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Entropy 2017, 19(5), 201; doi:10.3390/e19050201

Utility, Revealed Preferences Theory, and Strategic Ambiguity in Iterated Games

Complex Systems Research Group, Faculty of Engineering and Information Technologies, The University of Sydney, Sydney NSW 2006, Australia
Academic Editors: Mikhail Prokopenko and Kevin Knuth
Received: 28 February 2017 / Revised: 10 April 2017 / Accepted: 26 April 2017 / Published: 29 April 2017
(This article belongs to the Special Issue Complexity, Criticality and Computation (C³))
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Abstract

Iterated games, in which the same economic interaction is repeatedly played between the same agents, are an important framework for understanding the effectiveness of strategic choices over time. To date, very little work has applied information theory to the information sets used by agents in order to decide what action to take next in such strategic situations. This article looks at the mutual information between previous game states and an agent’s next action by introducing two new classes of games: “invertible games” and “cyclical games”. By explicitly expanding out the mutual information between past states and the next action we show under what circumstances the explicit values of the utility are irrelevant for iterated games and this is then related to revealed preferences theory of classical economics. These information measures are then applied to the Traveler’s Dilemma game and the Prisoner’s Dilemma game, the Prisoner’s Dilemma being invertible, to illustrate their use. In the Prisoner’s Dilemma, a novel connection is made between the computational principles of logic gates and both the structure of games and the agents’ decision strategies. This approach is applied to the cyclical game Matching Pennies to analyse the foundations of a behavioural ambiguity between two well studied strategies: “Tit-for-Tat” and “Win-Stay, Lose-Switch”. View Full-Text
Keywords: information theory; transfer entropy; game theory; logic gates; multilayer perceptrons; strategic behaviour; decision theory information theory; transfer entropy; game theory; logic gates; multilayer perceptrons; strategic behaviour; decision theory
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Harré, M. Utility, Revealed Preferences Theory, and Strategic Ambiguity in Iterated Games. Entropy 2017, 19, 201.

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