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Indirect reciprocity is one of the major mechanisms for the evolution of cooperation in human societies. There are two types of indirect reciprocity: upstream and downstream. Cooperation in downstream reciprocity follows the pattern, 'You helped someone, and I will help you'. The direction of cooperation is reversed in upstream reciprocity, which instead follows the pattern, 'You helped me, and I will help someone else'. In reality, these two types of indirect reciprocity often occur in combination. However, upstream and downstream reciprocity have mostly been studied theoretically in isolation. Here, we propose a new model that integrates both types. We apply the standard giving-game framework of indirect reciprocity and analyze the model by means of evolutionary game theory. We show that the model can result in the stable coexistence of altruistic reciprocators and free riders in well-mixed populations. We also found that considering inattention in the assessment rule can strengthen the stability of this mixed equilibrium, even resulting in a global attractor. Our results indicate that the cycles of forwarding help and rewarding help need to be established for creating and maintaining diversity and inclusion in a society., Comment: 14 pages, 4 figures, 2 tables

Potassium-ion ($\rm K$-ion) rechargeable batteries; considered to be lucrative low-cost battery options for large-scale and capacious energy storage systems, have been garnering tremendous attention in recent years. However, due to the scarcity of cathode materials that can condone the reversible re-insertion of the large $\rm K$-ions at feasible capacities, the viability of $\rm K$-ion batteries has been greatly undercut. In this paper, we explore a potential cathode material in the $\rm K_2O$-$\rm Fe_2O_3$-$\rm MnO_2$ ternary phase system, that not only demonstrates reversible $\rm K$-ion reinsertion but also manifests relatively fast rate capabilities. The titled cathode compound, $\rm K_{0.4}Fe_{0.5}Mn_{0.5}O_2$, demonstrates a reversible capacity of approximately $\rm120 $ mAh g$^{-1}$ at $\rm 10$ hours of (dis)charge ($viz.$, $\rm C/10$ rate) with $ca.$ $\rm 85$% of the capacity being retained at a $\rm 1$ hour of (dis)charge ($\rm 1 C$ rate) which is considered to be good capacity retention. Additionally, both hard and soft X-rays have been employed to unravel the mechanism by which $\rm K$-ion is reversibly inserted into $\rm K_{0.4}Fe_{0.5}Mn_{0.5}O_2$. The results revealed a cumulative participation of both manganese cations and oxygen anions in $\rm K_{0.4}Fe_{0.5}Mn_{0.5}O_2$ illustrating its potential as a high-capacity $\rm K$-ion battery cathode material that relies on both anion and cation redox. Further development of related high-capacity cathode compositions can be anticipated., Comment: 17 pages, 4 figures, 1 cover art

Although various norms for reciprocity-based cooperation have been suggested that are evolutionarily stable against invasion from free riders, the process of alternation of norms and the role of diversified norms remain unclear in the evolution of cooperation. We clarify the co-evolutionary dynamics of norms and cooperation in indirect reciprocity and also identify the indispensable norms for the evolution of cooperation. Inspired by the gene knockout method, a genetic engineering technique, we developed the norm knockout method and clarified the norms necessary for the establishment of cooperation. The results of numerical investigations revealed that the majority of norms gradually transitioned to tolerant norms after defectors are eliminated by strict norms. Furthermore, no cooperation emerges when specific norms that are intolerant to defectors are knocked out., Comment: 15 pages (incl. supplementary materials), 6 figures, 7 table

Despite recent advances in reputation technologies, it is not clear how reputation systems can affect human cooperation in social networks. Although it is known that two of the major mechanisms in the evolution of cooperation are spatial selection and reputation-based reciprocity, theoretical study of the interplay between both mechanisms remains almost uncharted. Here, we present a new individual-based model for the evolution of reciprocal cooperation between reputation and networks. We comparatively analyze four of the leading moral assessment rules---shunning, image scoring, stern judging, and simple standing---and base the model on the giving game in regular networks for Cooperators, Defectors, and Discriminators. Discriminators rely on a proper moral assessment rule. By using individual-based models, we show that the four assessment rules are differently characterized in terms of how cooperation evolves, depending on the benefit-to-cost ratio, the network-node degree, and the observation and error conditions. Our findings show that the most tolerant rule---simple standing---is the most robust among the four assessment rules in promoting cooperation in regular networks., Comment: 15 pages, 6 figures, and 1 table

Punishment is a popular tool when governing commons in situations where free riders would otherwise take over. It is well known that sanctioning systems, such as the police and courts, are costly and thus can suffer from those who free ride on other's efforts to maintain the sanctioning systems (second-order free riders). Previous game-theory studies showed that if populations are very large, pool punishment rarely emerges in public good games, even when participation is optional, because of second-order free riders. Here we show that a matching fund for rewarding cooperation leads to the emergence of pool punishment, despite the presence of second-order free riders. We demonstrate that reward funds can pave the way for a transition from a population of free riders to a population of pool punishers. A key factor in promoting the transition is also to reward those who contribute to pool punishment, yet not abstaining from participation. Reward funds eventually vanish in raising pool punishment, which is sustainable by punishing the second-order free riders. This suggests that considering the interdependence of reward and punishment may help to better understand the origins and transitions of social norms and institutions., Comment: 20 pages, 4 figures, supplementary information (10 pages, 8 figures)

In explaining altruistic cooperation and punishment, the challenging riddle is how transcendental rules can emerge within the empirical world. Game-theoretical studies showed that pool punishment, particularly second-order punishment, plays a key role in understanding the evolution of cooperation. Second-order pool punishment, however, is tautological in nature; the punishment system itself is caused by its own effects. The emergence of pool punishment poses a logical conundrum that, to date, has been overlooked in the study of the evolution of social norms and institutions. Here, we tackle the issue by considering the interplay of (a) cognitive biases in reasoning and (b) Agamben's notion of homo sacer (Agamben, G. 1998, Homo Sacer: Sovereign Power and Bare Life, Stanford University Press); that is, a person who may be killed without legal consequences. Based on the cognitive disposition of reversing the cause-and-effect relationship, we propose a new system: the preemptive punishment of homo sacer. This action can lead to retrospectively forming moral assessments, particularly for second-order pool punishment. This study potentially provides new insight into the evolutionary process behind the emergence of social norms and institutions., Comment: 5 pages, 1 figure

Properly coordinating cooperation is relevant for resolving public good problems such as clean energy and environmental protection. However, little is known about how individuals can coordinate themselves for a certain level of cooperation in large populations of strangers. In a typical situation, a consensus-building process hardly succeeds due to lack of face and standing. The evolution of cooperation in this type of situation is studied using threshold public good games in which cooperation prevails when it is initially sufficient, or otherwise, it perishes. While punishment is a powerful tool to shape human behaviours, institutional punishment is often too costly to start with only a few contributors, which is another coordination problem. Here we show that whatever the initial conditions, reward funds based on voluntary contribution can evolve. The voluntary reward paves the way for effectively overcoming the coordination problem and efficiently transforms freeloaders to cooperators with a perceived small risk of collective failure., Comment: 9 pages, 2 figures

Stern-judging is one of the best-known assessment rules in indirect reciprocity. Indirect reciprocity is a fundamental mechanism for the evolution of cooperation. It relies on mutual monitoring and assessments, i.e., individuals judge, following their own assessment rules, whether other individuals are "good" or "bad" according to information on their past behaviors. Among many assessment rules, stern-judging is known to provide stable cooperation in a population, as observed when all members in the population know all about others' behaviors (public information case) and when the members never commit an assessment error. In this paper, the effect of assessment error and private information on stern-judging is investigated. By analyzing the image matrix, which describes who is good in the eyes of whom in the population, we analytically show that private information and assessment error cause the collapse of stern-judging: all individuals assess other individuals as "good" at random with a probability of 1/2., Comment: 18 pages and 2 figures