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Our starting point is the observation that if graphs in a class C have low descriptive complexity in first order logic, then the isomorphism problem for C is solvable by a fast parallel algorithm (essentially, by a simple combinatorial…
The convergence of online learning algorithms in games under self-play is a fundamental question in game theory and machine learning. Among various notions of convergence, last-iterate convergence is particularly desirable, as it reflects…
Authorization is challenging in distributed systems that cannot rely on the identification of nodes. Proof-of-work offers an alternative gate-keeping mechanism, but its probabilistic nature is incompatible with conventional security…
Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…
A repeated game is an effective tool to model interactions and conflicts for players aiming to achieve their objectives in a long-term basis. Contrary to static noncooperative games that model an interaction among players in only one…
Two-player games on graphs provide the mathematical foundation for the study of reactive systems. In the quantitative framework, an objective assigns a value to every play, and the goal of player 1 is to minimize the value of the objective.…
We study the classical and quantum values of one- and two-party linear games, an important class of unique games that generalizes the well-known XOR games to the case of non-binary outcomes. We introduce a ``constraint graph" associated to…
We study the computational complexity of finding stable outcomes in hedonic games, which are a class of coalition formation games. We restrict our attention to symmetric additively-separable hedonic games, which are a nontrivial subclass of…
We establish a lower bound for deciding the satisfiability of the conjunction of any two Boolean formulas from a set called a full representation of Boolean functions of $n$ variables - a set containing a Boolean formula to represent each…
We begin by reviewing and proving the basic facts of combinatorial game theory. We then consider scoring games (also known as Milnor games or positional games), focusing on the "fixed-length" games for which all sequences of play terminate…
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…
Self-play, where the algorithm learns by playing against itself without requiring any direct supervision, has become the new weapon in modern Reinforcement Learning (RL) for achieving superhuman performance in practice. However, the…
We investigate a phenomenon of "one-to-two-player lifting" in infinite-duration two-player games on graphs with zero-sum objectives. More specifically, let $C$ be a class of strategies. It turns out that in many cases, to show that all…
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…
In this paper we present an assume-guarantee specification theory (aka interface theory from [14]) for modular synthesis and verification of real-time systems with critical timing constraints. It is a further step of our earlier work [10]…
In rational verification, the aim is to verify which temporal logic properties will obtain in a multi-agent system, under the assumption that agents ("players") in the system choose strategies for acting that form a game theoretic…
As multicore computing is now standard, it seems irresponsible for constraints researchers to ignore the implications of it. Researchers need to address a number of issues to exploit parallelism, such as: investigating which constraint…
We are concerned with the stability of a coalitional game, i.e., a transferable-utility (TU) cooperative game. First, the concept of core can be weakened so that the blocking of changes is limited to only those with multilateral backings.…
Our ability to know when to trust the decisions made by machine learning systems has not kept up with the staggering improvements in their performance, limiting their applicability in high-stakes domains. We introduce Prover-Verifier Games…
We explore links between the thin concurrent games of Castellan, Clairambault and Winskel, and the weighted relational models of linear logic studied by Laird, Manzonetto, McCusker and Pagani. More precisely, we show that there is an…