SSE/EFI Working Paper Series in Economics and Finance
The possibility of impossible stairways and greener grass
Abstract: 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
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
Keywords: coordination games; dominant strategies; payoff-dominance; nonexistence of equilibrium; tail events; (follow links to similar papers)
JEL-Codes: C72; (follow links to similar papers)
15 pages, August 28, 2007
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