The Possibility of Impossible Stairways and Greener Grass

M. Voorneveld

Research output: Working paperDiscussion paperOther research output

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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 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.
Original languageEnglish
Place of PublicationTilburg
PublisherMicroeconomics
Number of pages15
Volume2007-62
Publication statusPublished - 2007

Publication series

NameCentER Discussion Paper
Volume2007-62

Fingerprint

Coordination games
Hedge
Deviation
Nash equilibrium
Utility function
Game theory
Mixed strategy

Keywords

  • coordination games
  • dominant strategies
  • payoff-dominance
  • nonexistence of equi- librium
  • tail events

Cite this

Voorneveld, M. (2007). The Possibility of Impossible Stairways and Greener Grass. (CentER Discussion Paper; Vol. 2007-62). Tilburg: Microeconomics.
Voorneveld, M. / The Possibility of Impossible Stairways and Greener Grass. Tilburg : Microeconomics, 2007. (CentER Discussion Paper).
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Voorneveld, M 2007 'The Possibility of Impossible Stairways and Greener Grass' CentER Discussion Paper, vol. 2007-62, Microeconomics, Tilburg.

The Possibility of Impossible Stairways and Greener Grass. / Voorneveld, M.

Tilburg : Microeconomics, 2007. (CentER Discussion Paper; Vol. 2007-62).

Research output: Working paperDiscussion paperOther research output

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Voorneveld M. The Possibility of Impossible Stairways and Greener Grass. Tilburg: Microeconomics. 2007. (CentER Discussion Paper).