Related papers: The Category of Node-and-Choice Extensive-Form Gam…
Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide…
This paper has two central aims: first, to provide simple conditions under which the generalized games in choice form and, consequently, the abstract economies, admit equilibrium; second, to study the solvability of several types of systems…
Pursuing a new approach to the study of infinite games in combinatorics, we introduce the categories $\mathbf{Game}_{A}$ and $\mathbf{Game}_{B}$ and improve some classical results concerning topological games related to the duality between…
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…
Finite games in normal form and their mixed extensions are a corner stone of noncooperative game theory. Often generic finite games and their mixed extensions are considered. But the properties which one expects in generic games and the…
Network games provide a powerful framework for modeling agent interactions in networked systems, where players are represented by nodes in a graph and their payoffs depend on the actions taken by their neighbors. Extending the framework of…
In the flavour of categorical quantum mechanics, we extend nonlocal games to allow quantum questions and answers, using quantum sets (special symmetric dagger Frobenius algebras) and the quantum functions of Musto, Reutter, and Verdon…
Concavity and its refinements underpin tractability in multiplayer games, where players independently choose actions to maximize their own payoffs which depend on other players' actions. In concave games, where players' strategy sets are…
We build a cartesian closed category, called Cho, based on event structures. It allows an interpretation of higher-order stateful concurrent programs that is refined and precise: on the one hand it is conservative with respect to standard…
Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the…
This paper uses category theory to develop an entirely new approach to approximate game theory. Game theory is the study of how different agents within a multi-agent system take decisions. At its core, game theory asks what an optimal…
We use a reformulation of compositional game theory to reunite game theory with game semantics, by viewing an open game as the System and its choice of contexts as the Environment. Specifically, the system is jointly controlled by $n \geq…
We study the problem of computing all Nash equilibria of a subclass of finite normal form games. With algebraic characterization of the games, we present a method for computing all its Nash equilibria. Further, we present a method for…
We present a game semantics for intuitionistic type theory. Specifically, we propose categories with families of a new variant of games and strategies for both extensional and intensional variants of the type theory with dependent function,…
This paper introduces a unified framework called cooperative extensive form games, which (i) generalizes standard non-cooperative games, and (ii) allows for more complex coalition formation dynamics than previous concepts like…
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…
Several variants of nonlocal games have been considered in the study of quantum entanglement and nonlocality. This paper concerns two of these variants, called quantum-classical games and extended nonlocal games. We give a construction of…
We study pure-strategy Nash equilibria in multi-player concurrent deterministic games, for a variety of preference relations. We provide a novel construction, called the suspect game, which transforms a multi-player concurrent game into a…
Synchronous correlations provide a class of nonlocal games that behave like functions between finite sets. In this work we examine categories whose morphisms are games with synchronous classical, quantum, or general nonsignaling…
We consider two-player random extensive form games where the payoffs at the leaves are independently drawn uniformly at random from a given feasible set C. We study the asymptotic distribution of the subgame perfect equilibrium outcome for…