###
3rd International Symposium
on

Imprecise
Probabilities and Their Applications

ISIPTA '03

#####
University of Lugano

Lugano, Switzerland

14-17 July 2003

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ELECTRONIC PROCEEDINGS

# Game-Theoretic Learning Using the Imprecise Dirichlet Model

### 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. ** game theory, fictitious play, equilibria, imprecise Dirichlet model, learning

**Paper Download **

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** Authors addresses: **

Erik Quaeghebeur

research group SYSTeMS

Technologiepark - Zwijnaarde 914

B-9052 Zwijnaarde

Gert de Cooman

Universiteit Gent

Onderzoeksgroep SYSTeMS

Technologiepark - Zwijnaarde 9

9052 Zwijnaarde

Belgium

** E-mail addresses: **

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