A Review of Theoretical Studies on Indirect Reciprocity

Abstract

Despite the accumulation of research on indirect reciprocity over the past 30 years and the publication of over 100,000 related papers, there are still many issues to be addressed. Here, we look back on the research that has been done on indirect reciprocity and identify the issues that have been resolved and the ones that remain to be resolved. This manuscript introduces indirect reciprocity in the context of the evolution of cooperation, basic models of social dilemma situations, the path taken in the elaboration of mathematical analysis using evolutionary game theory, the discovery of image scoring norms, and the breakthroughs brought about by the analysis of the evolutionary instability of the norms. Moreover, it presents key results obtained by refining the assessment function, resolving the punishment dilemma, and presenting a complete solution to the social dilemma problem. Finally, it discusses the application of indirect reciprocity in various disciplines.

Cooperation through Image Scoring: A Replication

“…Participants also received an information sheet, consent form, debriefing sheet, and payment with receipt. During the game, participants viewed a series of screens that provided information: current balance (in GBP), indication of game round (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12), description of player's status in current round (donor/receiver), and all/some of the following information about player history: (1) If receiver in previous round, whether that player received money or not; (2) if donor in current round, then past donating behavior (e.g., "in the last 5 rounds as donor, you gave money 2 times and 3 times you did not give money"), and (3) if donor in current round, then donating history of prospective recipient (e.g., "The other person's record: In the last 5 times as donor, this person gave out money 3 times and did not give out money 2 times"). Also, for the donor, a choice was presented: (1) give £0.50 GBP to partner, or (2), nothing.…”

“…Indirect reciprocity [7,8] is just one proposed solution to the tragedy of the commons, expressed in positive form as "A observed B help C, therefore A helps B" [2]: generosity becomes self-serving because the generosity itself might be rewarded [1,7]. A substantial number of agent-based models have been published [8] that explore the conditions that allow indirect reciprocity, notably that of Nowak and Sigmund [4], who found that a discriminating "image scoring" strategy (give only to those who have given to others) was an evolutionarily stable strategy in contrast to undiscriminating/selfish strategies. Following the Nowak and Sigmund model [4], Wedekind and Milinski [9] (hereafter, WM) published a short paper in Science titled "cooperation by image scoring in humans".…”

Cooperation in spatial public good games depends on the locality effects of game, adaptation, and punishment

“…Even before it was selected as one of twenty-five big questions facing science in 2005 1 , numerous studies had tackled the fundamental puzzle of how cooperative behavior evolved. As a result of these academic efforts, several rationally understandable mechanisms have been proposed including kin-selection 2 , reciprocity 3 , structures 4 , and incentives 5 . However, many questions remain unanswered about the evolution of cooperation.…”

Playing soft with cooperators emerges as a moral norm and promotes cooperation in evolutionary games

“…This leaves everybody worse off than if otherwise, all had cooperated [1][2][3]. Indirect reciprocity is suggested as a way out of this dilemma [3][4][5][6], which can also bring insights into the evolution of morality [5,6].…”

“…In addition to the lack of a natural mechanism to break the chain of higher-order rules, this requires a relatively high cognitive ability and a large amount of information about the past actions of the individuals in moral assessment [17], which appears to limit its applicability [18]. Furthermore, the to what is a justified punishment [4,51].…”