Risk‐Sensitive Multiagent Decision‐Theoretic Planning Based on MDP and One‐Switch Utility Functions

Abstract

In high stakes situations decision‐makers are often risk‐averse and decision‐making processes often take place in group settings. This paper studies multiagent decision‐theoretic planning under Markov decision processes (MDPs) framework with considering the change of agent’s risk attitude as his wealth level varies. Based on one‐switch utility function that describes agent’s risk attitude change with his wealth level, we give the additive and multiplicative aggregation models of group utility and adopt maximizing expected group utility as planning objective. When the wealth level approaches infinity, the characteristics of optimal policy are analyzed for the additive and multiplicative aggregation model, respectively. Then a backward‐induction method is proposed to divide the wealth level interval from negative infinity to initial wealth level into subintervals and determine the optimal policy in states and subintervals. The proposed method is illustrated by numerical examples and the influences of agent’s risk aversion parameters and weights on group decision‐making are also analyzed.

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