Incorporating Ignorance within Game Theory: An Imprecise Probability Approach
Citation:
Bernard Fares and Mimi Zhang, Incorporating Ignorance within Game Theory: An Imprecise Probability Approach, International Journal of Approximate Reasoning, 154, March, 2023, 133 - 148Download Item:
FaresB_Incorporating Ignorance within Game Theory.pdf (Accepted for publication (author's copy) - Peer Reviewed) 1.570Mb
Abstract:
Ignorance within non-cooperative games, reflected as a player’s uncertain prefer-
ences towards a game’s outcome, is examined from a Bayesian point of view. This topic
has had scarce treatment in the literature, which emphasises exogenous uncertainties
caused by other players or nature and not by players themselves. That is primarily
because a player’s endogenous uncertainty over an outcome poses significant challenges
and complex sequences of reciprocal expectations. Therefore, it is often ignored, and
preferences are either assumed from a continuous domain or set using introspection,
resulting in non-optimal models. We here explore a solution concept based on recent
research in imprecise probabilities and de Finetti’s approach to defining subjective
probabilities, which utilises bets to assess beliefs. The resulting model allows players
to be ignorant about their initial preferences and learn about them in repeated games.
Furthermore, it permits improving the value of information in these situations. This
model is proposed as a possible solution to the problem of utility inference in game-
theoretic settings that include uncertainty over outcomes. We demonstrate it through
motivating repeated-game problems modified to have uncertainty and through a sim-
ulation over a case of extreme ignorance.
Author's Homepage:
http://people.tcd.ie/zhangm3Description:
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Author: Zhang, Mimi
Type of material:
Journal ArticleCollections:
Series/Report no:
International Journal of Approximate Reasoning154
March
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Full text availableKeywords:
Game theory, Imprecise probability, Uncertain utility, NonparametricsLicences: