Consistent bilateral assignment

In the bilateral assignment problem, source a holds the amount ra of resource of type a, while sink i must receive the total amount xi of the various resources. We look for assignment rules meeting the powerful separability property known as Consistency: “every subassignment of a fair assignment is fair”. They are essentially those rules selecting the feasible flow minimizing the sum ∑i,aW(yia), where W is smooth and strictly convex

On Proportionally Fair Solutions for the Divorced-Parents Problem

When Dutch parents divorce, Dutch law dictates that the parental contributions to cover the financial needs ofthe children have to be proportionally fair. This rule is clear when parents only have common children. However,cases can be considerably more complicated, for example when parents have financial responsibilities to childrenfrom previous marriages. We show that, mathematically, this settlement problem can be modelled as a bipartiterationing problem for which a unique global proportionally fair solution exists. Moreover, we develop two efficientalgorithms for obtaining this proportionally fair solution, and we show numerically that both algorithms areconsiderably faster than standard convex optimization techniques. The first algorithm is a novel tailor-madefixed-point iteration algorithm, whereas the second algorithm only iteratively applies simple lawsuits involvinga single child and its parents. The inspiration for this latter algorithm comes from our main convergence proofin which we show that iteratively applying settlements on smaller subnetworks eventually leads to the samesettlement on the network as a whole. This has significant societal importance since in practice lawsuits areoften only held between two or a few parents. Moreover, our iterative algorithm is easy to understand, alsoby parents, legal counselors, and judges, which is crucial for its acceptance in practice. Finally, as the methodprovides a unique solution to any dispute, it removes the legal inequality perceived by parents. Consequently, itmay considerably reduce the workload of courts because parents and lawyers can compute the proportionally fairparental contributions before bringing their case to court

Business fluctuations in a behavioral switching model: Gridlock effects and credit crunch phenomena in financial networks

In this paper we characterize the evolution over time of a credit network in the most general terms as a system of interacting banks and firms operating in a three-sector economy with goods, credit and interbank market. Credit connections change over time via an evolving fitness measure depending from lenders’ supply of liquidity and borrowers’ demand of credit. Moreover, an endogenous learning mechanism allows agents to switch between a loyal or a shopping-around strategy according to their degree of satisfaction. The crucial question we investigate is how financial bubbles and credit-crunch phenomena emerge from the implemented mechanism

An Axiomatization of the Proportional Rule in Financial Networks

Valós csődproblémákban a fizetések meghatározására használt legfontosabb módszer az arányos csődszabály. Sok csődproblémában megjelenik a hálózati aspektus, és ilyenkor a szereplők eszközeinek értéke endogén módon határozódik meg, mivel az is számít, hogy a többi szereplőtől mennyire lehet a követeléseket behajtani. Ezek a hálózati hatások megnehezítik az axiomatikus elemzést. Cikkünkben először adunk axiomatizációt pénzügyi hálózatokban az arányos csődszabályra. A fő axiómánk az osztódás invariancia. A további szükséges axiómák a követelések felső korlát jellege, a korlátolt felelősség, a hitelezők elsőbbsége, a folytonosság és a pártatlanság