Related papers: Quantitative Reductions and Vertex-Ranked Infinite…

Theory of Mind benchmarks for large language models typically produce aggregate scores without theoretical grounding, making it unclear whether high performance reflects strategic reasoning or surface-level heuristics. We introduce a…

We modify the concept of quantum strategic game to make it useful for extensive form games. We prove that our modification allows to consider the normal representation of any finite extensive game using the fundamental concepts of quantum…

We study repeated multi-player vector-valued games in which a player observes a payoff vector each round and evaluates outcomes through linear scalarizations of those vectors. Different from most prior works, the choice of scalarization is…

Methods from convex optimization are widely used as building blocks for deep learning algorithms. However, the reasons for their empirical success are unclear, since modern convolutional networks (convnets), incorporating rectifier units…

In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…

We examine two-player games over finite weighted graphs with quantitative (mean-payoff or energy) objective, where one of the players additionally needs to satisfy a fairness objective. The specific fairness we consider is called 'strong…

Deterministic game-solving algorithms are conventionally analyzed in the light of their average-case complexity against a distribution of random game-trees, where leaf values are independently sampled from a fixed distribution. This…

We present a new class of vertex cover and set cover games. The price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs -- in…

A game-theoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding…

We extend the classic regret minimization framework for approximating equilibria in normal-form games by greedily weighing iterates based on regrets observed at runtime. Theoretically, our method retains all previous convergence rate…

We show the existence and effective computability of optimal winning strategies for request-response games in case the quality of a play is measured by the limit superior of the mean accumulated waiting times between requests and their…

Game solving aims to find the optimal strategies for all players and determine the theoretical outcome of a game. However, due to the exponential growth of game trees, many games remain unsolved, even though methods like AlphaZero have…

Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning…

In game theory, mechanism design is concerned with the design of incentives so that a desired outcome of the game can be achieved. In this paper, we study the design of incentives so that a desirable equilibrium is obtained, for instance,…

Stochastic games are a classical model in game theory in which two opponents interact and the environment changes in response to the players' behavior. The central solution concepts for these games are the discounted values and the value,…

In this article, we introduce certain kinds of computable reduction games with imperfect information. One can view such a game as an extension of the notion of Turing reduction, and generalized Weihrauch reduction as well. Based on the work…

A binary constraint system game is a two-player one-round non-local game defined by a system of Boolean constraints. The game has a perfect quantum strategy if and only if the constraint system has a quantum satisfying assignment [R. Cleve…

Many problems in compositional synthesis and verification of multi-agent systems -- such as rational verification and assume-guarantee verification in probabilistic systems -- reduce to reasoning about two-player multi-objective stochastic…

We introduce frame-equivalence games tailored for reasoning about the size, modal depth, number of occurrences of symbols and number of different propositional variables of modal formulae defining a given frame-property. Using these games,…

Various decomposition of finite games have been proposed. The inner product of vectors plays a key role in the decomposition of finite games. This paper considers the effect of different inner products on the orthogonal decomposition of…