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Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…

Computer Science and Game Theory · Computer Science 2022-07-21 Jan Kretinsky , Emanuel Ramneantu , Alexander Slivinskiy , Maximilian Weininger

We axiomatize the first-order theories of exponential integer parts of real-closed exponential fields in a language with $2^x$, in a language with a predicate for powers of 2, and in the basic language of ordered rings. In particular, the…

Logic · Mathematics 2025-10-07 Emil Jeřábek

This project aims to motivate research in competitive human-robot interaction by creating a robot competitor that can challenge human users in certain scenarios such as physical exercise and games. With this goal in mind, we introduce the…

Robotics · Computer Science 2022-02-16 Boling Yang , Golnaz Habibi , Patrick E. Lancaster , Byron Boots , Joshua R. Smith

The containment game is a full information game for two players, initialised with a set of occupied vertices in an infinite connected graph $G$. On the $t$-th turn, the first player, called Spreader, extends the occupied set to $g(t)$…

Combinatorics · Mathematics 2025-12-30 Ohad Noy Feldheim , Itamar Israeli

A new mathematical model for evolutionary games on graphs is proposed to extend the classical replicator equation to finite populations of players organized on a network with generic topology. Classical results from game theory,…

Dynamical Systems · Mathematics 2021-09-01 Dario Madeo , Chiara Mocenni

The 'Cheating Robot' version of Cops and Robbers is played on a finite, simple, connected graph. The players move in the same time period. However, before moving, the robot observes to which vertices the cops are moving and it is fast…

Combinatorics · Mathematics 2021-03-12 Melissa A. Huggan , Richard J. Nowakowski

We consider an online vector balancing game where vectors $v_t$, chosen uniformly at random in $\{-1,+1\}^n$, arrive over time and a sign $x_t \in \{-1,+1\}$ must be picked immediately upon the arrival of $v_t$. The goal is to minimize the…

Data Structures and Algorithms · Computer Science 2020-07-14 Nikhil Bansal , Joel H. Spencer

We study two-player games with alternating moves played on infinite trees. Our main focus is on the case where the trees are full (regular) and the winning set is open (with respect to the product topology on the tree). Gale and Stewart…

Optimization and Control · Mathematics 2026-02-17 Dean Kraizberg

We introduce two-player games which build words over infinite alphabets, and we study the problem of checking the existence of winning strategies. These games are played by two players, who take turns in choosing valuations for variables…

Logic in Computer Science · Computer Science 2023-06-22 Diego Figueira , Anirban Majumdar , M. Praveen

Turn-based discounted-sum games are two-player zero-sum games played on finite directed graphs. The vertices of the graph are partitioned between player 1 and player 2. Plays are infinite walks on the graph where the next vertex is decided…

Computer Science and Game Theory · Computer Science 2024-05-21 Ali Asadi , Krishnendu Chatterjee , Raimundo Saona , Jakub Svoboda

In a monotonic sequence game, two players alternately choose elements of a sequence from some fixed ordered set. The game ends when the resulting sequence contains either an ascending subsequence of length a or a descending one of length d.…

Combinatorics · Mathematics 2007-05-23 M. Albert , R. Aldred , M. Atkinson , C. Handley , D. Holton , D. McCaughan , B. Sagan

We develop value iteration-based algorithms to solve in a unified manner different classes of combinatorial zero-sum games with mean-payoff type rewards. These algorithms rely on an oracle, evaluating the dynamic programming operator up to…

Computer Science and Game Theory · Computer Science 2024-11-12 Xavier Allamigeon , Stéphane Gaubert , Ricardo D. Katz , Mateusz Skomra

The winning condition of a parity game with costs requires an arbitrary, but fixed bound on the cost incurred between occurrences of odd colors and the next occurrence of a larger even one. Such games quantitatively extend parity games…

Logic in Computer Science · Computer Science 2023-06-22 Alexander Weinert , Martin Zimmermann

A binary game is introduced and analysed. N players have to choose one of the two sides independently and those on the minority side win. Players uses a finite set of ad hoc strategies to make their decision, based on the past record. The…

adap-org · Physics 2015-06-24 Damien Challet , Yi-Cheng Zhang

When are all positions of a game numbers? We show that two properties are necessary and sufficient. These properties are consequences of that, in a number, it is not an advantage to be the first player. One of these properties implies the…

Combinatorics · Mathematics 2021-01-26 Alda Carvalho , Melissa A. Huggan , Richard J. Nowakowski , Carlos Pereira dos Santos

We analyze the computational complexity of two 2-player games involving packing objects into a box. In the first game, players alternate drawing polycubes from a shared pile and placing them into an initially empty box in any available…

Computational Complexity · Computer Science 2019-11-19 Oliver Korten

An open problem posed by the first author is the complexity to decide whether a sequence of nonnegative integer numbers can be the final score of a football tournament. In this paper we propose polynomial time approximate and exponential…

Discrete Mathematics · Computer Science 2012-07-27 A. Iványi , J. E. Schoenfield

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

Computer Science and Game Theory · Computer Science 2017-04-05 Thomas Brihaye , Gilles Geeraerts , Axel Haddad , Engel Lefaucheux , Benjamin Monmege

We consider graph games of infinite duration with winning conditions in parameterized linear temporal logic, where the temporal operators are equipped with variables for time bounds. In model checking such specifications were introduced as…

Computer Science and Game Theory · Computer Science 2011-06-08 Martin Zimmermann

Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them…

Computer Science and Game Theory · Computer Science 2015-07-01 Hugo Gimbert , Florian Horn