Related papers: Progress on mis\`ere dead ends: game comparison, c…
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…
The theory of combinatorial game (like board games) and the theory of social games (where one looks for Nash equilibria) are normally considered as two separate theories. Here we shall see what comes out of combining the ideas. The central…
Games on recursive game graphs can be used to reason about the control flow of sequential programs with recursion. In games over recursive game graphs, the most natural notion of strategy is the modular strategy, i.e., a strategy that is…
These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person…
Fictitious play (FP) is one of the most fundamental game-theoretical learning frameworks for computing Nash equilibrium in $n$-player games, which builds the foundation for modern multi-agent learning algorithms. Although FP has provable…
Combinatorial games are widely used in finite model theory, constraint satisfaction, modal logic and concurrency theory to characterize logical equivalences between structures. In particular, Ehrenfeucht-Fraisse games, pebble games, and…
We prove a recent conjecture of Duch\^ene and Rigo, stating that every complementary pair of homogeneous Beatty sequences represents the solution to an \emph{invariant} impartial game. Here invariance means that each available move in a…
We establish the existence and uniqueness of distributed equilibria to possibly nonsymmetric $N$ player differential games with interactions through controls under displacement semimonotonicity assumptions. Surprisingly, the nonseparable…
Concurrent multi-player games with $\omega$-regular objectives are a standard model for systems that consist of several interacting components, each with its own objective. The standard solution concept for such games is Nash Equilibrium,…
This compendium features advances in Game Theory, to include: Classical Game Theory: Cooperative and non-cooperative. Zero-sum and non-zero sum games. Potential and Congestion games. Mean Field games. Nash Equilibrium, Correlated Nash…
We study turn-based quantitative games of infinite duration opposing two antagonistic players and played over graphs. This model is widely accepted as providing the adequate framework for formalizing the synthesis question for reactive…
Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. In this introduction we develop the fundamentals of…
This brief paper describes the single-player card game called "Perpetual Motion" and reports on a computational analysis of the game's outcome. The analysis follows a Monte Carlo methodology based on a sample of 10,000 randomly generated…
A computation in the continuation monad returns a final result given a continuation, ie. it is a function with type $(X \to R) \to R$. If we instead return the intermediate result at $X$ then our computation is called a selection function.…
We propose a model for games in which the players have shared access to a blockchain that allows them to deploy smart contracts to act on their behalf. This changes fundamental game-theoretic assumptions about rationality since a contract…
Most existing results about \emph{last-iterate convergence} of learning dynamics are limited to two-player zero-sum games, and only apply under rigid assumptions about what dynamics the players follow. In this paper we provide new results…
We show that partizan games admit canonical forms in mis\`ere play. The proof is a synthesis of the canonical form theorems for normal-play partizan games and mis\`ere-play impartial games. It is fully constructive, and algorithms readily…
The paper is devoted to inverse Stackelberg games with many players. We consider both static and differential games. The main assumption of the paper is the compactness of the strategy sets. We obtain the characterization of inverse…
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…
We study dynamic finite-player and mean-field stochastic games within the framework of Markov perfect equilibria (MPE). Our focus is on discrete time and space structures without monotonicity. Unlike their continuous-time analogues,…