Mathematical description and analysis of adaptive risk choice behavior

ACM Transactions on Intelligent Systems and Technology , 14(1), 17:1--17:21,2013(1)

Isamu Okada, Hitoshi Yamamoto


Which risk should one choose when facing alternatives with different levels of risk? We discuss here adaptive processes in such risk choice behavior by generalizing the study of Roos et al. [2010]. We deal with an n-choice game in which every player sequentially chooses n times of lotteries of which there are two types: a safe lottery and a risky lottery. We analyze this model in more detail by elaborating the game. Based on the results of mathematical analysis, replicator dynamics analysis, and numerical simulations, we derived some salient features of risk choice behavior. We show that all the risk strategies can be divided into two groups: persistence and nonpersistence. We also proved that the dynamics with perturbation in which a mutation is installed is globally asymptotically stable to a unique equilibrium point for any initial population. The numerical simulations clarify that the number of persistent strategies seldom increases regardless of the increase in n, and suggest that a rarity of dominant choice strategies is widely observed in many social contexts. These facts not only go hand-in-hand with some well-known insights from prospect theory, but may also provide some theoretical hypotheses for various fields such as behavioral economics, ecology, sociology, and consumer behavioral theory.

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