The possibility of impossible stairways and greener grass

Arbeitspapier

In 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 coordination 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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SSE/EFI Working Paper Series in Economics and Finance ; No. 673

Classification and Topics

• Classification: Wirtschaft ; Noncooperative Games
• Subject: coordination games ; dominant strategies ; payoff-dominance ; nonexistence of equilibrium ; tail events ; Nichtkooperatives Spiel ; Gleichgewicht ; Koordination ; Spieltheorie ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Voorneveld, Mark
• Event: Veröffentlichung
• (who): Stockholm School of Economics, The Economic Research Institute (EFI)
• (where): Stockholm
• (when): 2007

Further information

• Handle: http://hdl.handle.net/10419/56319
• Last update: 10.03.2025, 11:42 AM CET