The importance of subjectivity in perceptual errors on the emergence of indirect reciprocity
Introduction
Resource exchange is ubiquitous in all human societies. Without resource exchange, no society can hold. Among the various theories of exchange, only two have been established empirically. One is kin altruism (Hamilton, 1964), which explains unilateral giving towards kin who share the same genes, and the other is reciprocal altruism (Trivers, 1971; Axelrod, 1984), which explains resource giving in dyads over repeated interactions. Although these two explanations may be applied to certain animal species, there is yet another type of exchange that takes place only in human societies. That is, unilateral resource giving among n-persons. Social scientists call this type of exchange generalized-exchange, and biologists call this indirect reciprocity. Although this phenomenon has been known for decades, the existence of such exchanges has been puzzling. Recently, however, significant advances have been made in research in mathematical biology (e.g., Nowak and Sigmund, 1998a, Nowak and Sigmund, 1998b; Leimar and Hammerstein, 2001; Ohtsuki, 2004; Ohtsuki and Iwasa, 2004, Ohtsuki and Iwasa, 2006; Panchanathan and Boyd, 2003). Using computer simulations and mathematical analysis, this study extends and refines findings of these pioneering studies, and proposes that the requirements for the maintenance of indirect reciprocity are stricter than the previously suggested. The critical rule turns out to be: “the friend of my enemy is my enemy as well”.
Section snippets
Previous solutions to the problem of resource giving
In the 60s, kin selection was proposed (Hamilton, 1964). Reciprocal altruism, which extends the scope of resource giving behavior to unrelated individuals, was proposed in the 70s (Trivers, 1971) and continued to be the main focus of research throughout the 80s (e.g., Axelrod, 1984). In the 1990s, theoretical and empirical research on unilateral giving outside of kin relations and without repeated interactions began. In order for such giving behavior to be adaptive, a system of indirect
What made the difference?
Why did Takahashi and Mashima (2003) and Ohtsuki and Iwasa (2004) get different results? The most important factor that produced this discrepancy is, we believe, that these two studies conceptualized perceptual errors differently. Following Leimar and Hammerstein (2001), when an individual misperceives an action performed by another, it is called errors in perception. These errors can lead to misperception of the reputation score of others.6
Revisiting Takahashi and Mashima (2003)'s simulation
Although Takahashi and Mashima (2003) presented SDISC as the one (and only) strategy that makes indirect reciprocity possible, their emphasis was on whether indirect reciprocity can emerge in a population that is initially composed of equal numbers of three strategies: ALLC, ALLD, and the focal strategy. However, a given strategy is only stable if it can resist invasion by other strategies when the population is initially composed of the focal strategy only. Of course this is not a formal
Two-way implementation errors and two-way subjective perceptual errors
In this section, we examine the effect of perceptual errors (i.e., falsely perceiving giving as not-giving, and vice versa) on the emergence of indirect reciprocity. In the event that perception is subjective, the probability of making an error is calculated independently for each player in the population. Conversely, if perception is objective, the probability of attributing the wrong label is calculated once for all players. Thus, whereas objective perceptual errors are shared among all
Discussion
What is the definition of goodness that makes indirect reciprocity possible among n-persons in generalized exchange settings? Ohtsuki and Iwasa (2004) proposed eight evolutionarily stable combinations of reputation dynamics and strategies that achieved a high level of giving in generalized exchange settings. The common characteristics of these “leading eight” were (a) giving to “good” persons should be regarded as “good”, (b) not-giving to “good” persons should be regarded as “bad”, and (c)
Future directions
Although we have shown that it is a necessary condition for the emergence of generalized exchange to consider individuals who give to “bad” persons as “bad”, there is still much to accomplish. First, we would like to expand our analysis into the selective-play situation. In this paper we assume a situation in which a pair of individuals is chosen randomly from a population. Using Yamagishi and Hayashi (1996)'s terminology, such a situation is considered forced-play (players are “forced” to
Acknowledgement
We thank Hisashi Ohtsuki, Karthik Panchanathan, Yoh Iwasa for their valuable comments and suggestions. We also thank an anonymous reviewer for pointing out errors in equations in Appendix A of the original draft and suggesting the approximate solution for the unstable equilibrium along the ALLD-ES edge in Fig. 2 (Eq. (2)).
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2018, Journal of Theoretical BiologyCitation Excerpt :Sugden (1986) then proved that T1 is a stable equilibrium strategy. This resulted in consecutive theoretical studies into the evolution of indirect reciprocity in the giving game (Leimar and Hammerstein, 2001; Panchanathan and Boyd, 2003; Brandt and Sigmund, 2004; Ohtsuki and Iwasa, 2004; Takahashi and Mashima, 2006). Ohtsuki and Iwasa (2004) showed that conditional cooperators can resist the invasion of defectors under eight assessment rules called the leading eight, which have the following common features: (i) if a donor helps (does not help) a recipient with good standing, the donor's reputation becomes good (bad), and (ii) if a donor with good standing does not help a recipient with bad standing, the donor's reputation remains good.
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