An overview of the second-previous memory effect in the strictlyalternating donation game

Abstract

Game theory delves into the examination of strategic behaviour across diverse domains such as insurance, business, military, biology, and more, with the aim of deriving optimal decisions. Recent research focusing on the alteration of memory in the donation game with simultaneous iterated rounds has spurred our interest in investigating this phenomenon within the realm of the strictly alternating donation game. This study proposes a novel decision-making approach, utilizing the pre-previous unit instead of the most recent one. The scope narrows down to 16 employed strategies, each defined by finite two-state automata, while accounting for potential implementation errors in the computation of strategy payoffs. Dominant strategies are determined by assessing the interaction payoffs among strategy pairs. This article centers on the calculation of equilibrium points among heteroclinic three cycles, as there is a lack of a single strategy that is unequivocally dominant. Among the strategy landscapes, S 2 emerges as a standout performer, displaying remarkable stability that surpasses other strategies. Contrariwise, S 14 is the least effective tactic.