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Learning in games using the imprecise Dirichlet model

Erik Quaeghebeur (UGent) and Gert De Cooman (UGent)
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Abstract
We propose a new learning model for finite strategic-form two-player games based on fictitious play and Walley’s imprecise Dirichlet model [P. Walley, Inferences from multinomial data: learning about a bag of marbles, J. Roy. Statist. Soc. B 58 (1996) 3–57]. This model allows the initial beliefs of the players about their opponent’s strategy choice to be near-vacuous or imprecise instead of being precisely defined. A similar generalization can be made as the one proposed by Fudenberg and Kreps [D. Fudenberg, D.M. Kreps, Learning mixed equilibria, Games Econ. Behav. 5 (1993) 320–367] for fictitious play, where assumptions about immediate behavior are replaced with assumptions about asymptotic behavior. We also obtain similar convergence results for this generalization: if there is convergence, it will be to an equilibrium.
Keywords
Fictitious play, Imprecise probability models, Imprecise Dirichlet model, Decision making, Two-player games, Learning

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Chicago
Quaeghebeur, Erik, and Gert De Cooman. 2009. “Learning in Games Using the Imprecise Dirichlet Model.” Ed. Jean-Marc Bernard. International Journal of Approximate Reasoning 50 (2): 243–256.
APA
Quaeghebeur, E., & De Cooman, G. (2009). Learning in games using the imprecise Dirichlet model. (J.-M. Bernard, Ed.)International Journal of Approximate Reasoning, 50(2), 243–256.
Vancouver
1.
Quaeghebeur E, De Cooman G. Learning in games using the imprecise Dirichlet model. Bernard J-M, editor. International Journal of Approximate Reasoning. New York ; UNITED STATES: ELSEVIER SCIENCE INC; 2009;50(2):243–56.
MLA
Quaeghebeur, Erik, and Gert De Cooman. “Learning in Games Using the Imprecise Dirichlet Model.” Ed. Jean-Marc Bernard. International Journal of Approximate Reasoning 50.2 (2009): 243–256. Print.
@article{495971,
  abstract     = {We propose a new learning model for finite strategic-form two-player games based on fictitious play and Walley{\textquoteright}s imprecise Dirichlet model [P. Walley, Inferences from multinomial data: learning about a bag of marbles, J. Roy. Statist. Soc. B 58 (1996) 3--57]. This model allows the initial beliefs of the players about their opponent{\textquoteright}s strategy choice to be near-vacuous or imprecise instead of being precisely de\unmatched{fb01}ned. A similar generalization can be made as the one proposed by Fudenberg and Kreps [D. Fudenberg, D.M. Kreps, Learning mixed equilibria, Games Econ. Behav. 5 (1993) 320--367] for fictitious play, where assumptions about immediate behavior are replaced with assumptions about asymptotic behavior. We also obtain similar convergence results for this generalization: if there is convergence, it will be to an equilibrium.},
  author       = {Quaeghebeur, Erik and De Cooman, Gert},
  editor       = {Bernard, Jean-Marc},
  issn         = {0888-613X},
  journal      = {International Journal of Approximate Reasoning},
  keyword      = {Fictitious play,Imprecise probability models,Imprecise Dirichlet model,Decision making,Two-player games,Learning},
  language     = {eng},
  number       = {2},
  pages        = {243--256},
  publisher    = {ELSEVIER SCIENCE INC},
  title        = {Learning in games using the imprecise Dirichlet model},
  url          = {http://dx.doi.org/10.1016/j.ijar.2008.03.012},
  volume       = {50},
  year         = {2009},
}

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