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In this paper, we introduce a novel equilibrium concept, called the equilibrium cycle, which seeks to capture the outcome of oscillatory game dynamics. Unlike the (pure) Nash equilibrium, which defines a fixed point of mutual best…

Theoretical Economics · Economics 2025-10-07 Tushar Shankar Walunj , Shiksha Singhal , Veeraruna Kavitha , Jayakrishnan Nair

We provide a winning strategy for sums of games of MARK-t, an impartial game played on the nonnegative integers where each move consists of subtraction by an integer between 1 and t-1 inclusive, or division by t, rounding down when…

Combinatorics · Mathematics 2011-08-10 Alan Guo

We provide two methodologies in the area of computation theory to solve optimal strategies for board games such as Xi Gua Qi and Go. From experimental results, we find relevance to graph theory, matrix representation, and mathematical…

History and Overview · Mathematics 2025-03-05 Chun-Kai Hwang , John Reuben Gilbert , Tsung-Ren Huang , Chen-An Tsai , Yen-Jen Oyang

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

This paper unifies the concepts of evolutionary games and quantum strategies. First, we state the formulation and properties of classical evolutionary strategies, with focus on the destinations of evolution in 2-player 2-strategy games. We…

Quantum Physics · Physics 2011-04-21 Ming Lam Leung

The deduction game may be thought of as a variant on the classical game of cops and robber in which the cops (searchers) aim to capture an invisible robber (evader); each cop is allowed to move at most once, and cops situated on different…

Combinatorics · Mathematics 2025-10-30 Andrea C. Burgess , Nancy E. Clarke , Shannon L. Fitzpatrick , Melissa A. Huggan

Permutation sorting, one of the fundamental steps in pre-processing data for the efficient application of other algorithms, has a long history in mathematical research literature and has numerous applications. Two special-purpose sorting…

Combinatorics · Mathematics 2017-08-22 K. L. M. Adamyk , E. Holmes , G. R. Mayfield , D. J. Moritz , M. Scheepers , B. E. Tenner , H. C. Wauck

Graph Pebbling is a well-studied single-player game on graphs. We introduce the game of Blocking Pebbles which adapts Graph Pebbling into a two-player strategy game in order to examine it within the context of Combinatorial Game Theory.…

Combinatorics · Mathematics 2017-12-18 Michael Fisher , Craig Tennenhouse

The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…

Combinatorics · Mathematics 2024-05-14 David Gamarnik , Mihyun Kang , Pawel Pralat

The game of Nim as played on graphs was introduced in Nim on Graphs I and extended in Nim on Graphs II by Masahiko Fukuyama. His papers detail the calculation of Grundy numbers for graphs under specific circumstances. We extend these…

Combinatorics · Mathematics 2010-10-08 Lindsay Erickson

Snake is a classic computer game, which has been around for decades. Based on this game, we study the game of Snake on arbitrary undirected graphs. A snake forms a simple path that has to move to an apple while avoiding colliding with…

Discrete Mathematics · Computer Science 2025-06-27 Denise Graafsma , Bodo Manthey , Alexander Skopalik

The Jungle Game is used in population dynamics to describe cyclic competition among species that interact via a food chain. The dynamics of the Jungle Game supports a heteroclinic network whose cycles represent coexisting species. The…

Dynamical Systems · Mathematics 2024-01-17 Sofia B. S. D. Castro , Ana M. J. Ferreira , Isabel S. Labouriau

We introduce CUT, the class of 2-player partition games. These are NIM type games, played on a finite number of heaps of beans. The rules are given by a set of positive integers, which specifies the number of allowed splits a player can…

Combinatorics · Mathematics 2026-04-17 Antoine Dailly , Eric Duchene , Urban Larsson , Gabrielle Paris

We study a complementarity game as a systematic tool for the investigation of the interplay between individual optimization and population effects and for the comparison of different strategy and learning schemes. The game randomly pairs…

Populations and Evolution · Quantitative Biology 2010-11-17 Juergen Jost , Wei Li

In this paper I study the natural selection between two games to determine, which game will dominate in the community as a result of natural selection. The formalization of this question in the form of a parametrized game and the…

Populations and Evolution · Quantitative Biology 2024-09-25 Georgiy Karev

We consider two-player games played on finite graphs equipped with costs on edges and introduce two winning conditions, cost-parity and cost-Streett, which require bounds on the cost between requests and their responses. Both conditions…

Logic in Computer Science · Computer Science 2015-07-01 Nathanaël Fijalkow , Martin Zimmermann

Rock is wrapped by paper, paper is cut by scissors, and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart…

Concavity and its refinements underpin tractability in multiplayer games, where players independently choose actions to maximize their own payoffs which depend on other players' actions. In concave games, where players' strategy sets are…

Computer Science and Game Theory · Computer Science 2025-12-12 Vincent Leon , Iosif Sakos , Ryann Sim , Antonios Varvitsiotis

This paper describes a basic model of a gift economy in the shape of a Giving Game and reveals the fundamental structure of such a game. Main result is that the game shows a community effect in that a small subgroup of players eventually…

Theoretical Economics · Economics 2021-05-26 Peter Weijland

The authors (Cason, Friedman and Hopkins, Reviews of Economics Studies, 2014) claimed a result that the treatments (using simultaneous matching in discrete time) replicate previous results that exhibit weak or no cycles. After correct two…

Methodology · Statistics 2013-11-20 Zhijian Wang , Siqian Zhu , Bin Xu