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.
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Nisan, N.: Algorithms for selfish agents. In: Proceedings of the 16th Symposium on Theoretical Aspects of Computer Science, Trier, Germany (1999)
Nisan, N., Ronen, A.: Algorithmic mechanism design. Games and Economic Behaviour 35, 166–196 (2001)
Archer, A., Tardos, E.: Frugal path mechanisms. Technical report, Unpublished manuscript. Previously appeared as an extended abstract in Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (2002)
Hershberger, J., Suri, S.: Vickrey prices and shortest paths: What is an edge worth? In: IEEE Symposium on Foundations of Computer Science, pp. 252–259 (2001)
Fragnelli, V., Garcia-Jurado, I., Mendez-Naya, L.: On shortest path games. Mathematical Methods of Operations Research 52 (2000)
Voorneveld, M., Grahn, S.: Cost allocation in shortest path games. Technical report, Working Paper, Department of Mathematics, Utrecht University (2000)
Mas-Collel, A., Whinston, M.D., Green, J.R.: Micoreconomic Theory. Oxford University Press, Oxford (1995)
Feigenbaum, J., Papadimitriou, C., Sami, R., Shenker, S.: A BGP-based mechanism for lowest-cost routing. In: 21st ACM Symposium on Principles of Distributed Computing (PODC 2002), pp. 173–182 (2002)
Harsanyi, J.C.: Games with incomplete information played by Bayesian players I-III. Management Science 14(7), 486–502 (1968)
Myerson, R.B.: Cooperative games with incomplete information. International Journal of Game Theory 13, 69–96 (1984)
Holmstorm, B., Myerson, R.B.: Efficient and durable decision rules with incomplete information. Econometrica 51, 1799–1819 (1983)
Harsanyi, J.C., Selten, R.: A generalized Nash solution for two person bargaining games with incomplete information. Management Science 18(5), Part 2, 80–106 (1972)
Wilson, R.: Information, efficiency and the core of an economy. Econometrica 46(4), 807–816 (1978)
Myerson, R.B.: Two-person bargaining problems with incomplete information. Econometrica 52, 461–487 (1984)
Vohra, R.: Incomplete information, incentive compatibility and the core. Journal of Economic Theory 86, 123–147 (1999)
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Chandrashekar, T.S., Narahari, Y. (2005). Economic Mechanisms for Shortest Path Cooperative Games with Incomplete Information. In: Deng, X., Ye, Y. (eds) Internet and Network Economics. WINE 2005. Lecture Notes in Computer Science, vol 3828. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11600930_8
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DOI: https://doi.org/10.1007/11600930_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30900-0
Online ISBN: 978-3-540-32293-1
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