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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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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.
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.
Chicago author-date
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.
Chicago author-date (all authors)
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.
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.
IEEE
[1]
E. Quaeghebeur and G. De Cooman, “Learning in games using the imprecise Dirichlet model,” International Journal of Approximate Reasoning, vol. 50, no. 2, pp. 243–256, 2009.
@article{495971,
  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.}},
  author       = {{Quaeghebeur, Erik and De Cooman, Gert}},
  editor       = {{Bernard, Jean-Marc}},
  issn         = {{0888-613X}},
  journal      = {{International Journal of Approximate Reasoning}},
  keywords     = {{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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