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Parity games have important practical applications in formal verification and synthesis, especially to solve the model-checking problem of the modal mu-calculus. They are also interesting from the theory perspective, because they are widely…
Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, while understanding the dynamics of gradient algorithms for solving such formulations has remained a…
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…
A number of recent studies have focused on novel features in game theory when the games are played using quantum mechanical toolbox (entanglement, unitary operators, measurement). Researchers have concentrated in two-player-two strategy,…
Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for…
It is well-known that the winning region of a parity game with $n$ nodes and $k$ priorities can be computed as a $k$-nested fixpoint of a suitable function; straightforward computation of this nested fixpoint requires…
Admissibility has been studied for games of infinite duration with Boolean objectives. We extend here this study to games of infinite duration with quantitative objectives. First, we show that, un- der the assumption that optimal worst-case…
Graph games provide the foundation for modeling and synthesis of reactive processes. Such games are played over graphs where the vertices are controlled by two adversarial players. We consider graph games where the objective of the first…
We describe an algorithm for computing best response strategies in a class of two-player infinite games of incomplete information, defined by payoffs piecewise linear in agents' types and actions, conditional on linear comparisons of…
In a single-state repeated game, zero-determinant strategies can unilaterally force functions of the payoffs to take values in particular closed intervals. When the explicit use of a determinant is absent from the analysis, they are instead…
We present an algorithm for computing evolutionarily stable strategies (ESSs) in symmetric perfect-recall extensive-form games of imperfect information. Our main algorithm is for two-player games, and we describe how it can be extended to…
We show how solutions to many recursive arena equations can be computed in a natural way by allowing loops in arenas. We then equip arenas with winning functions and total winning strategies. We present two natural winning conditions…
Game Theory studies situations in which multiple agents having conflicting objectives have to reach a collective decision. The question of a compact representation language for agents utility function is of crucial importance since the…
In this paper, we extend the Descent framework, which enables learning and planning in the context of two-player games with perfect information, to the framework of stochastic games. We propose two ways of doing this, the first way…
In imperfect-information games, the optimal strategy in a subgame may depend on the strategy in other, unreached subgames. Thus a subgame cannot be solved in isolation and must instead consider the strategy for the entire game as a whole,…
We study the problem of computing optimal correlated equilibria (CEs) in infinite-horizon multi-player stochastic games, where correlation signals are provided over time. In this setting, optimal CEs require history-dependent policies; this…
Data mining and knowledge discovery are two important growing research fields in the last two decades due to the abundance of data collected from various sources. The exponentially growing volumes of generated data urge the development of…
We study the optimal use of information in Markov games with incomplete information on one side and two states. We provide a finite-stage algorithm for calculating the limit value as the gap between stages goes to 0, and an optimal strategy…
Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural…
Dynamic games are an effective paradigm for dealing with the control of multiple interacting actors. This paper introduces ALGAMES (Augmented Lagrangian GAME-theoretic Solver), a solver that handles trajectory-optimization problems with…