On the Evolutionary Selection of Sets of Nash Equilibria
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0022-0531
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Journal of Economic Theory, 2007, 133, 1, 295-315
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BALKENBORG, Dieter, SCHLAG, Karl H., On the Evolutionary Selection of Sets of Nash Equilibria, Journal of Economic Theory, 2007, 133, 1, 295-315 - https://hdl.handle.net/1814/16393
Abstract
It is well established for evolutionary dynamics in asymmetric games that a pure strategy combination is asymptotically stable if and only if it is a strict Nash equilibrium. We use an extension of the notion of a strict Nash equilibrium to sets of strategy combinations called 'strict equilibrium set' and show the following. For a large class of evolutionary dynamics, including all monotone regular selection dynamics, every asymptotically stable set of rest points that contains a pure strategy combination in each of its connected components is a strict equilibrium set. A converse statement holds for two-person games, for convex sets and for the standard replicator dynamic. (c) 2005 Elsevier Inc. All rights reserved.