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. 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

Agent Modeling in Antiair Defense

. This research addresses rational decision making and coordination among antiair units whose mission is to defend a specified territory from a number of attacking missiles. The automated units have to decide which missiles to attempt to intercept, given the characteristics of the threat, and given the other units' anticipated actions, in their attempt to minimize the expected overall damages to the defended territory. Thus, an automated defense unit needs to model the other agents, either human or automated, that control the other defense batteries. For the purpose of this case study, we assume that the units cannot communicate among themselves, say, due to an imposed radio silence. We use the Recursive Modeling Method (RMM), which enables an agent to select his rational action by examining the expected utility of his alternative behaviors, and to coordinate with other agents by modeling their decision making in a distributed multiagent environment. We describe how decision making usi..