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Two standard algorithms for approximately solving two-player zero-sum concurrent reachability games are value iteration and strategy iteration. We prove upper and lower bounds of 2^(m^(Theta(N))) on the worst case number of iterations…

Computer Science and Game Theory · Computer Science 2012-03-02 Kristoffer Arnsfelt Hansen , Rasmus Ibsen-Jensen , Peter Bro Miltersen

This paper presents Hamilton-Jacobi (HJ) formulations for two classes of two-player zero-sum games: one with a maximum cost value over time, and one with a minimum cost value over time. In the zero-sum game setting, player A minimizes the…

Optimization and Control · Mathematics 2021-06-30 Donggun Lee , Claire J. Tomlin

Synthesis of finite-state controllers from high-level specifications in multi-agent systems can be reduced to solving multi-player concurrent games over finite graphs. The complexity of solving such games with qualitative objectives for…

Computer Science and Game Theory · Computer Science 2018-09-28 Shaull Almagor , Rajeev Alur , Suguman Bansal

We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…

Computational Finance · Quantitative Finance 2012-10-10 Timothy C. Johnson

We analyze a zero-sum stochastic differential game between two competing players who can choose unbounded controls. The payoffs of the game are defined through backward stochastic differential equations. We prove that each player's priority…

Probability · Mathematics 2013-03-14 Erhan Bayraktar , Song Yao

We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated…

Analysis of PDEs · Mathematics 2018-07-13 Erhan Bayraktar , Asaf Cohen

We describe an efficient algorithm to compute solutions for the general two-player Blotto game on n battlefields with heterogeneous values. While explicit constructions for such solutions have been limited to specific, largely symmetric or…

Computer Science and Game Theory · Computer Science 2022-06-01 Vianney Perchet , Philippe Rigollet , Thibaut Le Gouic

We explicitly solve the optimal switching problem for one-dimensional diffusions by directly employing the dynamic programming principle and the excessive characterization of the value function. The shape of the value function and the…

Optimization and Control · Mathematics 2009-05-25 Erhan Bayraktar , Masahiko Egami

Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in…

Mathematical Finance · Quantitative Finance 2018-09-11 Masahiko Egami , Rusudan Kevkhishvili

State-of-the-art methods for solving 2-player zero-sum imperfect information games rely on linear programming or regret minimization, though not on dynamic programming (DP) or heuristic search (HS), while the latter are often at the core of…

Artificial Intelligence · Computer Science 2022-10-27 Aurélien Delage , Olivier Buffet , Jilles S. Dibangoye , Abdallah Saffidine

We consider a general nonzero-sum impulse game with two players. The main mathematical contribution of the paper is a verification theorem which provides, under some regularity conditions, a suitable system of quasi-variational inequalities…

Probability · Mathematics 2018-11-09 René Aïd , Matteo Basei , Giorgia Callegaro , Luciano Campi , Tiziano Vargiolu

Bayesian regression games are a special class of two-player general-sum Bayesian games in which the learner is partially informed about the adversary's objective through a Bayesian prior. This formulation captures the uncertainty in regard…

Machine Learning · Computer Science 2021-10-04 Wenshuo Guo , Michael I. Jordan , Tianyi Lin

In this paper, we revisit the two-player continuous-time infinite-horizon linear quadratic differential game problem, where one of the players can sample the state of the system only intermittently due to a sensing constraint while the…

Optimization and Control · Mathematics 2024-06-11 Shubham Aggarwal , Tamer Başar , Dipankar Maity

In this paper we introduce a new two-player zero-sum game whose value function approximates the level set formulation for the geometric evolution by mean curvature of a hypersurface. In our approach the game is played with symmetric rules…

Analysis of PDEs · Mathematics 2026-03-11 Irene Gonzalvez , Alfredo Miranda , Julio D. Rossi , Jorge Ruiz-Cases

We consider two-player random extensive form games where the payoffs at the leaves are independently drawn uniformly at random from a given feasible set C. We study the asymptotic distribution of the subgame perfect equilibrium outcome for…

Computer Science and Game Theory · Computer Science 2015-09-09 Itai Arieli , Yakov Babichenko

This paper introduces state abstraction for two-player zero-sum Markov games (TZMGs), where the payoffs for the two players are determined by the state representing the environment and their respective actions, with state transitions…

Computer Science and Game Theory · Computer Science 2024-12-23 Hiroki Ishibashi , Kenshi Abe , Atsushi Iwasaki

We give an algorithm for solving stochastic parity games with almost-sure winning conditions on {\it lossy channel systems}, under the constraint that both players are restricted to finite-memory strategies. First, we describe a general…

Logic in Computer Science · Computer Science 2019-03-14 Parosh Aziz Abdulla , Lorenzo Clemente , Richard Mayr , Sven Sandberg

Transitions between metastable equilibria in the low-temperature phase of dynamical Ising game with activity spillover are studied in the infinite time limit. It is shown that exponential enhancement due to activity spillover, which takes…

Statistical Mechanics · Physics 2023-08-23 A. Antonov , A. Leonidov , A. Semenov

We provide an algorithm to find the value and an optimal strategy of the solitaire variant of the Ten Thousand dice game in the framework of Markov Control Processes. Once an optimal critical threshold is found, the set of non-stopping…

Optimization and Control · Mathematics 2014-05-30 Fabián Crocce , Ernesto Mordecki

This paper studies a {\it reversible} investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good. Our model allows for general diffusion dynamics on the demand as…

Probability · Mathematics 2013-07-08 Salvatore Federico , Huyen Pham