Related papers: Restricted developments in partizan misere game th…

In game-theoretic learning, several agents are simultaneously following their individual interests, so the environment is non-stationary from each player's perspective. In this context, the performance of a learning algorithm is often…

Losing a game is difficult. Recent work of Larsson, Nowakowski, and Santos, as well as that of Siegel, has opened up enticing lines of research into partizan mis\`ere theory. The algebraic structure of mis\`ere monoids is not yet well…

The preference graph is a combinatorial representation of the structure of a normal-form game. Its nodes are the strategy profiles, with an arc between profiles if they differ in the strategy of a single player, where the orientation…

Algorithmic game theory (AGT) focuses on the design and analysis of algorithms for interacting agents, with interactions rigorously formalized within the framework of games. Results from AGT find applications in domains such as online…

The class of weakly acyclic games, which includes potential games and dominance-solvable games, captures many practical application domains. In a weakly acyclic game, from any starting state, there is a sequence of better-response moves…

In this paper, we consider impartial and partizan restricted chocolate bar games. In impartial restricted chocolate bar games, players cut a chocolate bar into two pieces along any horizontal or vertical line and eat whichever piece is…

Consider a two-player game repeated N times. Player 1 can choose between two styles (for interpretability, offensive and defensive), whereas Player 2 uses a single fixed style. Let X N\,:= \#wins -\#losses for Player 1 after N games, and…

We consider Subtraction Nim, where two players have exactly the same options, but which is partizan in the sense that at the game ending, a partizan rule is applied for the decision of the winner. We consider the following example: Let $S$…

We study potential games on unimodular random graphs of bounded degree, where players interact through the underlying network. Using the unimodular measure, we define a well-posed global potential that captures both finite- and…

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…

While fictitious play is guaranteed to converge to Nash equilibrium in certain game classes, such as two-player zero-sum games, it is not guaranteed to converge in non-zero-sum and multiplayer games. We show that fictitious play in fact…

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…

We encode arbitrary finite impartial combinatorial games in terms of lattice points in rational convex polyhedra. Encodings provided by these \emph{lattice games} can be made particularly efficient for octal games, which we generalize to…

In this paper, we investigate a partially observable zero sum games where the state process is a discrete time Markov chain. We consider a general utility function in the optimization criterion. We show the existence of value for both…

Unlike Poker where the action space $\mathcal{A}$ is discrete, differential games in the physical world often have continuous action spaces not amenable to discrete abstraction, rendering no-regret algorithms with…

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…

We derive robust predictions in games involving flexible information acquisition, also known as rational inattention (Sims 2003). These predictions remain accurate regardless of the specific methods players employ to gather information.…

An individual can only experience regret if she learns about an unchosen alternative. In many situations, learning about an unchosen alternative is possible only if someone else chose it. We develop a model where the ex-post information…

We present a version of the Banach-Mazur game, where open sets are replaced by elements of a fixed partially ordered set. We show how to apply it in the theory of Fraisse limits and beyond, obtaining simple proofs of universality of certain…

Gradient-based methods for two-player games produce rich dynamics that can solve challenging problems, yet can be difficult to stabilize and understand. Part of this complexity originates from the discrete update steps given by simultaneous…