Individuals reciprocate negative actions revealing negative upstream reciprocity.

Indirect reciprocity is widely recognized as a mechanism for explaining cooperation and can be divided into two sub-concepts: downstream and upstream reciprocity. Downstream reciprocity is supported by reputation; if someone sees you helping someone else, the person who sees this will think higher of you, and you will be more likely to be helped. Upstream reciprocity is helping someone because you are being helped by somebody else, which often happens in everyday life and experimental games. This paper focuses on the behavior of "take" and examines negative upstream reciprocity using an upstream reciprocity framework. The term "take" is defined as "to steal rather than give resources to others." "If something is taken from you, do you take from others?" is an important extension for indirect reciprocity research; subsequently, this paper discusses experiments conducted on whether negative upstream reciprocity is chained and what causes it. The results demonstrated differences between positive and negative upstream reciprocity. In analyzing the data of nearly 600 participants to determine the extent to which negative upstream reciprocity is observed and the causes of negative upstream reciprocity, the study found that If individual A takes resources from individual B, then B is more likely to take resources from a third-party, individual C. Notably, some causes of positive upstream reciprocity were found to have no effect or the opposite effect on negative upstream reciprocity. The results also demonstrate that the first person to take can cause a chain reaction. This paper demonstrates the importance of the first person not taking from someone else and suggests the need to consider various behavioral options for future research on cooperation.

Evolution of cooperation in multiplex networks through asymmetry between interaction and replacement.

Cooperation is the foundation of society and has been the subject of numerous studies over the past three decades. However, the mechanisms underlying the spread of cooperation within a group are not yet fully comprehended. We analyze cooperation in multiplex networks, a model that has recently gained attention for successfully capturing certain aspects of human social connections. Previous studies on the evolution of cooperation in multiplex networks have shown that cooperative behavior is promoted when the two key processes in evolution, interaction and strategy replacement, are performed with the same partner as much as possible, that is, symmetrically, in a variety of network structures. We focus on a particular type of symmetry, namely, symmetry in the scope of communication, to investigate whether cooperation is promoted or hindered when interactions and strategy replacements have different scopes. Through multiagent simulations, we found some cases where asymmetry can promote cooperation, contrasting with previous studies. These results hint toward the potential effectiveness of not only symmetrical but also asymmetrical approaches in fostering cooperation within particular groups under certain social conditions.

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

Despite intensive studies on the evolution of cooperation in spatial public goods games, there have been few investigations into locality effects in interaction games, adaptation, and punishment. Here we analyze locality effects using an agent-based model of a regular graph. Our simulation shows that a situation containing a local game, local punishment, and global adaptation leads to the most robustly cooperative regime. Further, we show an interesting feature in local punishment. Previous studies showed that a local game and global adaptation are likely to generate cooperation. However, they did not consider punishment. We show that if local punishment is introduced in spatial public goods games, a situation satisfying either local game or local adaptation is likely to generate cooperation. We thus propose two principles. One is if interactions in games can be restricted locally, it is likely to generate cooperation independent of the interaction situations on punishment and adaptation. The other is if the games must be played globally, a cooperative regime requires both local punishment and local adaptation.

A quantitative easing experiment.

We experimentally investigate the effect of a central bank buying bonds for cash in a quantitative easing (QE) operation. In our experiment, the bonds are perfect substitutes for cash and have a constant fundamental value which is not affected by QE in the rational expectations equilibrium. We find that QE raises bond prices above those in the benchmark treatment without QE. Subjects in the benchmark treatment learned to trade the bonds at their fundamental value but those in treatments with QE became more convinced after repeated exposure to the same treatment that QE boosts bond prices. This suggests the possibility of a behavioural channel for the observed effects of actual QE operations on bond yields.

Selection of opponents in the prisoner׳s dilemma in dynamic networks: an experimental approach.

To investigate how a human subject selects her neighbors (opponents) to play the Prisoner׳s Dilemma within a social network, we conducted a human-subject experiment. The results are as follows: (1) A subject is more likely to dismiss the links to her neighbors most frequently when the subject chooses C and when the neighbor chooses D; (2) a subject who has more neighbors is less likely to dismiss links than a subject who has fewer neighbors; and (3) a subject is more likely to create links to (=select) opponents who have more neighbors than to opponents who have fewer neighbors.

Neural basis of conditional cooperation.

Cooperation among genetically unrelated individuals is a fundamental aspect of society, but it has been a longstanding puzzle in biological and social sciences. Recently, theoretical studies in biology and economics showed that conditional cooperation-cooperating only with those who have exhibited cooperative behavior-can spread over a society. Furthermore, experimental studies in psychology demonstrated that people are actually conditional cooperators. In this study, we used functional magnetic resonance imaging to investigate the neural system underlying conditional cooperation by scanning participants during interaction with cooperative, neutral and non-cooperative opponents in prisoner's dilemma games. The results showed that: (i) participants cooperated more frequently with both cooperative and neutral opponents than with non-cooperative opponents; and (ii) a brain area related to cognitive inhibition of pre-potent responses (right dorsolateral prefrontal cortex) showed greater activation, especially when participants confronted non-cooperative opponents. Consequently, we suggest that cognitive inhibition of the motivation to cooperate with non-cooperators drives the conditional behavior.

Chaos, oscillation and the evolution of indirect reciprocity in n-person games.

Evolution of cooperation among genetically unrelated individuals has been of considerable concern in various fields such as biology, economics, and psychology. The evolution of cooperation is often explained by reciprocity. Under reciprocity, cooperation can prevail in a society because a donor of cooperation receives reciprocation from the recipient of the cooperation, called direct reciprocity, or from someone else in the community, called indirect reciprocity. Nowak and Sigmund [1993. Chaos and the evolution of cooperation. Proc. Natl. Acad. Sci. USA 90, 5091-5094] have demonstrated that directly reciprocal cooperation in two-person prisoner's dilemma games with mutation of strategies can be maintained dynamically as periodic or chaotic oscillation. Furthermore, Eriksson and Lindgren [2005. Cooperation driven by mutations in multi-person Prisoner's Dilemma. J. Theor. Biol. 232, 399-409] have reported that directly reciprocal cooperation in n-person prisoner's dilemma games (n>2) can be maintained as periodic oscillation. Is dynamic cooperation observed only in direct reciprocity? Results of this study show that indirectly reciprocal cooperation in n-person prisoner's dilemma games can be maintained dynamically as periodic or chaotic oscillation. This is, to our knowledge, the first demonstration of chaos in indirect reciprocity. Furthermore, the results show that oscillatory dynamics are observed in common in the evolution of reciprocal cooperation whether for direct or indirect.

Evolutionary stability of first-order-information indirect reciprocity in sizable groups.

Indirect reciprocity is considered as a key mechanism for explaining the evolution of cooperation in situations where the same individuals interact only a few times. Under indirect reciprocity, an individual who helps others gets returns indirectly from others who know her good reputation. Recently, many studies have discussed the effect of reputation criteria based only on the former actions of the others (first-order information) and of those based also on the former reputation of opponents of the others (second-order information) on the evolution of indirect reciprocity. In this study, we investigate the evolutionary stability of the indirectly reciprocal strategy (discriminating strategy: DIS), which cooperates only with opponents who have good reputations, in n(>2)-person games where more than two individuals take part in a single group (interaction). We show that in n-person games, DIS is an evolutionarily stable strategy (ESS) even under the image-scoring reputation criterion, which is based only on first-order information and where cooperations (defections) are judged to be good (bad). This result is in contrast to that of 2-person games where DIS is not an ESS under reputation criteria based only on first-order information.

Three-person game facilitates indirect reciprocity under image scoring.

Reputation building plays an important role in the evolution of reciprocal altruism when the same individuals do not interact repeatedly because, by referring to reputation, a reciprocator can know which partners are cooperative and can reciprocate with a cooperator. This reciprocity based on reputation is called indirect reciprocity. Previous studies of indirect reciprocity have focused only on two-person games in which only two individuals participate in a single interaction, and have claimed that indirectly reciprocal cooperation cannot be established under image scoring reputation criterion where the reputation of an individual who has cooperated (defected) becomes good (bad). In this study, we specifically examine three-person games, and reveal that indirectly reciprocal cooperation can be formed and maintained stably, even under image scoring, by a nucleus shield mechanism. In the nucleus shield, reciprocators are a shield that keeps out unconditional defectors, whereas unconditional cooperators are the backbone of cooperation that retains a good reputation among the population.

Evolution of indirect reciprocity in groups of various sizes and comparison with direct reciprocity.

Recently many studies have investigated the evolution of indirect reciprocity through which cooperative action is returned by a third individual, e.g. individual A helped B and then receives help from C. Most studies on indirect reciprocity have presumed that only two individuals take part in a single interaction (group), e.g. A helps B and C helps A. In this paper, we investigate the evolution of indirect reciprocity when more than two individuals take part in a single group, and compare the result with direct reciprocity through which cooperative action is directly returned by the recipient. Our analyses show the following. In the population with discriminating cooperators and unconditional defectors, whether implementation error is included or not, (i) both strategies are evolutionarily stable and the evolution of indirect reciprocity becomes more difficult as group size increases, and (ii) the condition for the evolution of indirect reciprocity under standing reputation criterion where the third individuals distinguish between justified and unjustified defections is more relaxed than that under image scoring reputation criterion in which the third individuals do not distinguish with. Furthermore, in the population that also includes unconditional cooperators, (iii) in the presence of errors in implementation, the discriminating strategy is evolutionarily stable not only under standing but also under image scoring if group size is larger than two. Finally, (iv) in the absence of errors in implementation, the condition for the evolution of direct reciprocity is equivalent to that for the evolution of indirect reciprocity under standing, and, in the presence of errors, the condition for the evolution of direct reciprocity is very close to that for the evolution of indirect reciprocity under image scoring.

Reputation and the evolution of cooperation in sizable groups.

The evolution of cooperation in social dilemmas has been of considerable concern in various fields such as sociobiology, economics and sociology. It might be that, in the real world, reputation plays an important role in the evolution of cooperation. Recently, studies that have addressed indirect reciprocity have revealed that cooperation can evolve through reputation, even though pairs of individuals interact only a few times. To our knowledge, most indirect reciprocity models have presumed dyadic interaction; no studies have attempted analysis of the evolution of cooperation in large communities where the effect of reputation is included. We investigate the evolution of cooperation in sizable groups in which the reputation of individuals affects the decision-making process. This paper presents the following: (i) cooperation can evolve in a four-person case, (ii) the evolution of cooperation becomes difficult as group size increases, even if the effect of reputation is included, and (iii) three kinds of final social states exist. In medium-sized communities, cooperative species can coexist in a stable manner with betrayal species.

Chaos in learning a simple two-person game.

We investigate the problem of learning to play the game of rock-paper-scissors. Each player attempts to improve her/his average score by adjusting the frequency of the three possible responses, using reinforcement learning. For the zero sum game the learning process displays Hamiltonian chaos. Thus, the learning trajectory can be simple or complex, depending on initial conditions. We also investigate the non-zero sum case and show that it can give rise to chaotic transients. This is, to our knowledge, the first demonstration of Hamiltonian chaos in learning a basic two-person game, extending earlier findings of chaotic attractors in dissipative systems. As we argue here, chaos provides an important self-consistency condition for determining when players will learn to behave as though they were fully rational. That chaos can occur in learning a simple game indicates one should use caution in assuming real people will learn to play a game according to a Nash equilibrium strategy.