Allocating the Cost of Congestion with the Nucleolus

  • Authors:
  • Gilles Reinhardt

  • Affiliations:
  • Department of Management, DePaul University, Chicago, IL 60604, U.S.A./ E-mail: greinhar@condor.depaul.edu

  • Venue:
  • Computational Economics
  • Year:
  • 2004

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Abstract

A natural approach to solve resource sharing problems is to model them ascooperative games and use the results to allocate the costs of the sharedresource. The nucleolus, a solution concept derived from cooperative gametheory, requires an exponential number of computations since the solution mustadhere to individual and coalitional rationality conditions. Littlechild(1974) provides a linear algorithm which produces the nucleolus of a costallocation game when the cost of a coalition is the cost of the largest playerin that coalition. In this paper, we show that for a large class of congestioncost allocation games, where each player has an independent impact on theshared resource, we can nonetheless bypass all the computational complexityand derive allocations in closed form.