A Measure to Compare Matchings in Marriage Markets

In matching markets the number of blocking pairs is often used as a criterion to compare matchings. We argue that this criterion is lacking an economic interpretation: In many circumstances it will neither reflect the expected extent of partner changes, nor will it capture the satisfaction of the players with the matching. As an alternative, we set up two principles which single out a particularly “disruptive” subcollection of blocking pairs. We propose to take the cardinality of that subset as a measure to compare matchings. This cardinality has an economic interpretation: the subset is a justified objection against the given matching according to a bargaining set characterization of the set of stable matchings. We prove multiple properties relevant for a workable measure of comparison.Stable Marriage Problem, Matching, Blocking Pair, Instability, Matching Comparison, Decentralized Market, Bargaining Set

Task Assignment with Autonomous and Controlled Agents

We analyse assignment problems in which not all agents are controlled by the central planner. The autonomous agents search for vacant tasks guided by their own preference orders defined over subsets of the available tasks. The goal of the central planner is to maximise the total value of the assignment, taking into account the behaviour of the uncontrolled agents. This setting can be found in numerous real-world situations, ranging from organisational economics to "crowdsourcing" and disaster response. We introduce the Disjunctively Constrained Knapsack Game and show that its unique Nash equilibrium reveals the optimal assignment for the controlled agents. This result allows us to find the solution of the problem using mathematical programming techniques.

Coarse Graining of Nonbonded Inter-particle Potentials Using Automatic Simplex Optimization to Fit Structural Properties

We implemented a coarse-graining procedure to construct mesoscopic models of complex molecules. The final aim is to obtain better results on properties depending on slow modes of the molecules. Therefore the number of particles considered in molecular dynamics simulations is reduced while conserving as many properties of the original substance as possible. We address the problem of finding nonbonded interaction parameters which reproduce structural properties from experiment or atomistic simulations. The approach consists of optimizing automatically nonbonded parameters using the simplex algorithm to fit structural properties like the radial distribution function as target functions. Moreover, any mix of structural and thermodynamic properties can be included in the target function. Different spherically symmetric inter-particle potentials are discussed. Besides demonstrating the method for Lennard--Jones liquids, it is applied to several more complex molecular liquids such as diphenyl carbonate, tetrahydrofurane, and monomers of poly(isoprene).Comment: 24 pages, 3 tables, 14 figures submitted to the Journal of Chemical Physics (JCP