acc 0 , 100 + previous out E2 in acc -50 , -50 + previous fight M in acc in acc 50 , 50 + previous Rollback • Trim the tree: Game Theory - Mike Shor

  23. Predatory Pricing • Since the Incumbent will not fight Entrant 3, he will not fight Entrant 2 • Same for Entrant 1 • Only one “Rollback Equilibrium” • All entrants play In • Incumbent plays Accommodate • Why do we see predatory pricing? Game Theory - Mike Shor

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