English
Related papers

Related papers: The game behind oriented percolation

200 papers

We consider 2-player zero-sum stochastic games where each player controls his own state variable living in a compact metric space. The terminology comes from gambling problems where the state of a player represents its wealth in a casino.…

Optimization and Control · Mathematics 2017-02-23 Rida Laraki , Jérôme Renault

We consider a two-player zero-sum game with integral payoff and with incomplete information on one side, where the payoff is chosen among a continuous set of possible payoffs. We prove that the value function of this game is solution of an…

Probability · Mathematics 2012-02-23 Pierre Cardaliaguet , Catherine Rainer

We study the ergodicity of deterministic two-person zero-sum differential games. This property is defined by the uniform convergence to a constant of either the infinite-horizon discounted value as the discount factor tends to zero, or…

Optimization and Control · Mathematics 2020-01-08 Antoine Hochart

We prove that for a class of zero-sum differential games with incomplete information on both sides, the value admits a probabilistic representation as the value of a zero-sum stochastic differential game with complete information, where…

Optimization and Control · Mathematics 2017-01-04 Fabien Gensbittel , Catherine Rainer

We introduce a zero-sum game problem of mean-field type as an extension of the classical zero-sum Dynkin game problem to the case where the payoff processes might depend on the value of the game and its probability law. We establish…

Optimization and Control · Mathematics 2022-05-06 Boualem Djehiche , Roxana Dumitrescu

We study a class of two-player zero-sum stochastic games known as \textit{blind stochastic games}, where players neither observe the state nor receive any information about it during the game. A central concept for analyzing long-duration…

Optimization and Control · Mathematics 2025-11-24 Krishnendu Chatterjee , David Lurie , Raimundo Saona , Bruno Ziliotto

In this paper we introduce and study {\em all-pay bidding games}, a class of two player, zero-sum games on graphs. The game proceeds as follows. We place a token on some vertex in the graph and assign budgets to the two players. Each turn,…

Computer Science and Game Theory · Computer Science 2019-11-20 Guy Avni , Rasmus Ibsen-Jensen , Josef Tkadlec

This paper considers the problem of two-player zero-sum stochastic differential game with both players adopting impulse controls in finite horizon under rather weak assumptions on the cost functions ($c$ and $\chi$ not decreasing in time).…

Optimization and Control · Mathematics 2018-09-26 Brahim El Asri , Sehail Mazid

Priced timed games are two-player zero-sum games played on priced timed automata (whose locations and transitions are labeled by weights modelling the cost of spending time in a state and executing an action, respectively). The goals of the…

Computer Science and Game Theory · Computer Science 2023-06-22 Thomas Brihaye , Gilles Geeraerts , Axel Haddad , Engel Lefaucheux , Benjamin Monmege

In this paper the set of value functions of all-possible zero-sum differential games with terminal payoff is characterized. The necessary and sufficient condition for a given function to be a value of some differential game with terminal…

Optimization and Control · Mathematics 2008-11-12 Yurii Averboukh

We consider a zero sum differential game with lack of observation on one side. The initial state of the system is drawn at random according to some probability $\mu_0$ on $\R^N$. Player-I is informed of the initial position of state while…

Optimization and Control · Mathematics 2012-12-20 Pierre Cardaliaguet , Anne Souquière

In a two-player zero-sum graph game the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. Traditionally, the players alternate turns in moving the token. In {\em bidding…

Theoretical Economics · Economics 2020-12-22 Guy Avni , Ismaël Jecker , Đorđe Žikelić

We study a zero-sum stochastic differential game (SDG) in which one controller plays an impulse control while their opponent plays a stochastic control. We consider an asymmetric setting in which the impulse player commits to, at the start…

Probability · Mathematics 2019-01-31 Parsiad Azimzadeh

We study the value of a two-player zero-sum game on a random matrix $M\in \mathbb{R}^{n\times m}$, defined by $v(M) = \min_{x\in\Delta_n}\max_{y\in \Delta_m}x^T M y$. In the setting where $n=m$ and $M$ has i.i.d. standard Gaussian entries,…

Probability · Mathematics 2026-01-13 Romain Cosson , Laurent Massoulié

Zero-sum stochastic games provide a rich model for competitive decision making. However, under general forms of state uncertainty as considered in the Partially Observable Stochastic Game (POSG), such decision making problems are still not…

Artificial Intelligence · Computer Science 2016-06-23 Auke J. Wiggers , Frans A. Oliehoek , Diederik M. Roijers

For a zero-sum stochastic game which does not satisfy the Isaacs condition, we provide a value function representation for an Isaacs-type equation whose Hamiltonian lies in between the lower and upper Hamiltonians, as a convex combination…

Probability · Mathematics 2016-09-30 Daniel Hernández-Hernández , Mihai Sîrbu

The $(m,b)$ Maker-Breaker percolation game on $(\mathbb{Z}^2)_p$, introduced by Day and Falgas-Ravry, is played in the following way. Before the game starts, each edge of $\mathbb{Z}^2$ is removed independently with probability $1-p$. After…

Probability · Mathematics 2024-02-28 Vojtěch Dvořák , Adva Mond , Victor Souza

We investigate a two-player zero-sum stochastic differential game in which one of the players has more information on the game than his opponent. We show how to construct numerical schemes for the value function of this game, which is given…

Computer Science and Game Theory · Computer Science 2011-11-18 Christine Grün

In the paper we consider the controlled continuous-time Markov chain describing the interacting particles system with the finite number of types. The system is controlled by two players with the opposite purposes. The limiting game as the…

Optimization and Control · Mathematics 2014-12-02 Yurii Averboukh

In this paper we introduce a game whose value functions converge (as a parameter that measures the size of the steps goes to zero) uniformly to solutions to the second order Pucci maximal operators.

Analysis of PDEs · Mathematics 2018-08-24 Pablo Blanc , Juan J. Manfredi , Julio D Rossi