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Consistency, dummy and independence of irrelevant strategies for strategic games

Author

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  • Indrajit Ray

    (Department of Economics, University of York, Heslington, York YO10 5DD, UK)

Abstract

The relationships between the consistency (CONS) principle and two other axioms, dummy (DUM) and independence of irrelevant strategies (IIS) for solution concepts on families of strategic form games are studied. If a solution satisfies DUM and IIS, then it also satisfies CONS (Peleg and Tijs 1996). The converse of this proposition is not true: CONS implies neither DUM nor IIS as shown in two simple examples, using the concept of coalition-proof Nash equilibrium. The axiom of weak dummy (WDUM) is introduced. WDUM, along with IIS, implies CONS. Moreover, CONS implies WDUM.

Suggested Citation

  • Indrajit Ray, 2000. "Consistency, dummy and independence of irrelevant strategies for strategic games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 217-222.
    • Handle: RePEc:spr:sochwe:v:17:y:2000:i:2:p:217-222
    Note: Received: 13 August 1998/Accepted: 19 January 1999
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    Cited by:

    1. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic foundations of a unifying concept of the core of games in effectiveness form," Post-Print halshs-01902122, HAL.
    2. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic Foundations of a Unifying Core," Working Papers 1817, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    3. Gonzalez, Stéphane & Lardon, Aymeric, 2021. "Axiomatic foundations of the core for games in effectiveness form," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 28-38.

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