Related papers: Positional Games
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…
In this paper, we introduce open parity games, which is a compositional approach to parity games. This is achieved by adding open ends to the usual notion of parity games. We introduce the category of open parity games, which is defined…
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…
Game theory is used by all behavioral sciences, but its development has long centered around tools for relatively simple games and toy systems, such as the economic interpretation of equilibrium outcomes. Our contribution, compositional…
Temporal graphs are a popular modelling mechanism for dynamic complex systems that extend ordinary graphs with discrete time. Simply put, time progresses one unit per step and the availability of edges can change with time. We consider the…
Coloring games are combinatorial games where the players alternate painting uncolored vertices of a graph one of $k > 0$ colors. Each different ruleset specifies that game's coloring constraints. This paper investigates six impartial…
We define a two-player combinatorial game in which players take alternate turns; each turn consists on deleting a vertex of a graph, together with all the edges containing such vertex. If any vertex became isolated by a player's move then…
Game theory provides a mathematical framework for analysing strategic situations involving at least two players. Normal-form games model situations where the players simultaneously pick their moves. In this thesis we explore the strategic…
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…
We show the value of positions of the combinatorial game ``Toads and Frogs''. We present new values of starting positions. Moreover, we discuss the values of all positions with exactly one $\Box, \regT^{a}\Box\Box \regF^{a}, \regT^{a} \Box…
Coordination games have been of interest to game theorists, economists, and ecologists for many years to study such problems as the emergence of local conventions and the evolution of cooperative behavior. Approaches for understanding the…
The classical Maker-Breaker positional game is played on a board which is a hypergraph $\mathcal{H}$, with two players, Maker and Breaker, alternately claiming vertices of $\mathcal{H}$ until all the vertices are claimed. When the game…
What payoffs are positionally determined for deterministic two-player antagonistic games on finite directed graphs? In this paper we study this question for payoffs that are continuous. The main reason why continuous positionally determined…
We study the class of potential games that are also graphical games with respect to a given graph $G$ of connections between the players. We show that, up to strategic equivalence, this class of games can be identified with the set of…
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
Game theoretical techniques have recently become prevalent in many engineering applications, notably in communications. With the emergence of cooperation as a new communication paradigm, and the need for self-organizing, decentralized, and…
Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model…
In this paper, we will be proving mathematically that scoring play combinatorial game theory covers all combinatorial games. That is, there is a sub-set of scoring play games that are identical to the set of normal play games, and a…
Independent set games are cooperative games defined on graphs, where players are edges and the value of a coalition is the maximum cardinality of independent sets in the subgraph defined by the coalition. In this paper, we investigate the…
Game theory has by now found numerous applications in various fields, including economics, industry, jurisprudence, and artificial intelligence, where each player only cares about its own interest in a noncooperative or cooperative manner,…