Related papers: Scoring Play Combinatorial Games
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,…
In recent work, Watanabe, Eberhart, Asada, and Hasuo have shown that parity games can be seen as string diagrams, that is, as the morphisms of a symmetric monoidal category, an algebraic structure with two different operations of…
Game-theoretic characterizations of process equivalences traditionally form a central topic in concurrency; for example, most equivalences on the classical linear-time / branching-time spectrum come with such characterizations. Recent work…
Combinatorial games are two-player games of pure strategy where the players, usually called Left and Right, move alternately. In this paper, we introduce Cheating Robot games. These arise from simultaneous-play combinatorial games where one…
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…
In this tutorial, the basics of game theory are introduced along with an overview of its most recent and emerging applications in signal processing. One of the main features of this contribution is to gather in a single paper some…
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.…
The sequential equilibrium is a standard solution concept for extensive-form games with imperfect information that includes an explicit representation of the players' beliefs. An assessment consisting of a strategy and a belief is a…
We study unique games and estimate some of their values. We prove that if a unique game has a quantum-assisted value close to 1, then it must have a perfect deterministic strategy. We introduce a family of unique games based on groups that…
We study games with finitely many participants, each having finitely many choices. We consider the following categories of participants: (I) populations: sets of nonatomic agents, (II) atomic splittable players, (III) atomic non splittable…
The $\mathscr{P}$-position sets of some combinatorial games have special combinatorial structures. For example, the $\mathscr{P}$-position set of the hexad game, first investigated by Conway and Ryba, is the block set of the Steiner system…
I present a formal connection between algebraic effects and game semantics, two important lines of work in programming languages semantics with applications in compositional software verification. Specifically, the algebraic signature…
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…
Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural…
A group of students in 7-9 grades are inventing combinatorial impartial games. The games are played on graphs, piles, and grids. We found winning positions, optimal strategies, and other interesting facts about the games.
In this paper the set of value functions of all-possible zero-sum differential games with terminal payoff is characterized. The necessary and sufficient condition for a given function to be a value of some differential game with terminal…
The computation of a solution concept of a cooperative game usually employs values of all coalitions. However, in some applications, the values of some of the coalitions might be unknown due to high costs associated with their determination…
We consider a setting in which a principal gets to choose which game from some given set is played by a group of agents. The principal would like to choose a game that favors one of the players, the social preferences of the players, or the…
Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…
We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. The language is well established in quantum physics, quantum computing and quantum linguistic with the…