Related papers: Affine Normal Play

We exhibit the rich structure of the set of correlated equilibria by analyzing the simplest of polynomial games: the mixed extension of matching pennies. We show that while the correlated equilibrium set is convex and compact, the structure…

We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…

Strategic interactions between a group of individuals or organisations can be modelled as games played on networks, where a player's payoff depends not only on their actions but also on those of their neighbours. Inferring the network…

Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier)…

We study variations of classical combinatorial games on two finite heaps of tokens, a.k.a. \emph{subtraction games}. Given non-negative integers $p_1,q_1, p_2,q_2$, where $p_1q_2 > q_1p_2$, $p_1>0$ and $q_2>0$, two players alternate in…

We study so-called invariant games played with a fixed number $d$ of heaps of matches. A game is described by a finite list $\mathcal{M}$ of integer vectors of length $d$ specifying the legal moves. A move consists in changing the current…

This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…

Sequential equilibrium is one of the most fundamental refinements of Nash equilibrium for games in extensive form. However, it is not defined for extensive-form games in which a player can choose among a continuum of actions. We define a…

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…

A classic model to study strategic decision making in multi-agent systems is the normal-form game. This model can be generalised to allow for an infinite number of pure strategies leading to continuous games. Multi-objective normal-form…

An interval in a combinatorial structure S is a set I of points which relate to every point from S I in the same way. A structure is simple if it has no proper intervals. Every combinatorial structure can be expressed as an inflation of a…

We present a new variant of the potential game and show that certain compact subsets of $\R^n$, including a large class of self-affine sets, are winning in our game. We prove that sets with sufficiently strong winning conditions are…

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…

Consider equipping an alphabet $\mathcal{A}$ with a group action that partitions the set of words into equivalence classes which we call patterns. We answer standard questions for the Penney's game on patterns and show non-transitivity for…

A new mathematical model for evolutionary games on graphs is proposed to extend the classical replicator equation to finite populations of players organized on a network with generic topology. Classical results from game theory,…

We present a general way of defining various reduction games on \omega\ which "represent" corresponding topologically defined classes of functions. In particular, we will show how to construct games for piecewise defined functions, for…

Quantum phenomena have remained largely inaccessible to the general public. This can be attributed to the fact that we do not experience quantum mechanics on a tangible level in our daily lives. Games can provide an environment in which…

In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…

Standard game theory assumes that the structure of the game is common knowledge among players. We relax this assumption by considering extensive games where agents may be unaware of the complete structure of the game. In particular, they…

We develop a theory of combinatorial games that is appropriate for describing positions in Hex and other monotone set coloring games. We consider two natural conditions on such games: a game is monotone if all moves available to both…