Related papers: The NTU Partitioned Matching Game for Internationa…
In cooperative game theory, games in partition function form are real-valued function on the set of so-called embedded coalitions, that is, pairs $(S,\pi)$ where $S$ is a subset (coalition) of the set $N$ of players, and $\pi$ is a…
We consider cost allocation for set covering problems. We allocate as much cost to the elements (players) as possible without violating the group rationality condition (no subset of players pays more than covering this subset would cost),…
Nguyen and Thomas (2016) claimed that they have found a method to compute the nucleoli of games with more than $50$ players using nested linear programs (LP). Unfortunately, this claim is false. They incorrectly applied the indirect proof…
LP-duality theory has played a central role in the study of cores of games, right from the early days of this notion to the present time. The classic paper of Shapley and Shubik \cite{Shapley1971assignment} introduced the "right" way of…
In the realm of distributed systems tasked with managing and processing large-scale graph-structured data, optimizing graph partitioning stands as a pivotal challenge. The primary goal is to minimize communication overhead and runtime cost.…
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…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
We tackle the problem of partitioning players into groups of fixed size, such as allocating eligible students to shared dormitory rooms. Each student submits preferences over the other individual students. We study several settings, which…
Modern software systems may exhibit a nondeterministic behavior due to many unpredictable factors. In this work, we propose the node coverage game, a two player turn-based game played on a finite game graph, as a formalization of the…
We consider the problem of packing node-disjoint directed paths in a directed graph. We consider a variant of this problem where each path starts within a fixed subset of root nodes, subject to a given bound on the length of paths. This…
Let G=(V,E) be a connected graph. A set U subseteq V is convex if G[U] is connected and all vertices of V\U have at most one neighbor in U. Let sigma(W) denote the unique smallest convex set that contains W subseteq V. Two players play the…
The deployment of deep neural networks (DNNs) on resource-constrained edge devices is frequently hindered by their significant computational and memory requirements. While partitioning and distributing a DNN across multiple devices is a…
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…
The Traveling Tournament Problem (TTP-$k$) is a well-known benchmark problem in sports scheduling, which asks us to design a double round-robin schedule such that each pair of teams plays one game in each other's home venue, no pair of…
A solution concept on a class of transferable utility coalitional games is a multifunction satisfying given criteria of economic rationality. Every solution associates a set of payoff allocations with a coalitional game. This general…
Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several…
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…
Let $T:X\to X $ and $S:Y \to Y$ be continuous maps defined on compact sets. Let $$\varphi_i(\mu,\nu)=\int_{X \times Y} A_i(x,y) d\mu(x) d\nu(y)\;\;{for} \;\; i=1,2,$$ where $\mu$ is $T$-invariant and $\nu$ is $S$-invariant, be pay-off…
LP-duality theory has played a central role in the study of the core, right from its early days to the present time. However, despite the extensive nature of this work, basic gaps still remain. We address these gaps using the following…
We study stochastic team (known also as decentralized stochastic control or identical interest stochastic dynamic game) problems with large or countably infinite number of decision makers, and characterize existence and structural…