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Game-theoretic learning using the imprecise Dirichlet model

Erik Quaeghebeur (UGent) and Gert De Cooman (UGent)
(2003) Proceedings in Informatics. 18. p.452-466
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Abstract
We discuss two approaches for choosing a strategy in a two-player game. We suppose that the game is played a large number of rounds, which allows the players to use observations of past play to guide them in choosing a strategy. Central in these approaches is the way the opponent's next strategy is assessed; both a precise and an imprecise Dirichlet model are used. The observations of the opponent's past strategies can then be used to update the model and obtain new assessments. To some extent, the imprecise probability approach allows us to avoid making arbitrary initial assessments. To be able to choose a strategy, the assessment of the opponent's strategy is combined with rules for selecting an optimal response to it: a so-called best response or a maximin strategy. Together with the updating procedure, this allows us to choose strategies for all the rounds of the game. The resulting playing sequence can then be analysed to investigate if the strategy choices can converge to equilibria.
Keywords
imprecise Dirichlet model, game theory, fictitious play, learning, equilibria

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Citation

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Chicago
Quaeghebeur, Erik, and Gert De Cooman. 2003. “Game-theoretic Learning Using the Imprecise Dirichlet Model.” In Proceedings in Informatics, ed. Jean-Marc Bernard, Teddy Seidenfeld, and Marco Zaffalon, 18:452–466. Carleton Scientific.
APA
Quaeghebeur, E., & De Cooman, G. (2003). Game-theoretic learning using the imprecise Dirichlet model. In J.-M. Bernard, T. Seidenfeld, & M. Zaffalon (Eds.), Proceedings in Informatics (Vol. 18, pp. 452–466). Presented at the 3rd International symposium on Imprecise Probabilities and Their Applications (ISIPTA  ’03), Carleton Scientific.
Vancouver
1.
Quaeghebeur E, De Cooman G. Game-theoretic learning using the imprecise Dirichlet model. In: Bernard J-M, Seidenfeld T, Zaffalon M, editors. Proceedings in Informatics. Carleton Scientific; 2003. p. 452–66.
MLA
Quaeghebeur, Erik, and Gert De Cooman. “Game-theoretic Learning Using the Imprecise Dirichlet Model.” Proceedings in Informatics. Ed. Jean-Marc Bernard, Teddy Seidenfeld, & Marco Zaffalon. Vol. 18. Carleton Scientific, 2003. 452–466. Print.
@inproceedings{213482,
  abstract     = {We discuss two approaches for choosing a strategy in a two-player game. We suppose that the game is played a large number of rounds, which allows the players to use observations of past play to guide them in choosing a strategy.
Central in these approaches is the way the opponent's next strategy is assessed; both a precise and an imprecise Dirichlet model are used. The observations of the opponent's past strategies can then be used to update the model and obtain new assessments. To some extent, the imprecise probability approach allows us to avoid making arbitrary initial assessments.
To be able to choose a strategy, the assessment of the opponent's strategy is combined with rules for selecting an optimal response to it: a so-called best response or a maximin strategy. Together with the updating procedure, this allows us to choose strategies for all the rounds of the game.
The resulting playing sequence can then be analysed to investigate if the strategy choices can converge to equilibria.},
  author       = {Quaeghebeur, Erik and De Cooman, Gert},
  booktitle    = {Proceedings in Informatics},
  editor       = {Bernard, Jean-Marc and Seidenfeld, Teddy and Zaffalon, Marco},
  isbn         = {9781894145176},
  keyword      = {imprecise Dirichlet model,game theory,fictitious play,learning,equilibria},
  language     = {eng},
  location     = {Lugano, Switzerland},
  pages        = {452--466},
  publisher    = {Carleton Scientific},
  title        = {Game-theoretic learning using the imprecise Dirichlet model},
  volume       = {18},
  year         = {2003},
}