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This paper explores the Nash equilibria of a variant of the Colonel Blotto game, which we call the Asymmetric Colonel Blotto game. In the Colonel Blotto game, two players simultaneously distribute forces across $n$ battlefields. Within each…

Computer Science and Game Theory · Computer Science 2017-08-29 Simon Rubinstein-Salzedo , Yifan Zhu

Cooperative 2-matching games are a generalization of cooperative matching games, where the value function is given by maximum-weight b-matchings, for a vertex capacity vector $b \leq 2$. We show how to separate over the core of 2-matching…

Computer Science and Game Theory · Computer Science 2025-02-12 Laura Sanità , Lucy Verberk

In repeated games, players choose actions concurrently at each step. We consider a parameterized setting of repeated games in which the players form a population of an arbitrary size. Their utility functions encode a reachability objective.…

Computer Science and Game Theory · Computer Science 2025-10-06 Nathalie Bertrand , Patricia Bouyer , Luc Lapointe , Corto Mascle

We prove that finding an $\epsilon$-approximate Nash equilibrium is PPAD-complete for constant $\epsilon$ and a particularly simple class of games: polymatrix, degree 3 graphical games, in which each player has only two actions. As…

Computer Science and Game Theory · Computer Science 2016-09-14 Aviad Rubinstein

We analyze the computational complexity of the video game "CELESTE" and prove that solving a generalized level in it is NP-Complete. Further, we also show how, upon introducing a small change in the game mechanics (adding a new game…

Computational Complexity · Computer Science 2022-12-02 Zeeshan Ahmed , Alapan Chaudhuri , Kunwar Shaanjeet Singh Grover , Ashwin Rao , Kushagra Garg , Pulak Malhotra

The class of totally balanced games is a class of transferable-utility coalitional games providing important models of cooperative behavior used in mathematical economics. They coincide with market games of Shapley and Shubik and every…

Combinatorics · Mathematics 2021-03-01 Tomáš Kroupa , Milan Studený

Creating and evaluating games manually is an arduous and laborious task. Procedural content generation can aid by creating game artifacts, but usually not an entire game. Evolutionary game design, which combines evolutionary algorithms with…

Artificial Intelligence · Computer Science 2024-02-02 Lana Bertoldo Rossato , Leonardo Boaventura Bombardelli , Anderson Rocha Tavares

We study the problem of checking for the existence of constrained pure Nash equilibria in a subclass of polymatrix games defined on weighted directed graphs. The payoff of a player is defined as the sum of nonnegative rational weights on…

Computer Science and Game Theory · Computer Science 2016-11-30 Sunil Simon , Dominik Wojtczak

We investigate the complexity of the platform video game Celeste. We prove that navigating Celeste is PSPACE-hard in five different ways, corresponding to different subsets of the game mechanics. In particular, we prove the game PSPACE-hard…

Computational Complexity · Computer Science 2022-11-23 Lily Chung , Erik D. Demaine

We study multiplayer turn-based games played on a finite directed graph such that each player aims at satisfying an omega-regular Boolean objective. Instead of the well-known notions of Nash equilibrium (NE) and subgame perfect equilibrium…

Computer Science and Game Theory · Computer Science 2018-08-16 Thomas Brihaye , Véronique Bruyère , Aline Goeminne , Jean-François Raskin

This paper considers a natural ruleset for playing a partisan combinatorial game on a directed graph, which we call Digraph Placement. Given a digraph $G$ with a not necessarily proper $2$-coloring of $V(G)$, the Digraph Placement game…

Combinatorics · Mathematics 2025-04-15 Alexander Clow , Neil A McKay

In this paper, we first devise two algorithms to determine whether or not a bimatrix game has a strategically equivalent zero-sum game. If so, we propose an algorithm that computes the strategically equivalent zero-sum game. If a given…

Computer Science and Game Theory · Computer Science 2021-08-12 Jianzong Pi , Joseph L. Heyman , Abhishek Gupta

We introduce and study pawn games, a class of two-player zero-sum turn-based graph games. A turn-based graph game proceeds by placing a token on an initial vertex, and whoever controls the vertex on which the token is located, chooses its…

Computer Science and Game Theory · Computer Science 2025-04-09 Guy Avni , Pranav Ghorpade , Shibashis Guha

We study the existence of mixed-strategy equilibria in concurrent games played on graphs. While existence is guaranteed with safety objectives for each player, Nash equilibria need not exist when players are given arbitrary terminal-reward…

Computer Science and Game Theory · Computer Science 2016-09-15 Patricia Bouyer , Nicolas Markey , Daniel Stan

We investigate a two-stage competitive model involving multiple contests. In this model, each contest designer chooses two participants from a pool of candidate contestants and determines the biases. Contestants strategically distribute…

Computer Science and Game Theory · Computer Science 2023-12-21 Xiaotie Deng , Hangxin Gan , Ningyuan Li , Weian Li , Qi Qi

We study a Stackelberg game to examine how two agents determine to cooperate while competing with each other. Each selects an arrival time to a destination, the earlier one fetching a higher reward. There is, however, an inherent penalty in…

Computer Science and Game Theory · Computer Science 2024-07-30 Chenlan Wang , Mehrdad Moharrami , Mingyan Liu

We discuss the game of Zombie Dice, published by Steve Jackson Games. This game includes green, yellow, and red dice. Each die has brain, footprint, and shotgun symbols on it, with each color of dice having a different amount of each…

Probability · Mathematics 2014-06-03 Heather L. Cook , David G. Taylor

Computing equilibria of games is a central task in computer science. A large number of results are known for \emph{Nash equilibrium} (NE). However, these can be adopted only when coalitions are not an issue. When instead agents can form…

Computer Science and Game Theory · Computer Science 2017-11-20 Nicola Gatti , Marco Rocco , Tuomas Sandholm

In this paper, we introduce a two-player impartial game on graphs, called a {\em feedback game}, which is a variant of the generalized geography. We study the feedback game on Eulerian graphs. In particular, we show that the…

Computer Science and Game Theory · Computer Science 2020-02-25 Naoki Matsumoto , Atsuki Nagao

The Hanano Puzzle is a one-player game with irreversible gravity, where the goal is to make colored blocks make contact with flowers of the corresponding color. The game Jelly no Puzzle shares similar mechanics. In general, determining if a…

Computational Complexity · Computer Science 2026-01-14 Michael C. Chavrimootoo , Jin Seok Youn