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Order Independence for Iterated Weak Dominance

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  • Leslie M. Marx
  • Jeroen M. Swinkels

Abstract

In general, the result of the elimination of weakly dominated strategies depends on order. We define nice weak dominance. Under nice weak dominance, order does not matter. We identify an important class of games under which nice weak dominance and weak dominance are equivalent, and so order under weak dominance does not matter. For all games, the result of iterative nice weak dominance is an upper bound on he result from any order of weak dominance. The result strengthen the intuitive relationship between backward induction and weak dominance, and shed light on some computational problems relating to weak dominance.

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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 1066R.

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Date of creation: Sep 1996
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Handle: RePEc:nwu:cmsems:1066

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  1. 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.
  2. 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.
  3. Mailath, G.J. & Samuelson, L. & Swinkels, J., 1991. "extensive Form Reasoning in Normal Form Games," Papers 9130, Tilburg - Center for Economic Research.
  4. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
  5. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
  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. Moulin, Herve, 1979. "Dominance Solvable Voting Schemes," Econometrica, Econometric Society, vol. 47(6), pages 1137-51, November.
  8. 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.
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