Related papers: Nash equilibrium payoffs for stochastic differenti…

Probabilistic model checking for stochastic games enables formal verification of systems that comprise competing or collaborating entities operating in a stochastic environment. Despite good progress in the area, existing approaches focus…

In this paper, we consider the problem of finding a Nash equilibrium in a multi-player game over generally connected networks. This model differs from a conventional setting in that players have partial information on the actions of their…

Many resources are provided by an ecological system that is vulnerable to tipping when exceeding a certain level of pollution, with a sudden big loss of ecosystem services. An ecological system is usually also a common-pool resource and…

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.…

We consider a symmetric two-player contest, in which the choice set of effort is constrained. We apply a fundamental property of the payoff function to show that, under standard assumptions, there exists a unique Nash equilibrium in pure…

We consider multi-player stopping games in continuous time. Unlike Dynkin games, in our games the payoff of each player is revealed after all the players stop. Moreover, each player can adjust her own stopping strategy by observing other…

Nash equilibrium is a solution concept in non-strictly competitive, non-cooperative game theory that finds applications in various scientific and engineering disciplines. A non-strictly competitive, non-cooperative game model is presented…

We propose a model of inter-bank lending and borrowing which takes into account clearing debt obligations. The evolution of log-monetary reserves of $N$ banks is described by coupled diffusions driven by controls with delay in their drifts.…

We study Nash equilibria for the deterministic ergodic N-players game. We introduce pure strategies, mixed strategies and Nash equilibria associated with those. We show that a Nash equilibrium in mixed strategies exists and it is a Mather…

We analyze a market impact game between $n$ risk averse agents who compete for liquidity in a market impact model with permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to…

This paper combines ideas from Q-learning and fictitious play to define three reinforcement learning procedures which converge to the set of stationary mixed Nash equilibria in identical interest discounted stochastic games. First, we…

We study a setting in which two players play a (possibly approximate) Nash equilibrium of a bimatrix game, while a learner observes only their actions and has no knowledge of the equilibrium or the underlying game. A natural question is…

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…

In this paper, we apply the idea of fictitious play to design deep neural networks (DNNs), and develop deep learning theory and algorithms for computing the Nash equilibrium of asymmetric $N$-player non-zero-sum stochastic differential…

We consider 2-player stochastic games with perfectly observed actions, and study the limit, as the discount factor goes to one, of the equilibrium payoffs set. In the usual setup where current states are observed by the players, we show…

In multi-agent dynamic games, the Nash equilibrium state trajectory of each agent is determined by its cost function and the information pattern of the game. However, the cost and trajectory of each agent may be unavailable to the other…

This paper addresses a class of network games played by dynamic agents using their outputs. Unlike most existing related works, the Nash equilibrium in this work is defined by functions of agent outputs instead of full agent states, which…

Starting from a heuristic learning scheme for N-person games, we derive a new class of continuous-time learning dynamics consisting of a replicator-like drift adjusted by a penalty term that renders the boundary of the game's strategy space…

In this paper we study the zero-sum and nonzero-sum differential games with not assuming Isaacs condition. Along with the partition $\pi$ of the time interval $[0,T]$, we choose the suitable random non-anticipative strategy with delay to…

Through a stochastic control theoretic approach, we analyze reputation games where a strategic long-lived player acts in a sequential repeated game against a collection of short-lived players. The key assumption in our model is that the…