相关论文: Minimal Stable Sets in Tournaments
We find an exact formula for the number of directed 5-cycles in a tournament in terms of its edge score sequence. We use this formula to find both upper and lower bounds on the number of 5-cycles in any $n$-tournament. In particular, we…
A tournament is a directed graph resulting from an orientation of the complete graph; so, if $M$ is a tournament's adjacency matrix, then $M + M^T$ is a matrix with $0$s on its diagonal and all other entries equal to $1$. An outstanding…
I introduce a stability notion, dynamic stability, for two-sided dynamic matching markets where (i) matching opportunities arrive over time, (ii) matching is one-to-one, and (iii) matching is irreversible. The definition addresses two…
According to recent empirical studies, the group draw of major sports tournaments can imply a high level of uncertainty, and some lucky teams enjoy an unfair advantage over the other teams. We propose a novel technique to quantify this draw…
We develop decomposition/composition tools for efficiently solving maximum weight stable sets problems as well as for describing them as polynomially sized linear programs (using "compact systems"). Some of these are well-known but need…
Ranking the participants of a tournament has applications in voting, paired comparisons analysis, sports and other domains. In this paper we introduce bipartite tournaments, which model situations in which two different kinds of entity…
In this paper, we consider one-to-one matchings between two disjoint groups of agents. Each agent has a preference over a subset of the agents in the other group, and these preferences may contain ties. Strong stability is one of the…
We study the Stable Fixtures problem, a many-to-many generalisation of the classical non-bipartite Stable Roommates matching problem. Building on the foundational work of Tan on stable partitions, we extend his results to this significantly…
This paper aims at investigating the contractibility of the solution sets for set optimization problems by utilizing strictly quasi cone-convexlikeness, which is an assumption weaker than strictly cone-convexity, strictly…
We consider a team formation setting where agents have varying levels of expertise in a global set of required skills, and teams are ranked with respect to how well the expertise of teammates complement each other. We model this setting as…
In this paper we study mean field games with possibly multiple mean field equilibria. Instead of focusing on the individual equilibria, we propose to study the set of values over all possible equilibria, which we call the set value of the…
Efficient computability is an important property of solution concepts in matching markets. We consider the computational complexity of finding and verifying various solution concepts in trading networks-multi-sided matching markets with…
This paper demonstrates the existence of a finite set of equilibria in the case of the indeterminacy of linear rational expectations models. The number of equilibria corresponds to the number of ways to select n eigenvectors among a larger…
Scheduling a sports tournament is a complex optimization problem, which requires a large number of hard constraints to satisfy. Despite the availability of several such constraints in the literature, there remains a gap since most of the…
The stable set associated to a given set S of nonerasing endomorphisms or substitutions is the set of all right infinite words that can be indefinitely desubstituted over S. This notion generalizes the notion of sets of fixed points of…
In several decision-making problems, alternatives should be ranked on the basis of paired comparisons between them. We present an axiomatic approach for the universal ranking problem with arbitrary preference intensities, incomplete and…
A class of non-compact billiards is introduced, namely the infinite step billiards, i.e., systems of a point particle moving freely in the domain $\Omega = \bigcup_{n\in\N} [n,n+1] \times [0,p_n]$, with elastic reflections on the boundary;…
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…
Finding a stable matching is one of the central problems in algorithmic game theory. If participants are allowed to have ties and incomplete preferences, computing a stable matching of maximum cardinality is known to be NP-hard. In this…
Two genres of heuristics that are frequently reported to perform much better on "real-world" instances than in the worst case are greedy algorithms and local search algorithms. In this paper, we systematically study these two types of…