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In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce…

We analyze strategic complexity across all 960 Chess960 (Fischer Random Chess) starting positions. Stockfish evaluations reveal a near-universal first-move advantage for White ($\langle E \rangle = +0.33 \pm 0.12$ pawns), indicating that…

We analyze the performance of the best-response dynamic across all normal-form games using a random games approach. The playing sequence -- the order in which players update their actions -- is essentially irrelevant in determining whether…

Aligning AI systems with human values remains a fundamental challenge, but does our inability to create perfectly aligned models preclude obtaining the benefits of alignment? We study a strategic setting where a human user interacts with…

This paper addresses the dynamic difficulty adjustment on MOBA games as a way to improve the player's entertainment. Although MOBA is currently one of the most played genres around the world, it is known as a game that offer less autonomy,…

In this paper, I formalize intelligence measurement in games by introducing mechanisms that assign a real number -- interpreted as an intelligence score -- to each player in a game. This score quantifies the ex-post strategic ability of the…

We present an end-to-end learning method for chess, relying on deep neural networks. Without any a priori knowledge, in particular without any knowledge regarding the rules of chess, a deep neural network is trained using a combination of…

Variational inequalities (VIs) are a broad class of optimization problems encompassing machine learning problems ranging from standard convex minimization to more complex scenarios like min-max optimization and computing the equilibria of…

Designing agents that are able to achieve different play-styles while maintaining a competitive level of play is a difficult task, especially for games for which the research community has not found super-human performance yet, like…

In this paper, we analyse inspection games with an evolutionary perspective. In our evolutionary inspection game with a large population, each individual is not a rational payoff maximiser, but periodically updates his strategy if he…

Decision making in modern large-scale and complex systems such as communication networks, smart electricity grids, and cyber-physical systems motivate novel game-theoretic approaches. This paper investigates big strategic (non-cooperative)…

Weak selection, which means a phenotype is slightly advantageous over another, is an important limiting case in evolutionary biology. Recently it has been introduced into evolutionary game theory. In evolutionary game dynamics, the…

We prove that finding an epsilon-Nash equilibrium in a succinctly representable game with many players is PPAD-hard for constant epsilon. Our proof uses succinct games, i.e. games whose payoff function is represented by a circuit. Our…

We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical…

Evolutionarily stable strategy (ESS) is an important solution concept in game theory which has been applied frequently to biological models. Informally an ESS is a strategy that if followed by the population cannot be taken over by a…

Weighted voting games are a well-known and useful class of succinctly representable simple games that have many real-world applications, e.g., to model collective decision-making in legislative bodies or shareholder voting. Among the…

This paper presents an empirical investigation of the relation between decision speed and decision quality for a real-world setting of cognitively-demanding decisions in which the timing of decisions is endogenous: professional chess.…

Designing efficient algorithms to find Nash equilibrium (NE) refinements in sequential games is of paramount importance in practice. Indeed, it is well known that the NE has several weaknesses, since it may prescribe to play sub-optimal…

A tournament is an orientation of a complete graph. A vertex that can reach every other vertex within two steps is called a \emph{king}. We study the complexity of finding $k$ kings in a tournament graph. We show that the randomized query…

Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…