Economic Mechanisms for Shortest Path Cooperative Games with Incomplete Information

Abstract

In this paper we present a cooperative game theoretic interpretation of the shortest path problem. We consider a buying agent who has a budget to go from a specified source node s to a specified target node t in a directed acyclic network. The budget may reflect the level of utility that he associates in going from node s to node t. The edges in the network are owned by individual utility maximizing agents each of whom incurs some cost in allowing its use. We investigate the design of economic mechanisms to obtain a least cost path from s to t and to share the surplus (difference between the budget and the cost of the shortest path) generated among the participating agents in a fair manner. Previous work related to this problem assumes that cost and budget information is common knowledge. This assumption can be severely restrictive in many common applications. We relax this assumption and allow both budget and cost information to be private, hence known only to the respective agents. We first develop the structure of the shortest path cooperative game with incomplete information. We then show the non-emptiness of the incentive compatible core of this game and the existence of a surplus sharing mechanism that is incentive efficient and individually rational in virtual utilities, and strongly budget balanced.