Model comparison is demonstrated using simulated and real data from a ‘stag-hunt’.

This rests on comparing generative models of choices with, and without, inference. We show it is possible to deduce whether players make inferences about each other and quantify their sophistication on the basis of choices in sequential games. This induces a problem of inferring the opponent's sophistication, given behavioural exchanges. However, if we assume that the degree of recursion is bounded, then players need to estimate the opponent's degree of recursion (i.e., sophistication) to respond optimally. Critically, the joint value functions and ensuing behaviour are optimised recursively, under the assumption that I represent your value function, your representation of mine, your representation of my representation of yours, and so on ad infinitum.

First, we consider the representations of goals in terms of value functions that are prescribed by utility or rewards. We draw on ideas from optimum control and game theory to provide a ‘game theory of mind’. This paper introduces a model of ‘theory of mind’, namely, how we represent the intentions and goals of others to optimise our mutual interactions.

Red button game game theory