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Reciprocity is an important feature of human social interaction and underpins our cooperative nature. What is more, simple forms of reciprocity have proved remarkably resilient in matrix game social dilemmas. Most famously, the tit-for-tat…
Repeated games have provided an explanation how mutual cooperation can be achieved even if defection is more favorable in a one-shot game in prisoner's dilemma situation. Recently found zero-determinant strategies have substantially been…
Individual choices are either based on personal experience or on information provided by peers. The latter case, causes individuals to conform to the majority in their neighborhood. Such herding behavior may be very efficient in aggregating…
A common assumption employed in most previous works on evolutionary game dynamics is that every individual player has full knowledge about and full access to the complete set of available strategies. In realistic social, economical, and…
Complex social behaviors lie at the heart of many of the challenges facing evolutionary biology, sociology, economics, and beyond. For evolutionary biologists in particular the question is often how such behaviors can arise \textit{de novo}…
We consider (random) strategic interactions in a large population consisting of a variety of players. A rational player chooses actions that maximize certain utility functions, while a behavioral player chooses actions based on preferences…
Learning to adapt and make real-time informed decisions in a dynamic and complex environment is a challenging problem. Monopoly is a popular strategic board game that requires players to make multiple decisions during the game.…
In an iterated game between two players, there is much interest in characterizing the set of feasible payoffs for both players when one player uses a fixed strategy and the other player is free to switch. Such characterizations have led to…
We generalize the Bush--Mosteller learning, the Roth--Erev learning, and the social learning to include mistakes such that the nonlinear replicator-mutator equation with either additive or multiplicative mutation is generated in an…
Direct reciprocity is a mechanism for the evolution of cooperation in repeated social interactions. According to this literature, individuals naturally learn to adopt conditionally cooperative strategies if they have multiple encounters…
We analyze a simple model of adaptive competition which captures essential features of a variety of adaptive competitive systems in the social and biological sciences. Each of N agents, at each time step of a game, joins one of two groups.…
Memory is inherently entangled with prediction and planning. Flexible behavior in biological and artificial agents depends on the interplay of learning from the past and predicting the future in ever-changing environments. This chapter…
Repeated game has long been the touchstone model for agents' long-run relationships. Previous results suggest that it is particularly difficult for a repeated game player to exert an autocratic control on the payoffs since they are jointly…
The Game of Poker Chips, Dominoes and Survival fosters team building and high level cooperation in large groups, and is a tool applied in management training exercises. Each player, initially given two colored poker chips, is allowed to…
We consider (N,r) games of predation with N species and r < N prey and predators, acting in a cyclic way. Further basic reactions include reproduction, decay and diffusion over a regular grid, without a hard constraint on the occupation…
We consider a group of agents on a graph who repeatedly play the prisoner's dilemma game against their neighbors. The players adapt their actions to the past behavior of their opponents by applying the win-stay lose-shift strategy. On a…
We consider a scenario in which two reinforcement learning agents repeatedly play a matrix game against each other and update their parameters after each round. The agents' decision-making is transparent to each other, which allows each…
Iterated games provide a framework to describe social interactions among groups of individuals. Recent work stimulated by the discovery of "zero-determinant" strategies has rapidly expanded our ability to analyze such interactions. This…
We study \emph{partial-information} two-player turn-based games on graphs with omega-regular objectives, when the partial-information player has \emph{limited memory}. Such games are a natural formalization for reactive synthesis when the…
A key challenge of evolutionary game theory and multi-agent learning is to characterize the limit behavior of game dynamics. Whereas convergence is often a property of learning algorithms in games satisfying a particular reward structure…