Related papers: Conway games, algebraically and coalgebraically

We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…

We use ideas from distributed computing and game theory to study dynamic and decentralized environments in which computational nodes, or decision makers, interact strategically and with limited information. In such environments, which arise…

We apply ideas from abstract argumentation theory to study cooperative game theory. Building on Dung's results in his seminal paper, we further the correspondence between Dung's four argumentation semantics and solution concepts in…

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…

In view of the complexity of the dynamics of learning in games, we seek to decompose a game into simpler components where the dynamics' long-run behavior is well understood. A natural starting point for this is Helmholtz's theorem, which…

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…

We present infinite extensive strategy profiles with perfect information and we show that replacing finite by infinite changes the notions and the reasoning tools. The presentation uses a formalism recently developed by logicians and…

Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…

The objective of this book is to give a comprehensive presentation of the research field concerned with infinite duration games on graphs. Historically, these game models appeared in the study of automata and logic, and they later became…

We extend the formalism of Conjectural Variations games to Stackelberg games involving multiple leaders and a single follower. To solve these nonconvex games, a common assumption is that the leaders compute their strategies having perfect…

We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…

Game Logic is an excellent setting to study proofs-about-programs via the interpretation of those proofs as programs, because constructive proofs for games correspond to effective winning strategies to follow in response to the opponent's…

We define solution concepts appropriate for computationally bounded players playing a fixed finite game. To do so, we need to define what it means for a \emph{computational game}, which is a sequence of games that get larger in some…

The beautiful theory of statistical gambling, started by Dubins and Savage (for subfair games) and continued by Kelly and Breiman (for superfair games) has mostly been studied under the unrealistic assumption that we live in a continuous…

Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this…

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…

Players are arranged on a regular lattice and coded with a specific strategy for a pre-defined game. Each player sums their payoffs from playing the game with each of their neighbors, and then adopts the strategy of the most successful…

We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect…

We develop an algebraic and operational framework for quantum isomorphisms of hypergraphs, using tools from compact quantum group theory. We introduce a new synchronous version of the hypergraph isomorphism game whose game algebra uniformly…

We study two-player games played on the infinite graph of sentential forms induced by a context-free grammar (that comes with an ownership partitioning of the non-terminals). The winning condition is inclusion of the derived terminal word…