{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:25:33Z","timestamp":1772252733302,"version":"3.50.1"},"reference-count":56,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2017,4,29]],"date-time":"2017-04-29T00:00:00Z","timestamp":1493424000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2019s next action by introducing two new classes of games: \u201cinvertible games\u201d and \u201ccyclical games\u201d. 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\u2019s Dilemma game and the Prisoner\u2019s Dilemma game, the Prisoner\u2019s Dilemma being invertible, to illustrate their use. In the Prisoner\u2019s Dilemma, a novel connection is made between the computational principles of logic gates and both the structure of games and the agents\u2019 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: \u201cTit-for-Tat\u201d and \u201cWin-Stay, Lose-Switch\u201d.<\/jats:p>","DOI":"10.3390\/e19050201","type":"journal-article","created":{"date-parts":[[2017,5,2]],"date-time":"2017-05-02T11:37:20Z","timestamp":1493725040000},"page":"201","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Utility, Revealed Preferences Theory, and Strategic Ambiguity in Iterated Games"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2199-2515","authenticated-orcid":false,"given":"Michael","family":"Harr\u00e9","sequence":"first","affiliation":[{"name":"Complex Systems Research Group, Faculty of Engineering and Information Technologies, The University of Sydney, Sydney NSW 2006, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,29]]},"reference":[{"key":"ref_1","unstructured":"Von Neumann, J., and Morgenstern, O. 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