Core-stable Equilibria in Markers with Budget Constraints

n many markets, buyers are forced operate under financial constraints. It is known that in combinatorial markets and exchanges, no mechanism can be implemented such that a stable allocation of goods can be found that achieves maximization of the social welfare. Therefore, financial constraints are usually either ignored (leading to significant efficiency losses and instabilities when considering the actual utility functions of participants), or approximation mechanisms are implemented that require some relaxation of budgets, efficiency, or stability. In this talk, we focus on core-stable outcomes of combinatorial exchanges in the case that buyers face budget constraints. We introduce mixed integer bilevel linear programs (MIBLP) to compute those allocations and prices in the core of the exchange that yield the highest social welfare. While full core stability becomes quickly intractable, we show that small but realistic problem sizes can actually be solved if the designer limits attention to core-stability against reasonably large coalitions of deviating agents.

About Stefan

Stefan Waldherr is an Assistant Professor at the Department of Operations Analytics at the School of Business and Economics of the VU Amsterdam. Stefan received his PhD from the University of Osnabrück where he was investigating scheduling problems. Later, Stefan was a PostDoc at the chair of Decision Support Systems at TU Munich. His main research interests lie in the intersection of combinatorial optimization and game theory with a focus on assignment problems with multiple self-interested decision makers.