Related papers: Solving Two-Player Games under Progress Assumption…

This paper concerns the analysis of the Shapley value in matching games. Matching games constitute a fundamental class of cooperative games which help understand and model auctions and assignments. In a matching game, the value of a…

In classical complexity theory, the two definitions of probabilistically checkable proofs -- the constraint satisfaction and the nonlocal games version -- are computationally equal in power. In the quantum setting, the situation is far less…

This paper studies a large class of two-player perfect-information turn-based parity games on infinite graphs, namely those generated by collapsible pushdown automata. The main motivation for studying these games comes from the connections…

We consider games played on the transtion graph of concurrent programs running under the Total Store Order (TSO) weak memory model. Games are frequently used to model the interaction between a system and its environment, in this case…

We consider two-player games played on finite graphs equipped with costs on edges and introduce two winning conditions, cost-parity and cost-Streett, which require bounds on the cost between requests and their responses. Both conditions…

We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals:…

We propose a new class of games, called Multi-Games (MG), in which a given number of players play a fixed number of basic games simultaneously. In each round of the MG, each player will have a specific set of weights, one for each basic…

We consider a randomized algorithm for the unique games problem, using independent multinomial probabilities to assign labels to the vertices of a graph. The expected value of the solution obtained by the algorithm is expressed as a…

This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games,…

We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a 2-player game. We exhibit a class of 2-player games having payoffs in the range [0,1] that show that Fictitious Play…

Feature-based SPL analysis and family-based model checking have seen rapid development. Many model checking problems can be reduced to two-player games on finite graphs. A prominent example is mu-calculus model checking, which is generally…

We continue the investigation of finite-duration variants of infinite-duration games by extending known results for games played on finite graphs to those played on infinite ones. In particular, we establish an equivalence between pushdown…

We construct several definitions of imbalance and playability, both of which are related to the existence of dominated strategies. Specifically, a maximally balanced game and a playable game cannot have dominated strategies for any player.…

We give new characterizations of core imputations for the following games: * The assignment game. * Concurrent games, i.e., general graph matching games having non-empty core. * The unconstrained bipartite $b$-matching game (edges can be…

Solving parity games is a major building block for numerous applications in reactive program verification and synthesis. While they can be solved efficiently in practice, no known approach has a polynomial worst-case runtime complexity. We…

We show that $\varepsilon$-additive approximations of the optimal value of fixed-size two-player free games with fixed-dimensional entanglement assistance can be computed in time $\mathrm{poly}(1/\varepsilon)$. This stands in contrast to…

The synthesis problem asks to construct a reactive finite-state system from an $\omega$-regular specification. Initial specifications are often unrealizable, which means that there is no system that implements the specification. A common…

The complexity of computing equilibrium refinements has been at the forefront of algorithmic game theory research, but it has remained open in the seminal class of potential games; we close this fundamental gap in this paper. We first show…

Correlated equilibria -- and their generalization $\Phi$-equilibria -- are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of…

Explainable Artificial Intelligence (XAI) has received widespread interest in recent years, and two of the most popular types of explanations are feature attributions, and counterfactual explanations. These classes of approaches have been…