Abstract
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.
Highlights
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
A utility function basic to game theory was shown to be dependent on current wealth as a conditional variable in a dynamic version of utility theory
Summary
We explain the derivation of the dynamic utility function[30,31]. Let time t = 0, ..., T (final time) and suppose that wt and rt are wealth at t and the growth rate at t, respectively. The dynamic utility function (Eq (5)) is translated into the function of gain, g (decision variable), given current wealth w (state variable), as follows:. When V ≥C, the optimal mix strategy (p* < 1) differs from the traditional hawk-dove game (porg* = 1) (Fig. 1b). The average payoffs of EH and ED at p = 0.5 are plotted against current wealth, w, when V ≥C (Fig. 1d) and V
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