Research On Risk-Sensitive Group Decision Theoretic Planning Based On One-Switch Utility Function And MDP

Emergency decision is a kind of decision to deal with unconventional emergencies.Unconventional emergencies may bring major losses to the society and the national, soemergency decision is a kind of decision that is related to national security and stability.Because the evolution of the unconventional emergencies is a dynamic, uncertain andcontinuous process, emergency decision is also a multi-stage decision process foruncertain problems. At the same time, because there is huge risk when emergencydecision makers face unconventional emergencies, emergency decision is risk sensitivedecision. Decision makers will bring their risk attitude into their choose in the decisionmaking process, and emergency decision maker’s risk attitude change with their wealthlevel.One-switch utility function is a kind of utility function that is used to describe howthe risk attitude of a decision maker changes with his wealth level. In this paper,one-switch utility function is used to describe the risk attitude of decision makers, andgroup utility addition and multiplication model are used to aggregate personal utility.Based on Markov decision processes, a dynamic, multi-stages and risk sensitive groupdecision model is proposed. In the model wealth level is introduced into the state ofMDP, and the optimal policy is defined as an optimal action sequence under different(state, wealth interval) pairs. According to the non-decomposable problem of decisiontheoretic planning which is caused by nonlinear utility function, a backward-inductionmethod is given to divide the wealth interval and solve the optimal action sequenceunder different (state, wealth interval) pairs. Numerical analysis shows that the proposedmodel and algorithm can effectively solve the dynamic decision problem when the riskattitudes of decision makers change with wealth level, and the risk attitude of decisionmakers has a great effect on group decision making.