Which activation function of cooperation describes human behavior?

TL;DR

This paper introduces a modified activation function for cooperation probability in Prisoner's Dilemma, revealing three behavioral phases that better capture human socio-economic behaviors.

Contribution

It proposes a hyperbolic tangent-based activation function, demonstrating its ability to model distinct phases of cooperation and defection in human-like behavior.

Findings

Three distinct behavioral phases identified based on the scaling parameter a.

Small a leads to random strategy changes and mixed choices.

Medium a results in stable strategies with occasional switches.

Abstract

Properties of cooperation's probability function in Prisoner`s Dilemma have impact on evolution of game. Basic model defines that probability of cooperation depends linearly, both on the player's altruism and the co-player's reputation. I propose modification of activation function to smooth one (hyperbolic tangent with scaling parameter a, which corresponds to its shape) and observe three phases for different range of a. (1) For small a, strategies seem to randomly change in time and situation of mixed choices (one cooperates and second defects) dominate. (2) For medium a, players choose only one strategy for given period of time (the common state can switch to opposite one with some probability). (3) For large a, mixed strategy (once defect, once cooperate) is coexisting with common strategies and no change is allowed. I believe that proposed function characterizes better socio-economical phenomena and especially phase 1 and 2 contain most of human behavior.