### 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.

Original language | English |
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Title of host publication | Proceedings of the third international symposium on imprecise probabilities and their applications |

Editors | Jean-Marc Bernard, Teddy Seidenfeld, Marco Zaffalon |

Place of Publication | Canada |

Publisher | Carleton Scientific, Canada |

Pages | 452-466 |

ISBN (Print) | 9781894145176 |

Publication status | Published - 2003 |

Externally published | Yes |

Event | 3rd International symposium on Imprecise Probabilities and Their Applications - University of Lugano, Lugano, Switzerland Duration: 14 Jul 2003 → 17 Jul 2003 http://www.sipta.org/isipta03/ |

### Publication series

Name | Proceedings in Informatics |
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Publisher | Carleton Scientific |

Volume | 18 |

### Conference

Conference | 3rd International symposium on Imprecise Probabilities and Their Applications |
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Abbreviated title | ISIPTA '03 |

Country | Switzerland |

City | Lugano |

Period | 14/07/03 → 17/07/03 |

Internet address |

## Cite this

Quaeghebeur, E., & de Cooman, G. (2003). Game-theoretic learning using the imprecise Dirichlet model. In J-M. Bernard, T. Seidenfeld, & M. Zaffalon (Eds.),

*Proceedings of the third international symposium on imprecise probabilities and their applications*(pp. 452-466). (Proceedings in Informatics; Vol. 18). Carleton Scientific, Canada. http://www.sipta.org/isipta03/proc/019.html