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Crowding games are sequentially solvable

Author

Listed:
  • Igal Milchtaich

    (Department of Mathematics and Center for Rationality and Interactive Decision Theory, Hebrew University of Jerusalem, Israel)

Abstract

A sequential-move version of a given normal-form game is an extensive-form game of perfect information in which each player chooses his action after observing the actions of all players who precede him and the payoffs are determined according to the payoff functions in . A normal-form game is sequentially solvable if each of its sequential-move versions has a subgame-perfect equilibrium in pure strategies such that the players' actions on the equilibrium path constitute an equilibrium of . A crowding game is a normal-form game in which the players share a common set of actions and the payoff a particular player receives for choosing a particular action is a nonincreasing function of the total number of players choosing that action. It is shown that every crowding game is sequentially solvable. However, not every pure-strategy equilibrium of a crowding game can be obtained in the manner described above. A sufficient, but not necessary, condition for the existence of a sequential-move version of the game that yields a given equilibrium is that there is no other equilibrium that Pareto dominates it.

Suggested Citation

  • Igal Milchtaich, 1998. "Crowding games are sequentially solvable," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 501-509.
    • Handle: RePEc:spr:jogath:v:27:y:1998:i:4:p:501-509
    Note: Received July 1997/Final version May 1998
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    Citations

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    Cited by:

    1. Milchtaich, Igal & Winter, Eyal, 2002. "Stability and Segregation in Group Formation," Games and Economic Behavior, Elsevier, vol. 38(2), pages 318-346, February.
    2. Igal Milchtaich, 2000. "Generic Uniqueness of Equilibrium in Large Crowding Games," Mathematics of Operations Research, INFORMS, vol. 25(3), pages 349-364, August.
    3. Igal Milchtaich, 2005. "Topological Conditions for Uniqueness of Equilibrium in Networks," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 225-244, February.
    4. repec:dau:papers:123456789/2347 is not listed on IDEAS
    5. José Correa & Jasper de Jong & Bart de Keijzer & Marc Uetz, 2019. "The Inefficiency of Nash and Subgame Perfect Equilibria for Network Routing," Management Science, INFORMS, vol. 44(4), pages 1286-1303, November.
    6. Andelman, Nir & Feldman, Michal & Mansour, Yishay, 2009. "Strong price of anarchy," Games and Economic Behavior, Elsevier, vol. 65(2), pages 289-317, March.
    7. Darryl Seale & Amnon Rapoport, 2000. "Elicitation of Strategy Profiles in Large Group Coordination Games," Experimental Economics, Springer;Economic Science Association, vol. 3(2), pages 153-179, October.
    8. Jasper Jong & Marc Uetz, 2020. "The quality of equilibria for set packing and throughput scheduling games," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 321-344, March.
    9. Renault, Jérôme & Scarlatti, Sergio & Scarsini, Marco, 2008. "Discounted and finitely repeated minority games with public signals," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 44-74, July.
    10. repec:dau:papers:123456789/6381 is not listed on IDEAS

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