The Possibility of Impossible Stairways and Greener Grass
AbstractIn classical game theory, players have finitely many actions and evaluate outcomes of mixed strategies using a von Neumann-Morgenstern utility function. Allowing a larger, but countable, player set introduces a host of phenomena that are impossible in finite games. Firstly, in coordination games, all players have the same preferences: switching to a weakly dominant action makes everyone at least as well off as before. Nevertheless, there are coordina- tion games where the best outcome occurs if everyone chooses a weakly dominated action, while the worst outcome occurs if everyone chooses the weakly dominant action. Secondly, the location of payoff-dominant equilibria behaves capriciously: two coordination games that look so much alike that even the consequences of unilateral deviations are the same may nevertheless have disjoint sets of payoff-dominant equilibria. Thirdly, a large class of games has no (pure or mixed) Nash equilibria. Following the proverb \the grass is always greener on the other side of the hedge", greener-grass games model constant discontent: in one part of the strategy space, players would rather switch to its complement. Once there, they'd rather switch back.
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Date of creation: 2007
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coordination games; dominant strategies; payoff-dominance; nonexistence of equi- librium; tail events;
Other versions of this item:
- Voorneveld, Mark, 2007. "The possibility of impossible stairways and greener grass," Working Paper Series in Economics and Finance 673, Stockholm School of Economics.
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-09-16 (All new papers)
- NEP-GTH-2007-09-16 (Game Theory)
- NEP-UPT-2007-09-16 (Utility Models & Prospect Theory)
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