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Order Independence for Iterated Weak Dominance


  • Leslie McFarland-Marx
  • Jeroen M. Swinkels


In general, the result of the elimination of weakly dominated strategies depends on order. We find a condition, satisfied by the normal form of any generic extensive form, and by some important games which do not admit generic extensive forms, under which any two games resulting from the elimination of weakly dominated strategies (subject to no more eliminations being possible) are equivalent. We also extend our condition and result to the case of elimination by mixed strategies. The result strengthens the intuitive connection between backward induction and weak dominance. And, under our condition, some computational problems relating to weak dominance, which are gnerally complex, become simple.

Suggested Citation

  • Leslie McFarland-Marx & Jeroen M. Swinkels, 1993. "Order Independence for Iterated Weak Dominance," Discussion Papers 1040, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1040

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    References listed on IDEAS

    1. Ehud Kalai & Eitan Zemel, 1988. "On The Order of Eliminating Dominated Strategies," Discussion Papers 789, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. 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.
    3. Mailath, George J & Samuelson, Larry & Swinkels, Jeroen M, 1993. "Extensive Form Reasoning in Normal Form Games," Econometrica, Econometric Society, vol. 61(2), pages 273-302, March.
    4. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
    5. Itzhak Gilboa & E. Kalai & E. Zemel, 1990. "On the order of eliminating dominated strategies," Post-Print hal-00481648, HAL.
    6. Moulin, Herve, 1979. "Dominance Solvable Voting Schemes," Econometrica, Econometric Society, vol. 47(6), pages 1137-1151, November.
    7. Itzhak Gilboa & Ehud Kalai & Eitan Zemel, 1993. "The Complexity of Eliminating Dominated Strategies," Mathematics of Operations Research, INFORMS, vol. 18(3), pages 553-565, August.
    8. Moulin, Herve, 1994. "Social choice," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 31, pages 1091-1125 Elsevier.
    9. Mark A. Satterthwaite & Hugo Sonnenschein, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," Review of Economic Studies, Oxford University Press, vol. 48(4), pages 587-597.
    10. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
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    JEL classification:

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


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