Preprint Article Version 1 This version is not peer-reviewed

Iterated Economic Games, Logic Gates, and the Flow of Shared Information in Strategic Interactions

Version 1 : Received: 28 February 2017 / Approved: 1 March 2017 / Online: 1 March 2017 (09:26:28 CET)

A peer-reviewed article of this Preprint also exists.

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

Journal reference: Entropy 2017, 19, 201
DOI: 10.3390/e19050201

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 these expressions can be simplified. 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'.

Subject Areas

information theory; transfer entropy; game theory; logic gates; multilayer perceptrons; strategic behaviour; decision theory

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