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Parity games are games that are played on directed graphs whose vertices are labeled by natural numbers, called priorities. The players push a token along the edges of the digraph. The winner is determined by the parity of the greatest…
We consider planning problems for graphs, Markov decision processes (MDPs), and games on graphs. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an…
We explore the twin questions of when and why the strategy method creates behavioral distortions in the elicitation of choices in laboratory studies of sequential games. While such distortions have been widely documented, the theoretical…
We study turn-based stochastic zero-sum games with lexicographic preferences over reachability and safety objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit…
Decision trees (DTs) epitomize the ideal of interpretability of machine learning (ML) models. The interpretability of decision trees motivates explainability approaches by so-called intrinsic interpretability, and it is at the core of…
Using semi-tensor product (STP) of matrices, the profile evolutionary equation (PEE) for repeated finite games is obtained. By virtue of PEE, the zero-determinant (ZD) strategies are developed for general finite games. A formula is then…
Iterated regret minimization has been introduced recently by J.Y. Halpern and R. Pass in classical strategic games. For many games of interest, this new solution concept provides solutions that are judged more reasonable than solutions…
We present a novel method to compute \emph{permissive winning strategies} in two-player games over finite graphs with $ \omega $-regular winning conditions. Given a game graph $G$ and a parity winning condition $\Phi$, we compute a…
Research on the similarity of a graph to being a tree - called the treewidth of the graph - has seen an enormous rise within the last decade, but a practically fast algorithm for this task has been discovered only recently by Tamaki (ESA…
Many real-world problems require making sequences of decisions where the outcomes of each decision are probabilistic and uncertain, and the availability of different actions is constrained by the outcomes of previous actions. There is a…
We study strategic interaction in data-driven games where players face uncertainty about payoff distributions inferred from finite samples. To model calibrated attitudes toward such uncertainty, we formulate distributionally robust games…
Deception plays a crucial role in strategic interactions with incomplete information. Motivated by security applications, we study a class of two-player turn-based deterministic games with one-sided incomplete information, in which player 1…
The strategic selection of resources by selfish agents has long been a key area of research, with Resource Selection Games and Congestion Games serving as prominent examples. In these traditional frameworks, agents choose from a set of…
Congestion games are a classical type of games studied in game theory, in which n players choose a resource, and their individual cost increases with the number of other players choosing the same resource. In network congestion games…
Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…
This paper studies the rational synthesis problem for multi-player games played on graphs when rational players are following subgame perfect equilibria. In these games, one player, the system, declares his strategy upfront, and the other…
In this chapter, we present an approach using formal methods to synthesize reactive defense strategy in a cyber network, equipped with a set of decoy systems. We first generalize formal graphical security models--attack graphs--to…
We investigate uniformity properties of strategies. These properties involve sets of plays in order to express useful constraints on strategies that are not \mu-calculus definable. Typically, we can state that a strategy is…
Two traditional paradigms are often used to describe the behavior of agents in multi-agent complex systems. In the first one, agents are considered to be fully rational and systems are seen as multi-player games. In the second one, agents…
Parity games play an important role for LTL synthesis as evidenced by recent breakthroughs on LTL synthesis, which rely in part on parity game solving. Yet state space explosion remains a major issue if we want to scale to larger systems or…