Abstract
We consider an extension of an almost strictly competitive game, introduced by Aumann (1961), inn-person extensive games by incorporating Selten's subgame perfection. We call it a subgame perfect weakly-almost (SPWA) strictly competitive game, in particular, an SPWA strictly competitive game in strategic form is simply called a WA strictly competitive game. We give some general results on the structure of this class of games. One result gives an easy way to verify almost strict competitiveness of a given extensive game. We show that a two-person weakly unilaterally competitive extensive game, introduced by Kats and Thisse (1992) for normal form games, is SPWA strictly competitive. We remark that some of our main results for SPWA strictly competitive games do not hold for the modification of almost strict competitiveness with trembling-hand perfection.
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The author is indebted to Mamoru Kaneko for valuable discussions, comments and criticism throughout the paper. He thanks N. Bose, M. Frascatore, R. Gilles, H. Haller, A. Kats, J. Kline and an anonymous referee for helpful comments on earlier drafts. The usual disclaimer applies.
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Raychaudhuri, S. Almost strict competitiveness in extensive games. Int J Game Theory 23, 167–182 (1994). https://doi.org/10.1007/BF01240181
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DOI: https://doi.org/10.1007/BF01240181