Two more classes of games with the continuous-time fictitious play property

by: Ulrich Berger

Games and Economic Behavior, Vol. 60, No. 2. (August 2007), pp. 247-261.

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Abstract

Fictitious Play is the oldest and most studied learning process for games. Since the already classical result for zero-sum games, convergence of beliefs to the set of Nash equilibria has been established for several classes of games, including weighted potential games, supermodular games with diminishing returns, and 3×3 supermodular games. Extending these results, we establish convergence of Continuous-time Fictitious Play for ordinal potential games and quasi-supermodular games with diminishing returns. As a by-product we obtain convergence for 3×m and 4×4 quasi-supermodular games.

@article{games_eql_fplay_smod_berger07, abstract = {Fictitious Play is the oldest and most studied learning process for games. Since the already classical result for zero-sum games, convergence of beliefs to the set of Nash equilibria has been established for several classes of games, including weighted potential games, supermodular games with diminishing returns, and 3×3 supermodular games. Extending these results, we establish convergence of Continuous-time Fictitious Play for ordinal potential games and quasi-supermodular games with diminishing returns. As a by-product we obtain convergence for 3×m and 4×4 quasi-supermodular games.}, author = {Berger, Ulrich }, citeulike-article-id = {2707909}, doi = {10.1016/j.geb.2006.10.008}, journal = {Games and Economic Behavior}, keywords = {game-theory, mathematics}, month = {August}, number = {2}, pages = {247--261}, posted-at = {2008-04-23 16:18:39}, priority = {4}, title = {Two more classes of games with the continuous-time fictitious play property}, url = {http://dx.doi.org/10.1016/j.geb.2006.10.008}, volume = {60}, year = {2007} }

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TY - JOUR ID - games_eql_fplay_smod_berger07 L3 - citeulike-article-id:2707909 TI - Two more classes of games with the continuous-time fictitious play property JF - Games and Economic Behavior VL - 60 IS - 2 SP - 247 EP - 261 N2 - Fictitious Play is the oldest and most studied learning process for games. Since the already classical result for zero-sum games, convergence of beliefs to the set of Nash equilibria has been established for several classes of games, including weighted potential games, supermodular games with diminishing returns, and 3×3 supermodular games. Extending these results, we establish convergence of Continuous-time Fictitious Play for ordinal potential games and quasi-supermodular games with diminishing returns. As a by-product we obtain convergence for 3×m and 4×4 quasi-supermodular games. KW - game-theory KW - mathematics AU - Berger, Ulrich PY - 2007/08// UR - http://dx.doi.org/10.1016/j.geb.2006.10.008 ER -

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