Related papers: Stochastic hybrid differential games and match rac…

The goal of the paper is to introduce a set of problems which we call mean field games of timing. We motivate the formulation by a dynamic model of bank run in a continuous-time setting. We briefly review the economic and game theoretic…

In this Note, assuming that the generator is uniform Lipschitz in the unknown variables, we relate the solution of a one dimensional backward stochastic differential equation with the value process of a stochastic differential game. Under a…

Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…

We study a class of second order variational inequalities with bilateral constraints. Under certain conditions we show the existence of a unique viscosity solution of these variational inequalities and give a stochastic representation to…

We consider an N-player hierarchical game in which the i-th player's objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of…

This article considers a mean field game model inspired by crowd motion models in which agents aim at reaching a given target set and wish to minimize a cost consisting of an individual running cost, an individual cost depending on the…

We investigate zero-sum turn-based two-player stochastic games in which the objective of one player is to maximize the amount of rewards obtained during a play, while the other aims at minimizing it. We focus on games in which the minimizer…

In this paper, we study a class of zero-sum two-player stochastic differential games with the controlled stochastic differential equations and the payoff/cost functionals of recursive type. As opposed to the pioneering work by Fleming and…

We formulate a new class of two-person zero-sum differential games, in a stochastic setting, where a specification on a target terminal state distribution is imposed on the players. We address such added specification by introducing…

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…

Game logic is a dynamic modal logic which models strategic two person games; it contains propositional dynamic logic (PDL) as a fragment. We propose an interpretation of game logic based on stochastic effectivity functions. A definition of…

Hybrid games are games played on a finite graph endowed with real variables which may model behaviors of discrete controllers of continuous systems. The synthesis problem for hybrid games is decidable for classical objectives (like LTL…

Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic…

We consider multi-player games played on graphs, in which the players aim at fulfilling their own (not necessarily antagonistic) objectives. In the spirit of evolutionary game theory, we suppose that the players have the right to repeatedly…

This paper presents new families of algorithms for the repeated play of two-agent (near) zero-sum games and two-agent zero-sum stochastic games. For example, the family includes fictitious play and its variants as members. Commonly, the…

This paper studies a stochastic dynamic game between two competing teams, each consisting of a network of collaborating agents. Unlike fully cooperative settings, where all agents share a common objective, each team in this game aims to…

In an incomplete market driven by time-changed L\'evy noises we consider the problem of hedging a financial position coupled with the underlying risk of model uncertainty. Then we study hedging under worst-case-scenario. The proposed…

This paper addresses a continuous-time risk-minimizing two-player zero-sum stochastic differential game (SDG), in which each player aims to minimize its probability of failure. Failure occurs in the event when the state of the game enters…

Stochastic games generalize Markov decision processes (MDPs) to a multiagent setting by allowing the state transitions to depend jointly on all player actions, and having rewards determined by multiplayer matrix games at each state. We…

Differential game logic (dGL) is a logic for specifying and verifying properties of hybrid games, i.e. games that combine discrete, continuous, and adversarial dynamics. Unlike hybrid systems, hybrid games allow choices in the system…