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Bidding Against Competitors
January 1990 (vol. 16 no. 1)
pp. 100-104

Consideration is given to a system of n competitors, where if a competitor selects its bids equally likely from a given set of bid values, its probability of winning is guaranteed to be 1/n, regardless of the bid values selected by other competitors in the system. A discussion is presented of several variations of this basic scheme, namely, bidding with unequal weights, bidding with more than one winner, and bidding with an unknown number of competitors. Two economical, but approximate, bidding schemes are discussed. In the first scheme, the competitors select their bids from a set with a constant size, and in the second, each competitor selects only one bid even though the total number of competitors is not known a priori. It is shown how to use these bidding schemes to construct solutions to several problems in distributed systems, including the mutual exclusion problem and the dining philosophers problem.

[1] J. E. Bums, "Symmetry in systems of asynchronous processes," inProc. 22nd Annu. ACM Symp. Foundations of Computer Science, 1981, pp. 169-174.
[2] S. Cohen, D. Lehmann, and A. Pnueli, "Symmetric and economical solution to the mutual exclusion problem in distributed systems,"Theoretical Comput. Sci., vol. 34, pp. 215-226, 1984.
[3] E. W. Dijkstra, "Solution of a problem in concurrent programming control,"Commun. ACM, vol. 8, pp. 569-569, Sept. 1965.
[4] E. Dijkstra, "Co-operating sequential processes," inProgramming Languages, F. Genuys, Ed. New York: Academic, 1968, pp. 43-112.
[5] M. J. Fischer, N. A. Lynch, and M. S. Paterson, "Impossibility of distributed consensus with one faulty process,"J. ACM, vol. 32, no. 2, pp. 374-382, Apr. 1985.
[6] N. Francez and M. Rodeh, "A distributed abstract data type implemented by a probabilistic communication scheme," inProc. 21th Annu. ACM Symp. Foundations of Computer Science, 1980, pp. 373- 379.
[7] A. Itai and M. Rodeh, "Symmetry breaking in distributive networks," inProc. 22nd Annu. ACM Symp. Foundations of Computer Science, 1981, pp. 150-158.
[8] D. Knuth, "Additional comments on a problem in concurrent control,"Commun. ACM, vol. 9, no. 5, pp. 321-322, 1966.
[9] L. Lamport, "Time, clocks, and the ordering of events in a distributed system,"Commun. ACM, vol. 21, no. 7, pp. 558-565, July 1978.
[10] D. Lehmann and M. O. Rabin, "On the advantages of free choice: A symmetric and fully distributed solution to the Dining Philosophers Problem," inProc. 8th Annu. ACM Symp. Principles of Programming Languages, 1981, pp. 133-138.
[11] A. Pnueli and L. Zuck, "Verification of multiprocess probabilistic protocols,"Distributed Comput., vol. 1, no. 1, pp. 53-72, 1986.
[12] M. O. Rabin, "N-process mutual exclusion with bounded waiting by 4. log2N-valued shared variable,"J. Comput. Syst. Sci., vol. 15, pp. 66-75, 1982.
[13] R.L. Rivest, A. Shamir, and L. Adleman, "A Method for Obtaining Digital Signatures and Public-Key Cryptosystems,"Comm. ACM, Vol. 21, No. 2, Feb. 1978, pp. 120-126.

Index Terms:
software engineering; probability of winning; bidding; mutual exclusion problem; distributed processing; probability; software engineering.
C.-K. Chang, "Bidding Against Competitors," IEEE Transactions on Software Engineering, vol. 16, no. 1, pp. 100-104, Jan. 1990, doi:10.1109/32.44368
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