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In order to analyze the dynamics of two languages in competition, one approach is to fit historical data on their numbers of speakers with a mathematical model in which the parameters are interpreted as the similarity between those…
We study the entanglement of a multipartite quantum state. An inequality between the bipartite concurrence and the multipartite concurrence is obtained. More effective lower and upper bounds of the multipartite concurrence are obtained. By…
We study the probabilistic assignment of items to platforms that satisfies both group and individual fairness constraints. Each item belongs to specific groups and has a preference ordering over platforms. Each platform enforces group…
We explore a model of duopolistic competition in which consumers learn about the fit of each competitor's product. In equilibrium, consumers comparison shop: they learn only about the relative values of the products. When information is…
We study the problem of assigning jobs to applicants. Each applicant has a weight and provides a preference list ranking a subset of the jobs. A matching M is popular if there is no other matching M' such that the weight of the applicants…
Tournament solutions play an important role within social choice theory and the mathematical social sciences at large. We construct a tournament of order 36 for which the Banks set and the bipartisan set are disjoint. This implies that…
The rate at which nodes in a network increase their connectivity depends on their fitness to compete for links. For example, in social networks some individuals acquire more social links than others, or on the www some webpages attract…
This paper studies multilateral matching in which agents may negotiate contracts within any coalition. We assume scale economies such that an agent substitutes some existing contracts with new ones only if the latter involve a set of…
Winners-take-all situations introduce an incentive for agents to diversify their behavior, since doing so will result in splitting an eventual price with fewer people. At the same time, when the payoff of a process depends on a parameter…
The partition of society into groups, polarization, and social networks are part of most conversations today. How do they influence price competition? We discuss Bertrand duopoly equilibria with demand subject to network effects. Contrary…
We study the problem of aggregating individual preferences over alternatives into a collective ranking. A distinctive feature of our setting is that agents are matched to alternatives. Applications include rankings of colleges or academic…
In this paper, we consider the problem of computing an optimal matching in a bipartite graph where elements of one side of the bipartition specify preferences over the other side, and one or both sides can have capacities and…
The Stable Roommates problems are characterized by the preferences of agents over other agents as roommates. A solution is a partition of the agents into pairs that are acceptable to each other (i.e., they are in the preference lists of…
The theory of two-sided matching has been extensively developed and applied to many real-life application domains. As the theory has been applied to increasingly diverse types of environments, researchers and practitioners have encountered…
We study the classical, two-sided stable marriage problem under pairwise preferences. In the most general setting, agents are allowed to express their preferences as comparisons of any two of their edges and they also have the right to…
Research on fairness in machine learning has been recently extended to recommender systems. One of the factors that may impact fairness is bias disparity, the degree to which a group's preferences on various item categories fail to be…
We investigate pooling problems in which multiple players vie with one another to maximize individual profit in a non-cooperative competitive market. This competitive setting is interesting and worthy of study because the majority of…
The Bipartite Polarization Problem is an optimization problem where the goal is to find the highest polarized bipartition on a weighted and labelled graph that represents a debate developed through some social network, where nodes represent…
In some scenarios ("anti-coordination games"), individuals are better off choosing different actions than their neighbors while in other scenarios ("coordination games"), it is beneficial for individuals to choose the same strategy as their…
We introduce a complete set of complementary quantities in bipartite, two-dimensional systems. Complementarity then relates the quantitative entanglement measure concurrence which is a bipartite property to the single-particle quantum…