Related papers: Affine Normal Play

In this paper we will discuss scoring play games. We will give the basic definitions for scoring play games, and show that they form a well defined set, with clear and distinct outcome classes under these definitions. We will also show that…

A class of discrete Bidding Combinatorial Games that generalize alternating normal play was introduced by Kant, Larsson, Rai, and Upasany (2022). The major questions concerning optimal outcomes were resolved. By generalizing standard game…

The traditional mathematical model for an impartial combinatorial game is defined recursively as a set of the options of the game, where the options are games themselves. We propose a model called gamegraph, together with its generalization…

Two players alternate moves in the following impartial combinatorial game: Given a finitely generated abelian group $A$, a move consists of picking some nonzero element $a \in A$. The game then continues with the quotient group $A/ \langle…

Incomplete cooperative games generalise the classical model of cooperative games by omitting the values of some of the coalitions. This allows to incorporate uncertainty into the model and study the underlying games as well as possible…

Relying on recent generalizations of the Fra\"iss\'e theory to a broader category-theoretic context, we study the class of abstract finite games played between two players and show the existence of an infinitetly countable game which is…

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…

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…

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…

It is non-trivial to design engaging and balanced sets of game rules. Modern chess has evolved over centuries, but without a similar recourse to history, the consequences of rule changes to game dynamics are difficult to predict. AlphaZero…

By resorting to the vector space structure of finite games, skew-symmetric games (SSGs) are proposed and investigated as a natural subspace of finite games. First of all, for two player games, it is shown that the skew-symmetric games form…

Although mixed extensions of finite games always admit equilibria, this is not the case for countable games, the best-known example being Wald's pick-the-larger-integer game. Several authors have provided conditions for the existence of…

We present a version of the Banach-Mazur game, where open sets are replaced by elements of a fixed partially ordered set. We show how to apply it in the theory of Fraisse limits and beyond, obtaining simple proofs of universality of certain…

Finite objects and more specifically finite games are formalized using induction, whereas infinite objects are formalized using coinduction. In this article, after an introduction to the concept of coinduction, we revisit on infinite…

The focus of this essay is a rigorous treatment of infinite games. An infinite game is defined as a play consisting of a fixed number of players whose sequence of moves is repeated, or iterated ad infinitum. Each sequence corresponds to a…

Candogan et al. (2011) provide an orthogonal direct-sum decomposition of finite games into potential, harmonic and nonstrategic components. In this paper we study the issue of decomposing games that are strategically equivalent from a…

We introduce the game of infinite Hex, extending the familiar finite game to natural play on the infinite hexagonal lattice. Whereas the finite game is a win for the first player, we prove in contrast that infinite Hex is a draw -- both…

Probabilistic concurrent/distributed strategies have so far not been investigated thoroughly in the context of imperfect information, where the Player has only partial knowledge of the moves made by the Opponent. In a situation where the…

We examine short combinatorial games for three or more players under a new play convention in which a player who cannot move on their turn is the unique loser. We show that many theorems of impartial and partizan two-player games under…

We consider extensive games with perfect information with well-founded game trees and study the problems of existence and of characterization of the sets of subgame perfect equilibria in these games. We also provide such characterizations…