Implementing egalitarianism in a class of Nash demand games

Emin Karagözoğlu, Shiran Rachmilevitch

Research output: Contribution to journalArticlepeer-review


We add a stage to Nash’s demand game by allowing the greedier player to revise his demand if the demands are not jointly feasible. If he decides to stick to his initial demand, then the game ends and no one receives anything. If he decides to revise it down to 1 - x, where x is his initial demand, the revised demand is implemented with certainty. The implementation probability changes linearly between these two extreme cases. We derive a condition on the feasible set under which the two-stage game has a unique subgame perfect equilibrium. In this equilibrium, there is first-stage agreement on the egalitarian demands. We also study two n-player versions of the game. In either version, if the underlying bargaining problem is “divide-the-dollar,” then equal division is sustainable in a subgame perfect equilibrium if and only if the number of players is at most four.

Original languageEnglish
Pages (from-to)495-508
Number of pages14
JournalTheory and Decision
Issue number3-4
StatePublished - 1 Oct 2018

Bibliographical note

Funding Information:
Acknowledgements The authors thank an anonymous referee for a helpful report. Emin Karagözog˘lu thanks TÜB˙TAK (The Scientific and Technological Research Council of Turkey) for the post-doctoral research fellowship. Usual disclaimers apply.

Publisher Copyright:
© 2018, 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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