Basins of attraction and equilibrium selection under different learning rules |
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Authors: | Russell Golman Scott E Page |
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Institution: | (1) Department of Applied and Interdisciplinary Mathematics, University of Michigan, 2082 East Hall, 530 Church Street, Ann Arbor, MI 48109, USA;(2) Center for the Study of Complex Systems, University of Michigan, 321A West Hall, 1085 S. University Ave., Ann Arbor, MI 48109, USA |
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Abstract: | A deterministic learning model applied to a game with multiple equilibria produces distinct basins of attraction for those
equilibria. In symmetric two-by-two games, basins of attraction are invariant to a wide range of learning rules including
best response dynamics, replicator dynamics, and fictitious play. In this paper, we construct a class of three-by-three symmetric
games for which the overlap in the basins of attraction under best response learning and replicator dynamics is arbitrarily
small. We then derive necessary and sufficient conditions on payoffs for these two learning rules to create basins of attraction
with vanishing overlap. The necessary condition requires that with probability one the initial best response is not an equilibrium
to the game. The existence of parasitic or misleading actions allows subtle differences in the learning rules to accumulate. |
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