Related papers: Sion's mini-max theorem and Nash equilibrium in a …
Learning in games discusses the processes where multiple players learn their optimal strategies through the repetition of game plays. The dynamics of learning between two players in zero-sum games, such as Matching Pennies, where their…
In a network game, players interact over a network and the utility of each player depends on his own action and on an aggregate of his neighbours' actions. Many real world networks of interest are asymmetric and involve a large number of…
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…
Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite…
Due to the lack of coordination, it is unlikely that the selfish players of a strategic game reach a socially good state. A possible way to cope with selfishness is to compute a desired outcome (if it is tractable) and impose it. However…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
In 1953, Kuhn showed that every sequential game has a Nash equilibrium by showing that a procedure, named ``backward induction'' in game theory, yields a Nash equilibrium. It actually yields Nash equilibria that define a proper subclass of…
We study the asymptotic organization among many optimizing individuals interacting in a suitable "moderate" way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player…
Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players…
We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum polynomial game in randomized…
We consider a class of two-player dynamic stochastic nonzero-sum games where the state transition and observation equations are linear, and the primitive random variables are Gaussian. Each controller acquires possibly different dynamic…
Nash equilibria are crucial for understanding game behavior and systems in economics, physics, biology, and computer science. A significant application arises from the connection between Nash equilibria and optimization problems . However,…
In this note we provide a new proof for the results of Lipton et al. on the existence of an approximate Nash equilibrium with logarithmic support size. Besides its simplicity, the new proof leads to the following contributions: 1. For…
We explore a version of the minimax theorem for two-person win-lose games with infinitely many pure strategies. In the countable case, we give a combinatorial condition on the game which implies the minimax property. In the general case, we…
We consider graphical $n$-person games with perfect information that have no Nash equilibria in pure stationary strategies. Solving these games in mixed strategies, we introduce probabilistic distributions in all non-terminal positions. The…
We consider finite $n$-person deterministic graphical games and study the existence of pure stationary Nash-equilibrium in such games. We assume that all infinite plays are equivalent and form a unique outcome, while each terminal position…
We show that for any $\epsilon>0$, as the number of agents gets large, the share of games that admit a pure $\epsilon$-equilibrium converges to 1. Our result holds even for pure $\epsilon$-equilibrium in which all agents, except for at most…
In this paper, we first devise two algorithms to determine whether or not a bimatrix game has a strategically equivalent zero-sum game. If so, we propose an algorithm that computes the strategically equivalent zero-sum game. If a given…
This paper develops a novel methodology to study robust stability properties of Nash equilibrium points in dynamic games. Small-gain techniques in modern mathematical control theory are used for the first time to derive conditions…
In this short note we study a class of multi-player, turn-based games with deterministic state transitions and reachability / safety objectives (this class contains as special cases "classic" two-player reachability and safety games as well…