We discuss related aspects of the simplest possible games, i.e. games where two players have two pure strategies each, and consider static games, population games, a generalization of evolutionary games, and dynamic games.

Game AI is the decision-making process of computer-controlled opponents in computer games. Adaptive game AI can improve the entertainment value of computer games. It allows computercontrolled opponents to automatically fix weaknesses in the game AI and respond to changes in human-player tactics. Dynamic scripting is a recently developed approach for adaptive game AI that learns which tactics (i...

Computing equilibria of multiplayer noncooperative normal form games is a difficult computational task. In games having more equilibria mathematical algorithms are not capable to detect all equilibria at a time. Evolutionary algorithms are powerful search tools for solving difficult optimization problems. It is shown how an evolutionary algorithm designed for multimodal optimization can be used...

This paper unifies the concepts of evolutionary games and quantum strategies. First, we state the formulation and properties of classical evolutionary strategies, with focus on the destinations of evolution in 2-player 2strategy games. We then introduce a new formalism of quantum evolutionary dynamics, and give an example where an evolving quantum strategy gives reward if played against its cla...

Population games describe strategic interactions among large numbers of small, anonymous agents. Behavior in these games is typically modeled dynamically, with agents occasionally receiving opportunities to switch strategies, basing their choices on simple myopic rules called revision protocols. Over finite time spans the evolution of aggregate behavior is well approximated by the solution of a...

References [1] Cressman, R. (2003), Evolutionary Dynamics and Extensive Form Games, MIT Press. [2] van Damme, E. (1991), Stability and Perfection of Nash Equilibria, Springer. [Chapter 9] [3] Fudenberg, D. and D. K. Levine (1998), The Theory of Learning in Games, MIT Press. [4] Gintis, H. (2000), Game Theory Evolving, Princeton University Press. [5] Hammerstein, P. and R. Selten (1994), “Game T...

We consider a simple model of stochastic evolution in population games. In our model, each agent occasionally receives opportunities to update his choice of strategy. When such an opportunity arises, the agent selects a strategy that is currently optimal, but only after his payoffs have been randomly perturbed. We prove that the resulting evolutionary process converges to approximate Nash equil...