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When applied to the same game, probability theory and game theory can disagree on calculated values of the Fisher information, the log likelihood function, entropy gradients, the rank and Jacobian of variable transforms, and even the…
Recent work in deep reinforcement learning has allowed algorithms to learn complex tasks such as Atari 2600 games just from the reward provided by the game, but these algorithms presently require millions of training steps in order to…
As large language models become increasingly capable, it is critical that their outputs can be easily checked by less capable systems. Prover-verifier games can be used to improve checkability of model outputs, but display a degradation in…
An important feature of a dynamic game is its monitoring structure namely, what the players effectively see from the played actions. We consider games with arbitrary monitoring structures. One of the purposes of this paper is to know to…
Fictitious play with reinforcement learning is a general and effective framework for zero-sum games. However, using the current deep neural network models, the implementation of fictitious play faces crucial challenges. Neural network model…
Graph games with {\omega}-regular winning conditions provide a mathematical framework to analyze a wide range of problems in the analysis of reactive systems and programs (such as the synthesis of reactive systems, program repair, and the…
We address the problem of solving parity games with imperfect information on finite graphs of bounded structural complexity. It is a major open problem whether parity games with perfect information can be solved in PTIME. Restricting the…
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…
Two-player games on graphs is central in many problems in formal verification and program analysis such as synthesis and verification of open systems. In this work we consider solving recursive game graphs (or pushdown game graphs) that can…
Infinitely repeated games can support cooperative outcomes that are not equilibria in the one-shot game. The idea is to make sure that any gains from deviating will be offset by retaliation in future rounds. However, this model of…
We introduce a natural notion of limit-deterministic parity automata and present a method that uses such automata to construct satisfiability games for the weakly aconjunctive fragment of the $\mu$-calculus. To this end we devise a method…
Sequential computation is well understood but does not scale well with current technology. Within the next decade, systems will contain large numbers of processors with potentially thousands of processors per chip. Despite this, many…
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…
First cycle games (FCG) are played on a finite graph by two players who push a token along the edges until a vertex is repeated, and a simple cycle is formed. The winner is determined by some fixed property Y of the sequence of labels of…
In a strong game played on the edge set of a graph G there are two players, Red and Blue, alternating turns in claiming previously unclaimed edges of G (with Red playing first). The winner is the first one to claim all the edges of some…
Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at most finitely repeated games have been widely studied, however…
A strong blocking set in a finite projective space is a set of points that intersects each hyperplane in a spanning set. We provide a new graph theoretic construction of such sets: combining constant-degree expanders with asymptotically…
In games with imperfect recall, players may forget the sequence of decisions they made in the past. When players also forget whether they have already encountered their current decision point, they are said to be absent-minded. Solving…
Hyperproperties generalize traditional trace properties by relating multiple execution traces rather than reasoning about individual runs in isolation. They provide a unified way to express important requirements such as information flow…
By resorting to the vector space structure of finite games, skew-symmetric games (SSGs) are proposed and investigated as a natural subspace of finite games. First of all, for two player games, it is shown that the skew-symmetric games form…