Regret-based continuous-time dynamics |
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Authors: | Sergiu Hart Andreu Mas-Colell |
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Institution: | a Center for Rationality and Interactive Decision Theory, Department of Mathematics, and Department of Economics, The Hebrew University of Jerusalem, Feldman Building, Givat Ram, 91904, Jerusalem, Israel;b Department of Economics and Business, Universitat Pompeu Fabra, Ramon Trias Fargas 25-27, 08005, Barcelona, Spain |
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Abstract: | Regret-based dynamics have been introduced and studied in the context of discrete-time repeated play. Here we carry out the corresponding analysis in continuous time. We observe that, in contrast to (smooth) fictitious play or to evolutionary models, the appropriate state space for this analysis is the space of distributions on the product of the players' pure action spaces (rather than the product of their mixed action spaces). We obtain relatively simple proofs for some results known in the discrete case (related to ‘no-regret’ and correlated equilibria), and also a new result on two-person potential games (for this result we also provide a discrete-time proof). |
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Keywords: | JEL classification codes: C7 D7 C6 |
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