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Game theory - 1

Game theory - 1. ECO 474 Economics of War and Peace. Game theory. Structure a simple game in both matrix and tree formats Specify a simple game Identify Nash equilibria Identify dominant strategies. Game theory overview. General analysis of strategic interaction

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Game theory - 1

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  1. Game theory - 1 ECO 474 Economics of War and Peace

  2. Game theory • Structure a simple game in both matrix and tree formats • Specify a simple game • Identify Nash equilibria • Identify dominant strategies

  3. Game theory overview • General analysis of strategic interaction • Optimal decision making when • all decision agents are presumed rational • each attempts to anticipate actions of rivals • Everyone knows the rules and acts in their self-interest

  4. Simultaneous-move,non-repeated interaction • Simultaneous? • Rivals must make decisions with no knowledge of each other’s decisions • Nonrepeated (One-Shot Game) • The interaction occurs only once Matrix, Normal, or Strategic Form

  5. Simultaneous-move,non-repeated interaction Classic Prisoner’s Dilemma Game

  6. Prisoner’s Dilemma In the classic prisoner’s dilemma game: • The dominant strategy is compete • The Nash Equilibrium is compete-compete • Cooperation would leave both better off, but there are powerful incentives to compete • Expect the same outcome in finite repeated competition • Cooperation may be possible in infinite repeated competition – need a facilitating mechanism

  7. Simultaneous-move,non-repeated interaction An Arms Race

  8. One-Shot, Arms Race Game • The Nash Equilibrium is Build Arms-Build Arms • The Cooperative Outcome Disarm-Disarm would be preferable, but would require repeated competition (do some signaling) or sequential competition (inflexible commitment) • Easier in market games where competition is not one-shot. More difficult in war games in which there may only be one shot.

  9. Example • Boeing and Airbus individually choose and simultaneously submit a bid price (high or low) for 10 planes • Each cell entry represents the payoffs • A dominant strategy is one the firm chooses no matter what its rival does

  10. Strategic formdominant strategy

  11. Nash equilibriumrevisited • Boeing and Airbus each have a dominant strategy, yielding Nash equilibrium • Nash equilibrium is set of strategies where firm does its best given rival’s actions • Use arrow technique to identify Nash equilibrium • In the absence of a dominant strategy, Nash equilibrium may predict outcome

  12. Nash equilibrium(no dominant strategy for Boeing)(2 arrows going into cell)

  13. Competition versus cooperation • Boeing and Airbus make simultaneous choices of new communications systems • two technologies: Alpha & Beta • both benefit with same choice • Results in two Nash equilibria • benefits from pre-commitment communication

  14. Coordination gametwo Nash equilibria(2 arrows into 2 cells)

  15. Coordination/competition game(Boeing prefers Alpha, Airbus prefers Beta

  16. Sequential interactions • Boeing & Airbus communications technology choice • Boeing chooses first • Analyze with backward induction • Boeing must take Airbus’s best response into account in making its choice • Boeing has first mover advantage • Credible commitment by second mover can alter first mover choice (more than talk)

  17. Extensive formsequential game

  18. Repeated strategic interaction • Cooperative theory • “Repetition Enables Cooperation” Aumann • Repetition is like an enforcement mechanism • Consider Aumann’s “H” game

  19. Simultaneous-move,non-repeated interaction Aumann’s H Game

  20. Aumann’s H Game • With simultaneous-move, non-repeated interaction the Nash Equilibrium is (G,A) • The cooperative outcome (E,A) could be achieved by enforceable contract (treaty) or by repetition • Grim Trigger Strategy (MAD) • Tit-for-Tat

  21. Grim Trigger Strategy (MAD) • Requires long-run thinking • Low discount rate • Long-term gains larger than short-term gains • Need transparency – verify cooperation • Infinite repetition • Tit-for-Tat is a superior strategy

  22. Strategic interaction and organizational architecture • Kiana manages Lenin • Len must choose between working/cooperating and shirking/cheating • Kiana must choose whether to incur monitoring/inspection costs • No pure strategy equilibrium exists • Mixed-strategy equilibrium (randomized strategies)

  23. Interactive gameno pure strategy equilibrium

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