Game Theory of Mind

Abstract

This paper introduces a model of ‘theory of mind’, namely, how we represent the intentions and goals of others to optimise our mutual interactions. We draw on ideas from optimum control and game theory to provide a ‘game theory of mind’. First, we consider the representations of goals in terms of value functions that are prescribed by utility or rewards. 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. 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. This induces a problem of inferring the opponent's sophistication, given behavioural exchanges. 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 rests on comparing generative models of choices with, and without, inference. Model comparison is demonstrated using simulated and real data from a ‘stag-hunt’. Finally, we note that exactly the same sophisticated behaviour can be achieved by optimising the utility function itself (through prosocial utility), producing unsophisticated but apparently altruistic agents. This may be relevant ethologically in hierarchal game theory and coevolution.

Harm to others outweighs harm to self in moral decision making

“…Instead, we must rely on our best estimates of others' beliefs and preferences to guide social decision making (21,43) and tread carefully when their fate rests in our hands. Here, we provide evidence for an apparently hyperaltruistic valuation of others' pain that is associated with slower choices when making decisions that affect others.…”

Vasopressin increases human risky cooperative behavior

“…Our experiments delineated AVP's role in mutually beneficial cooperation in an environment where altruistic concerns, reputation building, and strategically learning the partner's intentions and beliefs did not play a role (35,36). Most importantly, AVP did not change behavior in the social preferences control task, which rules out AVP working purely through increased altruistic one-sided prosociality.…”

“…However, previous work has shown that AVP administration increased cooperation following a cooperative gesture by one's partner in a repeated prisoner's dilemma (37), where cooperation might be mutually beneficial (38)-in line with the interdependent hypothesis (5). We believe that further investigation of AVP's role in social behavior would benefit from using computational theories that distinguish the different mechanism through which AVP may foster cooperative behavior in repeated interactions (35), particularly belief inference (33,36,39) and inferential limits in disorder (40).…”

Optimal control as a graphical model inference problem

“…It is argued that these two possible outcomes makes the game socially more interesting, than for example the prisoners dilemma, which has only one Nash equilibrium. The stag hunt allows for the study of cooperation within social structures (Skyrms 1996) and for studying the collaborative behavior of multi-agent systems (Yoshida et al 2008).…”