Dynamic decision-making in uncertain environments I. The principle of dynamic utility

Miller

et al. 2013

J Ethol

Self Cite

In both animal and human behavioral repertoires, classical expected utility theory is considered a fundamental element of decision making under conditions of uncertainty. This theory has been widely applied to problems of animal behavior and evolutionary game theory, as well as to human economic behavior. The Allais paradox hinges on the expression of avoidance of bankruptcy by humans, or death by starvation in animals. This paradox reveals that human behavioral patterns are often inconsistent with predictions under the classical expected utility theory as formulated by von Neumann and Morgenstern. None of the many attempts to reformulate utility theory has been entirely successful in resolving this paradox with rigorous logic. We present a simple, but novel approach to the theory of decision making, in which utility is dependent on current wealth, and in which losses are more heavily weighted than gains. Our approach resolves the Allais paradox in a manner that is consistent with how humans formulate decisions under uncertainty. Our results indicate that animals, including humans, are in principle risk-averse. Our restructuring of dynamic utility theory presents a basic optimization scheme for sequential or dynamic decisions in both animals and humans.

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic decision-making in uncertain environments II. Allais paradox in human behavior

Yoshimura

Miller

et al. 2013

J Ethol

Self Cite

“…Because dynamic utility theory optimizes Markov chains (stochastic processes) as a form of sequential decision making, it maximizes the geometric mean of multiplicative growth rates [ 20 ]. The DUF is derived as follows [ 21 , 22 ]. Let time t = 0, … , T (final time), and let w t and r t represent wealth and the growth rate, respectively, at time t .…”

Section: Introductionmentioning

confidence: 99%

Dynamic utility: the sixth reciprocity mechanism for the evolution of cooperation

Tanimoto

2020

R. Soc. open sci.

Self Cite

Game theory has been extensively applied to elucidate the evolutionary mechanism of cooperative behaviour. Dilemmas in game theory are important elements that disturb the promotion of cooperation. An important question is how to escape from dilemmas. Recently, a dynamic utility function (DUF) that considers an individual's current status (wealth) and that can be applied to game theory was developed. The DUF is different from the famous five reciprocity mechanisms called Nowak's five rules. Under the DUF, cooperation is promoted by poor players in the chicken game, with no changes in the prisoner's dilemma and stag-hunt games. In this paper, by comparing the strengths of the two dilemmas, we show that the DUF is a novel reciprocity mechanism (sixth rule) that differs from Nowak's five rules. We also show the difference in dilemma relaxation between dynamic game theory and (traditional) static game theory when the DUF and one of the five rules are combined. Our results indicate that poor players unequivocally promote cooperation in any dynamic game. Unlike conventional rules that have to be brought into game settings, this sixth rule is universally (canonical form) applicable to any game because all repeated/evolutionary games are dynamic in principle.

“…Much previous work has indicated that “risk‐averse” behaviors are common in nature and theory (Stephens et al, ; Stephens & Krebs, ; Yoshimura, Ito, Miller III, & Tainaka, ; Zhang, Brennan, & Lo, ). In our previous model of risk‐sensitive foraging, we found a preference for a “risk‐prone” strategy when the foraging time is longer than optimal foraging time that maximizes the arithmetic mean fitness ( x A * ) (Ito, Uehara, Morita, Tainaka, & Yoshimura, ).…”

Section: Introductionmentioning

confidence: 99%

Risk sensitivity of a forager with limited energy reserves in stochastic environments

2019

Ecological Research

Self Cite

Long‐term environmental stochasticity is known to affect the adaptive evolution of life history traits. In stochastic environments, there are two different levels of behavioral optimization, as follows: Level 1, the optimal strategy under an intrageneration stochastic environment and Level 2, the optimal strategy under an intergeneration stochastic environment. This article presents a simple optimal foraging model under predation risks and verified the effect of behavioral optimization on the foraging time ratio. In this model, foragers are exposed to predation risks during foraging but are safe if they stay in their nests without any food. The foraging time allocation strategies that optimize the geometric mean fitness (Level 2) were compared with the arithmetic mean fitness (Level 1) to verify the effects of intergenerational stochasticity, whereby there is an alternation in good/bad environments across generations. As in previous studies, risk‐averse strategies (a shorter foraging time is adopted for Level 2 than for Level 1) were commonly observed using this model. Unexpectedly, the model showed a tendency toward a preference for risk‐prone strategies. This qualitative difference became prominent when food was abundant and the maximum energy reserves were small. Theoretical studies have shown that risk‐averse strategies are commonly adopted during food shortages and result in starvation. However, the current results indicate that risk‐prone strategies may become optimal under a limited reserve capacity. Thus, the optimal strategy depends not only on the individual status and environmental conditions, but also on the detailed selection regimes.