https://research-explorer.ista.ac.at 2000-01-01T00:00+00:00 1 monthly https://research-explorer.ista.ac.at/record/9402 Schmid, Laura ; https://orcid.org/0000-0002-6978-7329 Chatterjee, Krishnendu ; https://orcid.org/0000-0002-4561-241X Hilbe, Christian ; https://orcid.org/0000-0001-5116-955X Nowak, Martin A. 2021 Direct and indirect reciprocity are key mechanisms for the evolution of cooperation. Direct reciprocity means that individuals use their own experience to decide whether to cooperate with another person. Indirect reciprocity means that they also consider the experiences of others. Although these two mechanisms are intertwined, they are typically studied in isolation. Here, we introduce a mathematical framework that allows us to explore both kinds of reciprocity simultaneously. We show that the well-known ‘generous tit-for-tat’ strategy of direct reciprocity has a natural analogue in indirect reciprocity, which we call ‘generous scoring’. Using an equilibrium analysis, we characterize under which conditions either of the two strategies can maintain cooperation. With simulations, we additionally explore which kind of reciprocity evolves when members of a population engage in social learning to adapt to their environment. Our results draw unexpected connections between direct and indirect reciprocity while highlighting important differences regarding their evolvability. https://research-explorer.ista.ac.at/record/9402 https://research-explorer.ista.ac.at/download/9402/14496 eng Springer Nature info:eu-repo/semantics/altIdentifier/doi/10.1038/s41562-021-01114-8 info:eu-repo/semantics/altIdentifier/e-issn/2397-3374 info:eu-repo/semantics/altIdentifier/wos/000650304000002 info:eu-repo/semantics/altIdentifier/pmid/33986519 info:eu-repo/semantics/openAccess Schmid L, Chatterjee K, Hilbe C, Nowak MA. A unified framework of direct and indirect reciprocity. <i>Nature Human Behaviour</i>. 2021;5(10):1292–1302. doi:<a href="https://doi.org/10.1038/s41562-021-01114-8">10.1038/s41562-021-01114-8</a> ddc:000 A unified framework of direct and indirect reciprocity info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/17329 Alistarh, Dan-Adrian ; https://orcid.org/0000-0003-3650-940X Chatterjee, Krishnendu ; https://orcid.org/0000-0002-4561-241X Karrabi, Mehrdad ; https://orcid.org/0009-0007-5253-9170 Lazarsfeld, John M 2024 We initiate the study of game dynamics in the population protocol model: n agents each maintain a current local strategy and interact in pairs uniformly at random. Upon each interaction, the agents play a two-person game and receive a payoff from an underlying utility function, and they can subsequently update their strategies according to a fixed local algorithm. In this setting, we ask how the distribution over agent strategies evolves over a sequence of interactions, and we introduce a new distributional equilibrium concept to quantify the quality of such distributions. As an initial example, we study a class of repeated prisoner's dilemma games, and we consider a family of simple local update algorithms that yield non-trivial dynamics over the distribution of agent strategies. We show that these dynamics are related to a new class of high-dimensional Ehrenfest random walks, and we derive exact characterizations of their stationary distributions, bounds on their mixing times, and prove their convergence to approximate distributional equilibria. Our results highlight trade-offs between the local state space of each agent, and the convergence rate and approximation factor of the underlying dynamics. Our approach opens the door towards the further characterization of equilibrium computation for other classes of games and dynamics in the population setting. https://research-explorer.ista.ac.at/record/17329 https://research-explorer.ista.ac.at/download/17329/17335 eng Association for Computing Machinery info:eu-repo/semantics/altIdentifier/doi/10.1145/3662158.3662768 info:eu-repo/semantics/altIdentifier/isbn/9798400706684 info:eu-repo/semantics/openAccess Alistarh D-A, Chatterjee K, Karrabi M, Lazarsfeld JM. Game dynamics and equilibrium computation in the population protocol model. In: <i>Proceedings of the 43rd Annual ACM Symposium on Principles of Distributed Computing</i>. Association for Computing Machinery; 2024:40-49. doi:<a href="https://doi.org/10.1145/3662158.3662768">10.1145/3662158.3662768</a> ddc:000 Game dynamics and equilibrium computation in the population protocol model info:eu-repo/semantics/conferenceObject doc-type:ConferenceObject ConferenceObject http://purl.org/coar/resource_type/c_5794