The Sumo Coach Problem

Review of Economic Design

We address the optimal allocation of stochastically dependent resource bundles to a set of simultaneous contests. For this purpose, we study a modification of the Colonel Blotto Game called the Sumo Coach Problem. We devise a thoroughly probabilistic method of payoff representation and fully characterize equilibria in this class of games. We further formalize the idea of strategic team training in a comparative static setting. The problem applies to several distinct economic interactions but seems most prevalent in team sports with individual matches, for instance, in Tennis and Sumo.

Official link
Rehsmann, D. The Sumo coach problem. (2023).
Review of Economic Design 27, 669–700.


Properties of bundle valuations in carrier collaboration

Central European Journal of Operations Research

Combinatorial auctions are an important part of many frameworks for carrier collaboration in logistics. In the last years, many innovative auction mechanisms have been developed in the economic literature that could potentially be applied in this context and that could significantly simplify the process of determining efficient allocations of requests. These mechanisms rely on certain assumptions about the valuations of bidders. In this paper, we perform computational experiments to analyze to which extent these requirements are fulfilled for valuations derived from a simple logistics problem, the Traveling Salesman Problem. We find that bidders’ valuations typically violate even very elementary requirements, but that these violations affect only a limited number of request bundles. We further analyze whether these violations exhibit a consistent pattern across multiple carriers and check consistency if route lengths are calculated exactly or approximated.

Official link
Vetschera, R., Knyazev, D. & Rehsmann, D. Properties of bundle valuations in carrier collaboration. (2023).
Central European Journal of Operations Research.