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Consistency, dummy and independence of irrelevant strategies for strategic games

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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.

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Authors and Affiliations

  1. Department of Economics, University of York, Heslington, York YO10 5DD, UK (e-mail: ir2@york.ac.uk), , , , , , GB

    Indrajit Ray

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  1. Indrajit Ray
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Received: 13 August 1998/Accepted: 19 January 1999

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Ray, I. Consistency, dummy and independence of irrelevant strategies for strategic games. Soc Choice Welfare 17, 217–222 (2000). https://doi.org/10.1007/s003550050016

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  • DOI: https://doi.org/10.1007/s003550050016

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