What Is True Halving in the Payoff Matrix of Game Theory?

Katsumata

Hasegawa

et al. 2017

Sci Rep

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The evolution of cooperative behavior is one of the most important issues in game theory. Previous studies have shown that cooperation can evolve only under highly limited conditions, and various modifications have been introduced to games to explain the evolution of cooperation. Recently, a utility function basic to game theory was shown to be dependent on current wealth as a conditional (state) variable in a dynamic version of utility theory. Here, we introduce this dynamic utility function to several games. Under certain conditions, poor players exhibit cooperative behavior in two types of chicken games (the hawk-dove game and the snowdrift game) but not in the prisoner’s dilemma game and the stag hunt game. This result indicates that cooperation can be exhibited by the poor in some chicken games. Thus, the evolution of cooperation may not be as limited as has been suggested in previous studies.

mentioning

confidence: 99%

The promotion of cooperation by the poor in dynamic chicken games

Katsumata

Hasegawa

et al. 2017

Sci Rep

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“…We assume that the pay-off (utility) matrix depends on the player's current state, but more realistically, we can expect that the pay-off matrix also depends on the current state of opponent [ 24 , 26 ]. We also currently assume that r t are independent, identically distributed random variables (i.e.…”

Section: Discussionmentioning

confidence: 99%

“…The concept of the DUF is a possible alternative framework to the five reciprocity protocols elucidated by Nowak, leading to the evolution of mutual cooperation. More importantly, any games played by human and animal societies are dynamic [ 17 , 24 ]. Therefore, the current DUF should apply to any game in any society.…”

Section: Discussionmentioning

confidence: 99%

“…Note that the value of g satisfies − w < g . This analytical solution demonstrates that the utility function depends on the current gain (decision variable) and the current wealth status (state variable) at the time of decision making, as in dynamic programming [ 17 – 24 ]. These properties show that cooperative behaviour evolves with the introduction of a DUF that accommodates the current wealth condition of individuals (decision makers) without the known five reciprocity mechanisms.…”

Section: Introductionmentioning

confidence: 99%

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

Tanimoto

2020

R. Soc. open sci.

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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.

“…Namely, in this model, the amount of food intake is assumed to be equal to the fitness gain of an individual. However, both the expected utility theory (Caraco, ; Caraco et al, ; Real, , ) and dynamic utility theory (Ito, Katsumata, Hasegawa, & Yoshimura, , ; Yoshimura et al, ; Yoshimura, Ito, Miller III, & Tainaka, ) suggest that fitness consequences are not linearly associated with food intake. The introduction of utility functions (either static or dynamic) further complicates the calculations and analyses.…”

Section: Discussionmentioning

confidence: 99%

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

2019

Ecological Research

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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.