Related papers: Conway games, algebraically and coalgebraically

Combinatorial Scoring games, with the property `extra pass moves for a player does no harm', are characterized. The characterization involves an order embedding of Conway's Normal-play games. Also, we give a theorem for comparing games with…

In the game theory literature, there appears to be little research on equilibrium selection for normal-form games with an infinite strategy space and discontinuous utility functions. Moreover, many existing selection methods are not…

We introduce operational semantics into games. And based on the operational semantics, we establish a full algebra of games, including basic algebra of games, algebra of concurrent games, recursion and abstraction. The algebra can be used…

Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specification, and the other represents a hostile environment. The evolution of the system…

We present what we argue is the generic generalization of Conway's "Game of Life" to a continuous domain. We describe the theoretical model and the explicit implementation on a computer.

We begin by reviewing and proving the basic facts of combinatorial game theory. We then consider scoring games (also known as Milnor games or positional games), focusing on the "fixed-length" games for which all sequences of play terminate…

Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…

Under what conditions do the behaviors of players, who play a game repeatedly, converge to a Nash equilibrium? If one assumes that the players' behavior is a discrete-time or continuous-time rule whereby the current mixed strategy profile…

For a collection of papers in memory of Elwyn Berlekamp (1940-2019), John Conway (1937-2020), and Richard Guy (1916-2020). The Sprague-Grundy theory for finite games without cycles was extended to general finite games by Cedric Smith and by…

In an investigation of the applications of Combinatorial Game Theory to chess, we construct novel mutual Zugzwang positions, explain an otherwise mysterious pawn endgame from "A Guide to Chess Endings" (Euwe and Hooper), show positions…

Game semantics provides an interactive point of view on proofs, which enables one to describe precisely their dynamical behavior during cut elimination, by considering formulas as games on which proofs induce strategies. We are specifically…

We present a definition for the sum of a sequence of combinatorial games. This sum coincides with the classical sum in the case of a converging sequence of real numbers and with the infinitary natural sum in the case of a sequence of…

In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the…

Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players…

Compositional Game Theory is a new, recently introduced model of economic games based upon the computer science idea of compositionality. In it, complex and irregular games can be built up from smaller and simpler games, and the equilibria…

Hybrid games are models which combine discrete, continuous, and adversarial dynamics. Game logic enables proving (classical) existence of winning strategies. We introduce constructive differential game logic (CdGL) for hybrid games, where…

We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals:…

We propose a unifying additive theory for standard conventions in Combinatorial Game Theory, including normal-, mis\`ere- and scoring-play, studied by Berlekamp, Conway, Dorbec, Ettinger, Guy, Larsson, Milley, Neto, Nowakowski, Renault,…

Conways Game of Life is a cellular automaton noted for its rich, complex, and emergent behavior, which seems qualitatively lifelike it exists within a wider space of different rule-sets of cellular automata none of which have been found to…

In this paper, we address a natural question at the intersection of combinatorial game theory and computational complexity: "Can a sum of simple tepid games in canonical form be intractable?" To resolve this fundamental question, we…