Non‐Parametric Bayesian Inference of Strategies in Repeated Games

18 Pages Posted: 3 Oct 2018

See all articles by Max Kleiman-Weiner

Max Kleiman-Weiner

Massachusetts Institute of Technology (MIT)

Joshua B. Tenenbaum

Massachusetts Institute of Technology (MIT) - Department of Brain and Cognitive Sciences

Penghui Zhou

Massachusetts Institute of Technology (MIT) - Department of Economics

Date Written: October 2018

Abstract

Inferring underlying cooperative and competitive strategies from human behaviour in repeated games is important for accurately characterizing human behaviour and understanding how people reason strategically. Finite automata, a bounded model of computation, have been extensively used to compactly represent strategies for these games and are a standard tool in game theoretic analyses. However, inference over these strategies in repeated games is challenging since the number of possible strategies grows exponentially with the number of repetitions yet behavioural data are often sparse and noisy. As a result, previous approaches start by specifying a finite hypothesis space of automata that does not allow for flexibility. This limitation hinders the discovery of novel strategies that may be used by humans but are not anticipated a priori by current theory. Here we present a new probabilistic model for strategy inference in repeated games by exploiting non‐parametric Bayesian modelling. With simulated data, we show that the model is effective at inferring the true strategy rapidly and from limited data, which leads to accurate predictions of future behaviour. When applied to experimental data of human behaviour in a repeated prisoner's dilemma, we uncover strategies of varying complexity and diversity.

Keywords: Bayesian inference, Computational economics, Finite‐state automata, Non‐parametric inference, Repeated games

Suggested Citation

Kleiman-Weiner, Max and Tenenbaum, Joshua B. and Zhou, Penghui, Non‐Parametric Bayesian Inference of Strategies in Repeated Games (October 2018). The Econometrics Journal, Vol. 21, Issue 3, pp. 298-315, 2018, Available at SSRN: https://ssrn.com/abstract=3259469 or http://dx.doi.org/10.1111/ectj.12112

Max Kleiman-Weiner (Contact Author)

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Joshua B. Tenenbaum

Massachusetts Institute of Technology (MIT) - Department of Brain and Cognitive Sciences ( email )

43 Vassar Street
Cambridge, MA 02139
United States

Penghui Zhou

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
E52-391
Cambridge, MA 02142
United States

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