Reasonable Nash demand games

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In the Nash demand game (NDG) n players announce utility demands, the demands are implemented if they are jointly feasible, and otherwise no one gets anything. If the utilities set is the simplex, the game is called “divide-the-dollar”. Brams and Taylor (Theory Decis 37:211–231, 1994) studied variants of divide-the-dollar, on which they imposed reasonableness conditions. I explore the implications of these conditions on general NDGs. In any reasonable NDG, the egalitarian demand profile cannot be obtained via iterated elimination of weakly dominated strategies. Further, a reasonable NDG may fail to have a Nash equilibrium, even in mixed strategies. In the 2-person case, existence of pure strategy equilibrium is equivalent to the existence of a value, in the sense that each player can secure the egalitarian payoff level independent of his opponent’s play. This result does not extend to reasonable NDGs with more than two players. Interestingly, there are results for reasonable NDGs that hold for two and three players, but not for n≥ 4 players.

Original languageEnglish
Pages (from-to)319-330
Number of pages12
JournalTheory and Decision
Issue number2
StatePublished - Sep 2022

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Divide-the-dollar
  • Fair division
  • Nash demand game

ASJC Scopus subject areas

  • Decision Sciences (all)
  • Developmental and Educational Psychology
  • Arts and Humanities (miscellaneous)
  • Applied Psychology
  • Social Sciences (all)
  • Economics, Econometrics and Finance (all)
  • Computer Science Applications


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