The Evolution of Cooperation and Diversity under Integrated Indirect Reciprocity

Tatsuya Sasaki (), Satoshi Uchida, Isamu Okada and Hitoshi Yamamoto
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Tatsuya Sasaki: Department of Community Development, Koriyama Women’s College, Fukushima 963-8503, Japan
Satoshi Uchida: Research Center for Ethi-Culture Studies, RINRI Institute, Tokyo 102-8561, Japan
Isamu Okada: Department of Business Administration, Soka University, Tokyo 192-8577, Japan
Hitoshi Yamamoto: Faculty of Business Administration, Rissho University, Tokyo 141-8602, Japan

Games, 2024, vol. 15, issue 2, 1-16

Abstract: Indirect reciprocity is one of the major mechanisms driving the evolution of cooperation in human societies. There are two types of indirect reciprocity: upstream and downstream reciprocity. Cooperation in downstream reciprocity follows the pattern ‘You helped someone, and I will help you’, while the direction of cooperation is reversed in upstream reciprocity, which follows the pattern ‘You helped me, and I will help someone else’. These two types of indirect reciprocity often occur in combination. However, upstream and downstream reciprocity have mostly been theoretically studied in isolation. In this study, we propose a new model that integrates both types of reciprocity. In particular, we apply the standard giving-game framework of indirect reciprocity and analyze the three-strategy model including reciprocal altruists, indiscriminate altruists, and free riders using evolutionary game theory. We show that the model allows reciprocal altruists and free riders to coexist stably in well-mixed populations. We also find that by accounting for inattention in the assessment rule, the stability of this mixed equilibrium can be strengthened to prevent the invasion of infamous indiscriminate altruists and can even be made globally stable.

Keywords: evolutionary game; evolution of cooperation; indirect reciprocity; downstream reciprocity; upstream reciprocity; pay it forward (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2024
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