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We study the concurrence of arbitrary dimensional bipartite quantum systems. By using a positive but not completely positive map, we present an analytical lower bound of concurrence. Detailed examples are used to show that our bound can…

Motivated by online platforms such as job markets, we study an agent choosing from a list of candidates, each with a hidden quality that determines match value. The agent observes only a noisy ranking of the candidates plus a binary signal…

We consider the many-to-many bipartite matching problem in the presence of two-sided preferences and two-sided lower quotas. The input to our problem is a bipartite graph G=(A U B, E), where each vertex in A U B specifies a strict…

Many set selection and ranking algorithms have recently been enhanced with diversity constraints that aim to explicitly increase representation of historically disadvantaged populations, or to improve the overall representativeness of the…

An improved mathematical model of social group competition is proposed. The utility obtained by a member of a certain group from each other member is assumed to be group size-dependent. Obtained results are close to available census data.…

Tournaments are frequently used incentive mechanisms to enhance performance. In this paper, we use field data and show that skill disparities among contestants asymmetrically affect the performance of contestants. Skill disparities have…

We study one-sided matching problems where $n$ agents have preferences over $m$ objects and each of them need to be assigned to at most one object. Most work on such problems assume that the agents only have ordinal preferences and usually…

Many centralized mechanisms for two-sided matching markets that enjoy strong theoretical properties assume that the planner solicits full information on the preferences of each participating agent. In particular, they expect that…

In a multi-party machine learning system, different parties cooperate on optimizing towards better models by sharing data in a privacy-preserving way. A major challenge in learning is the incentive issue. For example, if there is…

Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…

In a dynamic matching market, such as a marriage or job market, how should agents balance accepting a proposed match with the cost of continuing their search? We consider this problem in a discrete setting, in which agents have cardinal…

In many matching markets, one side "applies" to the other, and these applications are often expensive and time-consuming (e.g. students applying to college). It is tempting to think that making the application process easier should benefit…

We consider an agent community wishing to decide on several binary issues by means of issue-by-issue majority voting. For each issue and each agent, one of the two options is better than the other. However, some of the agents may be…

Recent advances in reinforcement learning with social agents have allowed us to achieve human-level performance on some interaction tasks. However, most interactive scenarios do not have as end-goal performance alone; instead, the social…

We consider a two-sided matching problem in which the agents on one side have dichotomous preferences and the other side representing institutions has strict preferences (priorities). It captures several important applications in matching…

In real life situations often paired comparisons involving alternatives of either full or partial profiles to mitigate cognitive burden are presented. For this situation the problem of finding optimal designs is considered in the presence…

Cooperation and competition coexist and coevolve in natural and social systems. Cooperation generates resources, which in turn, drive non-cooperative competition to secure individual shares. How this complex interplay between cooperation…

The challenge in the widely applicable online matching problem lies in making irrevocable assignments while there is uncertainty about future inputs. Most theoretically-grounded policies are myopic or greedy in nature. In real-world…

In frequently repeated matching scenarios, individuals may require diversification in their choices. Therefore, when faced with a set of potential outcomes, each individual may have an ideal lottery over outcomes that represents their…

We study the effects of data sharing between firms on prices, profits, and consumer welfare. Although indiscriminate sharing of consumer data decreases firm profits due to the subsequent increase in competition, selective sharing can be…