Terrorist's attack has become a severe challenge for human society. Both terrorists and government anti-terrorist force possess the obvious characteristics of scenario-dependent decision and irrational emotion decision. For example, the player with the optimistic emotion usually overestimates the probability of the event, and the player with the pessimistic emotion usually underestimates the probability of the event. Obviously, it has important influence on the optimal decision and equilibrium results. In this paper, the Rank-Dependent Expected Utility model of terrorists and government anti-terrorist force is proposed. The Rank-Dependent Expected Utility can be expressed as V(X,u,ω)=π(x_i)u(x_i), where p_i is the objective probability of the event x_i, p_i∈[0,1], the emotion function ω(p_i)=p_i^r is the subjective probability function of affected by the emotion. When r_i > 1 means the pessimistic emotion, 0 < r_i < 1 means the optimistic emotion, and r_i=1 means no emotion. The weight function is defined as π(x_i)=ω(p₁+p₂+…+p_i)-ω(p₁+p₂+…+p_i-1), and u(x_i) is the traditional on Von Neumann-Morgenstern Expected Utility.
And then, the effect of emotion on the equilibrium outcomes of the traditional government-terrorist game model is discussed, where governmental anti-terrorist force or terrorist has an optimistic or pessimistic expectation on the subjective probability about terror attack. Taken by the method of case analysis, the special scenario that both two parties have an optimistic or pessimistic emotion based on Xinjiang 6.28 terrorist incident in Moyu County is further discussed. Lastly, the paper discusses the management meaning on improving anti-terrorist strategy.
The results show that when any one player has an optimistic or pessimistic expectation, the opponent without any emotion should adjust his/her equilibrium probability. That is to say, any party's emotion should influence the opponent's strategy selection. When both two parties have the emotional factor, the terrorist with optimistic expectation should be more inclined to take excessive risk, which causes the equilibrium outcome has the more uncertainty.
The paper's results are useful for the anti-terrorism and emergency plans. First, the government should avoid the short-sighted optimism in order to reduce the unnecessary loss. Second, the government should come to a more serious appraisal of the situation and think of more difficulties, because a stronger defense can banish every attack thought. Third, the government should strengthen the intelligence collecting and information analysis. Thus, anti-terrorism need to strengthen intelligence for accurately judging terrorist's psychological states.