Aspirations, adaptive learning and cooperation in repeated games

Game Theory;Repeated Games

Words without Near-Repetitions

We find an infinite word w on four symbols with the following property: Two occurrences of any block in w must be separated by more than the length of the block. That is, in any subword of w of the form xyx, the length of y is greater than the length of x. This answers a question of C. Edmunds connected to the Burnside problem for groups.The research of the first author was supported by an NSERC Operating Grant. The second author was supported by an NSERC Undergraduate Summer Research Award.https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/words-without-nearrepetitions/F86509D865F222F1FC63ACA8545C069

A gauge invariant chiral unitary framework for kaon photo- and electroproduction on the proton

We present a gauge invariant approach to photoproduction of mesons on nucleons within a chiral unitary framework. The interaction kernel for meson-baryon scattering is derived from the chiral effective Lagrangian and iterated in a Bethe-Salpeter equation. Within the leading order approximation to the interaction kernel, data on kaon photoproduction from SAPHIR, CLAS and CBELSA/TAPS are analyzed in the threshold region. The importance of gauge invariance and the precision of various approximations in the interaction kernel utilized in earlier works are discussed.Comment: 23 pages, 13 figs, EPJ A styl

Cooperation, Norms, and Revolutions: A Unified Game-Theoretical Approach

Cooperation is of utmost importance to society as a whole, but is often challenged by individual self-interests. While game theory has studied this problem extensively, there is little work on interactions within and across groups with different preferences or beliefs. Yet, people from different social or cultural backgrounds often meet and interact. This can yield conflict, since behavior that is considered cooperative by one population might be perceived as non-cooperative from the viewpoint of another. To understand the dynamics and outcome of the competitive interactions within and between groups, we study game-dynamical replicator equations for multiple populations with incompatible interests and different power (be this due to different population sizes, material resources, social capital, or other factors). These equations allow us to address various important questions: For example, can cooperation in the prisoner's dilemma be promoted, when two interacting groups have different preferences? Under what conditions can costly punishment, or other mechanisms, foster the evolution of norms? When does cooperation fail, leading to antagonistic behavior, conflict, or even revolutions? And what incentives are needed to reach peaceful agreements between groups with conflicting interests? Our detailed quantitative analysis reveals a large variety of interesting results, which are relevant for society, law and economics, and have implications for the evolution of language and culture as well

How to overcome the detrimental effects of noise in social interaction: the benefits of generosity

Interpersonal misunderstanding is often rooted in noise, or discrepancies between intended and actual outcomes for an interaction partner due to unintended errors (e.g., not being able to respond to an E-mail because of a local network breakdown). How can one effectively cope with noise in social dilemmas, situations in which self-interest and collective interests are conflicting? Consistent with hypotheses, the present research revealed that incidents of noise exert a detrimental effect on level of cooperation when a partner follows strict reciprocity (i.e., tit for tat) but that this effect can be overcome if a partner behaves somewhat more cooperatively than the actor did in the previous interaction (i.e., tit for tat plus 1). Also, when noise was present, tit for tat plus 1 elicited greater levels of cooperation than did tit for tat, thereby underscoring the benefits of adding generosity to reciprocity in coping with noise in social dilemmas. The Discussion outlines implications of the present work for theories focusing on self-presentation and attribution, communication, and trust and prorelationship behavior

How to cope with "noise" social dilemmas: The benefits of communication

Interactions in social life may be seriously affected by negative noise, whereby actual or perceived behavior is less cooperative than was intended (e.g., arriving late due to an unforeseen traffic jam). The present research examines whether negative noise exerts detrimental effects on impressions and cooperation and whether such effects could be reduced by communication. Consistent with hypotheses, Study 1 revealed that negative noise exerts detrimental effects on both impressions of partners' benign intent and cooperation and that these detrimental effects could be effectively reduced by communication about noise. Study 2 replicated both findings but only for individuals with low trust. Mediation analysis revealed that impressions of benign intent and prosocial interaction goals underlie the positive effects of communication on cooperation

Asymmetric Power Among Agents and the Generation and Maintenance of Cooperation in International Relations

The question addressed in this analysis is whether endowing agents with various forms of asymmetric power makes cooperation more likely across a variety of structural settings of conflict and cooperation present in international relations. To address this question, an agent-based model incorporating asymmetric power among agents in a set of (2 Â 2) games that represent different forms of conflict and cooperation prevalent in international relations (Chicken, Stag, Assurance, Deadlock, and Prisoner's Dilemma) is developed and analyzed via simulation. Simulation results indicate that the introduction of asymmetric power substantially increases the chances that both cooperative agents survive and cooperative worlds evolve. This is particularly the case when agents are endowed with the ability to selectively interact with other agents. Also, anticipated variations in outcomes across the game structures regarding the likelihood of cooperation are supported. Whether and how cooperation evolves in social settings characterized by the presence of selfish agents engaged in repeated relations without central authority has been of considerable importance to scholars of international politics and of interest to scholars across all the social sciences as well as philosophy, biology, and computer science. 1 International relations scholars have been particularly interested in various features of nation-states, the relations among nation-states, and the structural environment in which nation-states are embedded that make cooperation either possible or more likely. Studying the evolution of cooperation in the context of the Repeated Prisoner's Dilemma (RPD) has proven to be quite fruitful for international relations scholars. Yet, the RPD framework is also restrictive in a variety of ways. 3 For instance, while the RPD captures one important type of relationship among nation-states in the international system, there are a number of other structural settings that (1984), the Repeated Prisoner's Dilemma (RPD) has become the central metaphor for the evolution of cooperation in populations of selfish agents without central authority

Axelrod’s metanorm games on networks

Metanorms is a mechanism proposed to promote cooperation in social dilemmas. Recent experimental results show that network structures that underlie social interactions influence the emergence of norms that promote cooperation. We generalize Axelrod’s analysis of metanorms dynamics to interactions unfolding on networks through simulation and mathematical modeling. Network topology strongly influences the effectiveness of the metanorms mechanism in establishing cooperation. In particular, we find that average degree, clustering coefficient and the average number of triplets per node play key roles in sustaining or collapsing cooperationSpanish MICINN projects CSD2010-00034 (CONSOLIDER-INGENIO 2010) and DPI2010-16920, and by the Junta de Castilla y Leo´ n, references BU034A08 and GREX251-2009

The emergence of altruism as a social norm

Expectations, exerting influence through social norms, are a very strong candidate to explain how complex societies function. In the Dictator game (DG), people expect generous behavior from others even when they cannot enforce any sharing of the pie. Here we assume that people donate following their expectations, and that they update their expectation after playing a DG by reinforcement learning to construct a model that explains the main experimental results in the DG. Full agreement with the experimental results is reached when some degree of mismatch between expectations and donations is added into the model. These results are robust against the presence of envious agents, but affected if we introduce selfish agents that do not update their expectations. Our results point to social norms being on the basis of the generous behavior observed in the DG and also to the wide applicability of reinforcement learning to explain many strategic interactions