A Theoretical Approach to Norm Ecosystems: Two Adaptive Architectures of Indirect Reciprocity Show Different Paths to the Evolution of Cooperation

Abstract

Indirect reciprocity is one of the basic mechanisms to sustain mutual cooperation, by which beneficial acts are returned, not by the recipient, but by third parties. This mechanism relies on the ability of individuals to know the past actions of others, and to assess those actions. There are many different systems of assessing others, which can be interpreted as rudimentary social norms (i.e., views on what is "good" or "bad"). In this paper, impacts of different adaptive architectures, i.e., ways for individuals to adapt to environments, on indirect reciprocity are investigated. We examine two representative architectures: one based on replicator dynamics and the other on genetic algorithm. Different from the replicator dynamics, the genetic algorithm requires describing the mixture of all possible norms in the norm space under consideration. Therefore, we also propose an analytic method to study norm ecosystems in which all possible second order social norms potentially exist and compete. The analysis reveals that the different adaptive architectures show different paths to the evolution of cooperation. Especially we find that so called Stern-Judging, one of the best studied norms in the literature, exhibits distinct behaviors in both architectures. On one hand, in the replicator dynamics, Stern-Judging remains alive and gets a majority steadily when the population reaches a cooperative state. On the other hand, in the genetic algorithm, it gets a majority only temporarily and becomes extinct in the end.

Evolution of empathetic moral evaluation

“…Whereas we have studied empathy as a fixed trait, an individual’s tendency for empathetic evaluation might instead depend in a non-linear way on the current make-up of strategies in the population. Another question involves the competition of social norms for moral evaluation – a topic that has been studied in some contexts, such as when errors do not occur (Uchida et al, 2018), or in the presence of population structure (Masuda, 2012; Pacheco et al, 2006). Perhaps an even more fundamental question is whether and how population-wide social norms can evolve from individual moral beliefs to begin with.…”

Justified defection is neither justified nor unjustified in indirect reciprocity

“…However this assumption clearly oversimplifies the reality. In recent years, researchers have tackled this assumption by developing a model in which various norms coexist in the population [30,31]. However, if any of the norms proposed in the theoretical studies are actually adopted by people, the assessment of the donor by observers should be widely distributed.…”

Effect of voluntary participation on an alternating and a simultaneous prisoner's dilemma

“…Another factor that is out of the scope of this research is a comparison with an adaptive architecture, i.e., a way for individuals to adapt to their environments. Besides GA, some architectures have been argued for evolutionary computation [29,31,42]. This point also provides an interesting direction for potential future research.…”

“…In a study on indirect reciprocity, Yamamoto et al [28] and Uchida et al [29] developed a "norm ecosystem" approach that describes the coevolution of strategies and cooperation among various strategies.…”