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Iterated Weak Dominance in Strictly Competitive Games of Perfect Information

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  • Ewerhart, Christian

Abstract

We prove that any strictly competitive perfect-information two-person game with n outcomes is solvable in n-1 steps of elimination of weakly dominated strategies - regardless of the length of the game tree. The derivation is based on the fact that if player i does not possess a winning strategy, then any of player j's strategies that enables i to win is eliminated by two steps of iterated dominance. The given bound is shown to be tight using a variant of Rosenthal's centipede game.
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  • Ewerhart, Christian, 2002. "Iterated Weak Dominance in Strictly Competitive Games of Perfect Information," Journal of Economic Theory, Elsevier, vol. 107(2), pages 474-482, December.
    • Handle: RePEc:eee:jetheo:v:107:y:2002:i:2:p:474-482
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    1. Moulin, Herve, 1979. "Dominance Solvable Voting Schemes," Econometrica, Econometric Society, vol. 47(6), pages 1137-1151, November.
    2. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
    3. Ewerhart, Christian, 2000. "Chess-like Games Are Dominance Solvable in at Most Two Steps," Games and Economic Behavior, Elsevier, vol. 33(1), pages 41-47, October.
    4. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    5. Gretlein, Rodney, J, 1982. "Dominance Solvable Voting Schemes: A Comment," Econometrica, Econometric Society, vol. 50(2), pages 527-528, March.
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    2. Osterdal, Lars Peter, 2005. "Iterated weak dominance and subgame dominance," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 637-645, September.

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