Evolutionary dynamics under combined regret-based learning and random exploration

Zhu, Mengfan and Xu, Jianhua and Chen, Xiaojie and Szolnoki, Attila (2026) Evolutionary dynamics under combined regret-based learning and random exploration. CHAOS SOLITONS & FRACTALS, 208 (4). ISSN 0960-0779 (Unpublished)

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Abstract

Individual decisions in population games are often grounded on various motivations, including regret-based learning or random exploration of the strategy space. Despite the intensively growing interest in these microscopic rules, their simultaneous consequences on strategic behaviors remain largely unexplored. Motivated by this shortage, here we propose a novel protocol that combines regret-based learning and random exploration into a general two-player, two-strategy game between individuals and their neighbors arranged in a network. During the evolutionary process, agents randomly explore alternative strategies with a certain probability or employ regret-based learning using a Boltzmann-type regret function. We derive an analytical condition under which a strategy can prevail and find that the condition depends solely on the game parameters, and is independent of the regret function, random exploration rate, and network structure under weak regret strength. On the other hand, the chance of a random exploration weakens the evolutionary advantage of the dominant strategy and enhances the fitness of the less-favored one. Furthermore, we reveal through computer simulations that increasing the regret strength enhances the position of more dominant strategy, while the evolutionary chances is suppressed when it is not favored.

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