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Order Independence for Iterated Weak Dominance

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  • Leslie McFarland-Marx
  • Jeroen M. Swinkels

Abstract

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.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1040.

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Date of creation: Apr 1993
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Handle: RePEc:nwu:cmsems:1040

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  1. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
  2. Leslie M. Marx & Jeroen M. Swinkels, 1996. "Order Independence for Iterated Weak Dominance," Discussion Papers 1066R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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. Satterthwaite, Mark A & Sonnenschein, Hugo, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," Review of Economic Studies, Wiley Blackwell, vol. 48(4), pages 587-97, October.
  5. Itzhak Gilboa & Ehud Kalai & Eitan Zemel, 1989. "The Complexity of Eliminating Dominated Strategies," Discussion Papers 853, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. 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.
  7. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
  8. Moulin, Herve, 1979. "Dominance Solvable Voting Schemes," Econometrica, Econometric Society, vol. 47(6), pages 1137-51, November.
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