Related papers: An Introduction to Complex Game Theory

We consider extensive games with perfect information with well-founded game trees and study the problems of existence and of characterization of the sets of subgame perfect equilibria in these games. We also provide such characterizations…

Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…

In this paper, we provide an effective characterization of all the subgame-perfect equilibria in infinite duration games played on finite graphs with mean-payoff objectives. To this end, we introduce the notion of requirement, and the…

Consider a very simple class of (finite) games: after an initial move by nature, each player makes one move. Moreover, the players have common interests: at each node, all the players get the same payoff. We show that the problem of…

We study the problem of finding equilibrium strategies in multi-agent games with incomplete payoff information, where the payoff matrices are only known to the players up to some bounded uncertainty sets. In such games, an ex-post…

Zero-sum stochastic games generalize the notion of Markov Decision Processes (i.e. controlled Markov chains, or stochastic dynamic programming) to the 2-player competitive case : two players jointly control the evolution of a state…

In a zero-sum stochastic game, at each stage, two adversary players take decisions and receive a stage payoff determined by them and by a controlled random variable representing the state of nature. The total payoff is the normalized…

Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games (that can be seen as a refinement of the well-studied mean-payoff games) are the variant where the payoff of a play is computed as the…

In two-player games on graph, the players construct an infinite path through the game graph and get a reward computed by a payoff function over infinite paths. Over weighted graphs, the typical and most studied payoff functions compute the…

In classical game theory, optimal strategies are determined for games with complete information; this requires knowledge of the opponent's goals. We analyze games when a player is mistaken about their opponents goals. For definitiveness, we…

We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…

We study symmetric bimatrix games that also have the common-payoff property, i.e., the two players receive the same payoff at any outcome of the game. Due to the symmetry property, these games are guaranteed to have symmetric Nash…

The equivalence between von Neumann's Minimax Theorem for zero-sum games and the LP Duality Theorem connects cornerstone problems of the two fields of game theory and optimization, respectively, and has been the subject of intense scrutiny…

In this work, we present a novel characterization of approximate Nash equilibria in a class of convex games over the simplex. To achieve this, we regularize the utility functions using the Shannon entropy term, connect the solutions to the…

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…

We study a class of two-player zero-sum Colonel Blotto games in which, after allocating soldiers across battlefields, players engage in (possibly distinct) normal-form games on each battlefield. Per-battlefield payoffs are parameterized by…

The minimax theorem for zero-sum games is easily proved from the strong duality theorem of linear programming. For the converse direction, the standard proof by Dantzig (1951) is known to be incomplete. We explain and combine classical…

Unlike Poker where the action space $\mathcal{A}$ is discrete, differential games in the physical world often have continuous action spaces not amenable to discrete abstraction, rendering no-regret algorithms with…

Game Theory has been frequently applied in biological research since 1970s. While the key idea of Game Theory is Nash Equilibrium, it is critical to understand and figure out the payoff matrix in order to calculate Nash Equilibrium. In this…

In a finite two player game consider the matrix of one player's payoff difference between any two consecutive pure strategies. Define the half space induced by a column vector of this matrix as the set of vectors that form an obtuse angle…