Related papers: Compositional Game Theory with Mixed Strategies: P…

Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…

Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…

Probabilistic game structures combine both nondeterminism and stochasticity, where players repeatedly take actions simultaneously to move to the next state of the concurrent game. Probabilistic alternating simulation is an important tool to…

Inspired by the theory of poset games, we introduce a new compound of impartial combinatorial games and provide a complete analysis in the spirit of the Sprague-Grundy theory. Furthermore, we establish several substitution and reduction…

Evolutionary game theory is a common framework to study the evolution of cooperation, where it is usually assumed that the same game is played in all interactions. Here, we investigate a model where the game that is played by two…

Conventional noncooperative game theory hypothesizes that the joint strategy of a set of players in a game must satisfy an "equilibrium concept". All other joint strategies are considered impossible; the only issue is what equilibrium…

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 comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…

When applied to the same game, probability theory and game theory can disagree on calculated values of the Fisher information, the log likelihood function, entropy gradients, the rank and Jacobian of variable transforms, and even the…

We provide a compositional coalgebraic semantics for strategic games. In our framework, like in the semantics of functional programming languages, coalgebras represent the observable behaviour of systems derived from the behaviour of the…

Evolutionary games on networks traditionally involve the same game at each interaction. Here we depart from this assumption by considering mixed games, where the game played at each interaction is drawn uniformly at random from a set of two…

We announce misere-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misere quotients--commutative monoids that encode the additive structure of specific misere-play games. We also…

Often, a given selection game studied in the literature has a known dual game. In dual games, a winning strategy for a player in either game may be used to create a winning strategy for the opponent in the dual. For example, the Rothberger…

Game-theoretic probability uses the structure of gambles to define a concept like probability, but which is more flexible and robust. We show that results in game-theoretic probability can be thought of as minimax theorems for specific…

Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…

In this paper we define the canonical mixed extension of a decision form game. We motivate the necessity to introduce this concept and we show several examples about the new concept. In particular we focus our study upon the mixed…

We present an index theory of equilibria for extensive form games. This requires developing an index theory for games where the strategy sets of players are general polytopes and their payoff functions are multiaffine in the product of…

This book summarizes ongoing research introducing probability space isomorphic mappings into the strategy spaces of game theory. This approach is motivated by discrepancies between probability theory and game theory when applied to the same…

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…

Game semantics has provided adequate models for a variety of programming languages, in which types are interpreted as two-player games and programs as strategies. Melli\`es (2018) suggested that such categories of games and strategies may…