Related papers: On zero-sum game formulation of non zero-sum game

In this paper, we consider a differential stochastic zero-sum game in which two players intervene by adopting impulse controls in a finite time horizon. We provide a numerical solution as an approximation of the value function, which turns…

In this paper, we investigate Nash equilibrium payoffs for nonzero-sum stochastic differential games with reflection. We obtain an existence theorem and a characterization theorem of Nash equilibrium payoffs for nonzero-sum stochastic…

In this paper, we investigate a competitive market involving two agents who consider both their own wealth and the wealth gap with their opponent. Both agents can invest in a financial market consisting of a risk-free asset and a risky…

Motivated by Generative Adversarial Networks, we study the computation of Nash equilibrium in concave network zero-sum games (NZSGs), a multiplayer generalization of two-player zero-sum games first proposed with linear payoffs. Extending…

Since the 1990s, AI systems have achieved superhuman performance in major zero-sum games where "winning" has an unambiguous definition. However, most social interactions are mixed-motive games, where measuring the performance of AI systems…

Zero-sum games arise in a wide variety of problems, including robust optimization and adversarial learning. However, algorithms deployed for finding a local Nash equilibrium in these games often converge to non-Nash stationary points. This…

In this paper we study a game where every player is to choose a vertex (facility) in a given undirected graph. All vertices (customers) are then assigned to closest facilities and a player's payoff is the number of customers assigned to it.…

We present a novel variant of fictitious play dynamics combining classical fictitious play with Q-learning for stochastic games and analyze its convergence properties in two-player zero-sum stochastic games. Our dynamics involves players…

The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive…

In this paper, we establish the existence of optimal bounded memory strategy profiles in multi-player discounted sum games. We introduce a non-deterministic approach to compute optimal strategy profiles with bounded memory. Our approach can…

We study zero-sum repeated games where the minimizing player has to pay a certain cost each time he changes his action. Our contribution is twofold. First, we show that the value of the game exists in stationary strategies, depending solely…

Multi-leader multi-follower games are a class of hierarchical games in which a collection of leaders compete in a Nash game constrained by the equilibrium conditions of another Nash game amongst the followers. The resulting equilibrium…

This paper investigates mixed strategies in dynamic games with perfect information. We present an example to show that a player may obtain higher payoff by playing mixed strategy. By contrast, the main result of the paper shows that every…

In the nonzero-sum setting, we establish a connection between Nash equilibria in games of optimal stopping (Dynkin games) and generalised Nash equilibrium problems (GNEP). In the Dynkin game this reveals novel equilibria of threshold type…

Standard game theory assumes that the structure of the game is common knowledge among players. We relax this assumption by considering extensive games where agents may be unaware of the complete structure of the game. In particular, they…

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…

Frequent violations of fair principles in real-life settings raise the fundamental question of whether such principles can guarantee the existence of a self-enforcing equilibrium in a free economy. We show that elementary principles of…

We analyze a two-player, nonzero-sum Dynkin game of stopping with incomplete information. We assume that each player observes his own Brownian motion, which is not only independent of the other player's Brownian motion but also not…

We study the problem of computing approximate Nash equilibria (epsilon-Nash equilibria) in normal form games, where the number of players is a small constant. We consider the approach of looking for solutions with constant support size. It…

This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource.…