How cooperation can evolve between players is an unsolved problem of biology. Here we use Hamiltonian dynamics of models of the Ising type to describe populations of cooperating and defecting players to show that the equilibrium fraction of cooperators is given by the expectation value of a thermal observable akin to a magnetization. We apply the formalism to the Public Goods game with three pl...

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of...

– We discuss a population of sequences subject to mutations and frequencydependent selection, where the fitness of a sequence depends on the composition of the entire population. This type of dynamics is crucial to understand, for example, the coupled evolution of different strands in a viral population. Mathematically, it takes the form of a reactiondiffusion problem that is nonlinear in the p...

We investigate the correspondence between discrete-trait games (for example, matrix games) and continuous-trait games, paying particular attention to the standard criteria for evolutionary stability. We show that the standard evolutionarily stable strategy conditions for discretetrait games can be seen as a special case of the conditions employed in continuous-trait games.

Adaptationism maintains that natural selection is the principal factor causing evolutionary change. This statement is in need of qualification. Indeed, Peter Godfrey-Smith finds several possible usages of the term adaptationism. Steven Orzack and Elliott Sober argue that for adaptationism to be an interesting research program it has to be given in a reasonably strong form. Such a reasonably str...

This paper shows how games can be played that involve natural language, learning, and evolutionary ctitious play. This is implemented using respectively fuzzy logic, neural networks, and evolutionary programming. Because of this combination, they can be called soft games. The algorithm is described, and placed in the context of related research.

We introduce evolutionary dynamics for two-action games where agents with diverse preferences use statistical inference to guide their behavior. show that the dynamic converges a Bayesian sampling equilibrium (SESI) and set of SESIs is globally asymptotically stable. discuss global convergence unique SESI in anti-coordination games, welfare-improving tax scheme, selection coordination an applic...

Nonlocal interactions such as spatial interaction are ubiquitous in nature and may alter the equilibrium in evolutionary dynamics. Models including nonlocal spatial interactions can provide a further understanding on the preservation and emergence of cooperation in evolutionary dynamics. In this paper, we consider a variety of two-strategy evolutionary spatial games with nonlocal interactions b...

AI in computer games has been highlighted in recent, but manual designing costs a great deal. An evolutionary algorithm has developed strategies to play games without using features that would commonly require the knowledge of developers. Since the real-time reactive selection of behaviors for NPCs is required for better playing, a reactive behavior system consisting neural networks is presente...

Game theory focuses on payoffs and typically ignores time constraints that play an important role in evolutionary processes where the repetition of games can depend on the strategies, too. We introduce a matrix game under time constraints, where each pairwise interaction has two consequences: both players receive a payoff and they cannot play the next game for a specified time duration. Thus ou...