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Utility proportional beliefs

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Abstract

In game theory, basic solution concepts often conflict with experimental findings or intuitive reasoning. This fact is possibly due to the requirement that zero probability is assigned to irrational choices in these concepts. Here, we introduce the epistemic notion of common belief in utility proportional beliefs which also attributes positive probability to irrational choices, restricted however by the natural postulate that the probabilities should be proportional to the utilities the respective choices generate. Besides, we propose a procedural characterization of our epistemic concept. With regards to experimental findings common belief in utility proportional beliefs fares well in explaining observed behavior.

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Notes

  1. A type’s belief function projected on some opponent’s type space or projected on the set of opponents’ choice combinations are examples for projected belief functions.

  2. Given a game \(\varGamma \) and a player \(i \in I\), a randomized choice for \(i\) is a probability distribution \(\sigma _i \in \varDelta (C_i)\) on \(i\)’s choice space.

  3. Given some set \(W\) a lexicographic belief is a finite sequence \(\rho =(\rho ^1,\rho ^2,\ldots ,\rho ^K)\) of probability distributions such that \(\rho ^k \in \varDelta (W)\) for all \(k \in \{1,2,\ldots ,K\}\).

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Acknowledgments

We are grateful to conference participants at the Eleventh Conference of the Society for the Advancement of Economic Theory (SAET2011) as well as to seminar participants at Maastricht University, City University of New York (CUNY), and University of Helsinki for useful and constructive comments. Besides, valuable remarks by two anonymous referees are highly appreciated.

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Authors and Affiliations

  1. Department of Quantitative Economics, School of Business and Economics, Maastricht University, 6200 MD , Maastricht, The Netherlands

    Christian W. Bach & Andrés Perea

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  1. Christian W. Bach
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  2. Andrés Perea
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Correspondence to Andrés Perea.

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Bach, C.W., Perea, A. Utility proportional beliefs. Int J Game Theory 43, 881–902 (2014). https://doi.org/10.1007/s00182-013-0409-3

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  • DOI: https://doi.org/10.1007/s00182-013-0409-3

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