1 / 23

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

albert
Download Presentation

Game Theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related