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This paper provides theoretical bounds for empirical game theoretical analysis of complex multi-agent interactions. We provide insights in the empirical meta game showing that a Nash equilibrium of the meta-game is an approximate Nash…

Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games -- in which the pure strategy space is (potentially uncountably) infinite -- is far more…

We study adaptive learning in a typical p-player game. The payoffs of the games are randomly generated and then held fixed. The strategies of the players evolve through time as the players learn. The trajectories in the strategy space…

Parrondo's paradox indicates a paradoxical situation in which a winning expectation may occur in sequences of losing games. There are many versions of the original Parrondo's games in the literature, but the games are played by two players…

In this paper, a quantum variant of chess is introduced, which can be played on a traditional board, without using computers or other electronic devices. The rules of the game arise naturally by combining the rules of conventional chess…

In this article, we study the decision-making process of chess players by using a chess engine to evaluate the moves across different pools of games. We quantified the decisiveness of each move during the games using a metric derived from…

Learning in zero-sum games studies a situation where multiple agents competitively learn their strategy. In such multi-agent learning, we often see that the strategies cycle around their optimum, i.e., Nash equilibrium. When a game…

In this paper, we formulate an evolutionarymultiple access control game with continuousvariable actions and coupled constraints. We characterize equilibria of the game and show that the pure equilibria are Pareto optimal and also resilient…

Games often incorporate random elements in the form of dice or shuffled card decks. This randomness is a key contributor to the player experience and the variety of game situations encountered. There is a tension between a level of…

We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…

Games can be a powerful tool for learning about statistical methodology. Effective game design involves a fine balance between caricature and realism, to simultaneously illustrate salient concepts in a controlled setting and serve as a…

A natural goal in multiagent learning besides finding equilibria is to learn rationalizable behavior, where players learn to avoid iteratively dominated actions. However, even in the basic setting of multiplayer general-sum games, existing…

Multi-agent football poses an unsolved challenge in AI research. Existing work has focused on tackling simplified scenarios of the game, or else leveraging expert demonstrations. In this paper, we develop a multi-agent system to play the…

A new game theoretical solution concept for open spectrum sharing in cognitive radio (CR) environments is presented, the Lorenz equilibrium (LE). Both Nash and Pareto solution concepts have limitations when applied to real world problems.…

Several notions of game enjoy a Nash-like notion of equilibrium without guarantee of existence. There are different ways of weakening a definition of Nash-like equilibrium in order to guarantee the existence of a weakened equilibrium.…

Complexity develops via the incorporation of innovative properties. Chess is one of the most complex strategy games, where expert contenders exercise decision making by imitating old games or introducing innovations. In this work, we study…

Coordination games have been of interest to game theorists, economists, and ecologists for many years to study such problems as the emergence of local conventions and the evolution of cooperative behavior. Approaches for understanding the…

While many dynamical systems of mechanical origin, in particular billiards, are strongly chaotic -- enjoy exponential mixing, the rates of mixing in many other models are slow (algebraic, or polynomial). The dynamics in the latter are…

This report presents Giraffe, a chess engine that uses self-play to discover all its domain-specific knowledge, with minimal hand-crafted knowledge given by the programmer. Unlike previous attempts using machine learning only to perform…

We consider the task of building strong but human-like policies in multi-agent decision-making problems, given examples of human behavior. Imitation learning is effective at predicting human actions but may not match the strength of expert…