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Iterated weak dominance and subgame dominance

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  • Osterdal, Lars Peter

Abstract

In this paper, we consider finite normal form games satisfying transference of decisionmaker indifference. We show that any set of strategies surviving k rounds of elimination of some weakly dominated strategies can be reduced to a set of strategies equivalent to the set of strategies surviving k rounds of elimination of all weakly dominated strategies in every round by (at most k) further rounds of elimination of weakly dominated strategies. The result develops work by Gretlein (Dominance Elimination Procedures on Finite Alternative Games, Int J Game Theory 12, 107-113, 1983). We then consider applications and demonstrate how we may obtain a unified approach to the above mentioned work by Gretlein and recent work by Ewerhart (Iterated Weak Dominance in Strictly Competitive Games of Perfect Information, J Econ Theory 107, 474-482, 2002) and Marx and Swinkels (Order Independence for Iterated Weak Dominance, Games Econ Behav 18, 219-245, 1997).
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Suggested Citation

  • Osterdal, Lars Peter, 2005. "Iterated weak dominance and subgame dominance," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 637-645, September.
    • Handle: RePEc:eee:mateco:v:41:y:2005:i:6:p:637-645
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    1. Marx, Leslie M. & Swinkels, Jeroen M., 2000. "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 31(2), pages 324-329, May.
    2. 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.
    3. Moulin, Herve, 1979. "Dominance Solvable Voting Schemes," Econometrica, Econometric Society, vol. 47(6), pages 1137-1151, November.
    4. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    5. 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.
    6. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    7. Gretlein, Rodney, J, 1982. "Dominance Solvable Voting Schemes: A Comment," Econometrica, Econometric Society, vol. 50(2), pages 527-528, March.
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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