Skip to main content
×
Home
    • Aa
    • Aa

From coin tossing to rock-paper-scissors and beyond: a log-exp gap theorem for selecting a leader

  • Michael Fuchs (a1), Hsien-Kuei Hwang (a2) and Yoshiaki Itoh (a3)
Abstract
Abstract

A class of games for finding a leader among a group of candidates is studied in detail. This class covers games based on coin tossing and rock-paper-scissors as special cases and its complexity exhibits similar stochastic behaviors: either of logarithmic mean and bounded variance or of exponential mean and exponential variance. Many applications are also discussed.

Copyright
Corresponding author
* Postal address: Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 300, Taiwan. Email address: mfuchs@math.nctu.edu.tw
** Postal address: Institute of Statistical Science, Academia Sinica, Taipei, 115, Taiwan.
*** Postal address: Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo, 190-8562, Japan.
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] P. N. Bajaj and G. R. Mendieta (1993).An open toss problem.Internat. J. Math. Math. Sci. 16,621623.

[2] O. I. Bogoyavlensky (1988).Integrable discretizations of the KdV equation.Phys. Lett. A 134,3438.

[3] F. T. Bruss and C. A. O’Cinneide (1990).On the maximum and its uniqueness for geometric random samples.J. Appl. Prob. 27,598610.

[4] J. Capetanakis (1979).Tree algorithms for packet broadcast channels.IEEE Trans. Inf. Theory 25,505515.

[5] W.-M. Chen and H.-K. Hwang (2003).Analysis in distribution of two randomized algorithms for finding the maximum in a broadcast communication model.J. Algorithms 46,140177.

[6] L. Devroye (1992).A limit theory for random skip lists.Ann. Appl. Prob. 2,597609.

[7] B. Eisenberg (2008).On the expectation of the maximum of IID geometric random variables.Statist. Prob. Lett. 78,135143.

[9] G. Fayolle , P. Flajolet and M. Hofri (1986).On a functional equation arising in the analysis of a protocol for a multi-access broadcast channel.Adv. Appl. Prob. 18,441472.

[11] P. Flajolet and R. Sedgewick (2009).Analytic Combinatorics.Cambridge University Press.

[12] P. Flajolet , X. Gourdon and P. Dumas (1995).Mellin transforms and asymptotics: harmonic sums.Theoret. Comput. Sci. 144,358.

[14] L. Frachebourg and P. L. Krapivsky (1998).Fixation in a cyclic Lotka–Volterra model.J. Phys. A 31,L287L293.

[15] M. Fuchs , H.-K. Hwang and V. Zacharovas (2014).An analytic approach to the asymptotic variance of trie statistics and related structures.Theoret. Comput. Sci. 527,136.

[16] M. Fuchs , H.-K. Hwang , Y. Itoh and H. M. Mahmoud (2014).A binomial splitting process in connection with corner parking problems.J. Appl. Prob. 51,971989.

[17] A. V. Gnedin (2010).Regeneration in random combinatorial structures.Prob. Surveys 7,105156.

[21] Y. Itoh (1971).Boltzmann equation on some algebraic structure concerning struggle for existence.Proc. Japan Acad. 47,854858.

[22] Y. Itoh (1975).An H-theorem for a system of competing species.Proc. Japan Acad. 51,374379.

[23] Y. Itoh (1987).Integrals of a Lotka–Volterra system of odd number of variables.Prog. Theoret. Phys. 78,507510.

[24] Y. Itoh , H. Maehara and N. Tokushige (2000).Oriented graphs generated by random points on a circle.J. Appl. Prob. 37,534539.

[26] P. Jacquet and W. Szpankowski (1998).Analytical depoissonization and its applications.Theoret. Comput. Sci. 201,162.

[27] R. Kalpathy and H. Mahmoud (2014).Perpetuities in fair leader election algorithms.Adv. Appl. Prob. 46,203216.

[28] A. W. Kemp (1984).Bulk buying of possibly defective items.J. Operat. Res. Soc. 35,859864.

[29] J. Knebel , T. Krüer , M. F. Weber and E. Frey (2013).Coexistence and survival in conservative Lotka–Volterra networks.Phys. Rev. Lett. 110,168106.

[33] H. Maehara and S. Ueda (2000).On the waiting time in a Janken game.J. Appl. Prob. 37,601605.

[34] B. H. Margolin and H. S. Jr. Winokur (1967).Exact moments of the order statistics of the geometric distribution and their relation to inverse sampling and reliability of redundant systems.J. Amer. Statist. Assoc. 62,915925.

[35] K. Nakano and S. Olariu (2002).Randomized initialization protocols for radio networks. In Handbook of Wireless Networks and Mobile Computing, ed. I. Stojmenovic.John Wiley,New York.

[38] H. Prodinger (1993).How to select a loser.Discrete Math. 120,149159.

[39] V. Rego and A. P. Mathur (1990).Exploiting parallelism across program execution: a unification technique and its analysis.IEEE Trans. Parallel Distrib. Syst. 1,399414.

[41] B. Sinervo and C. M. Lively (1996).The rock-paper-scissors game and the evolution of alternative male strategies.Nature 380,240243.

[42] J. M. Smith (1982).Evolution and the Theory of Games.Cambridge University Press.

[43] J. E. Spencer (1981).Probability, defectives and mail ordering.J. Operat. Res. Soc. 32,899906.

[47] G. Szabó and G. Fath (2007).Evolutionary games on graphs.Phys. Rep. 446,97216.

[48] K. I. Tainaka (1988).Lattice model for the Lotka–Volterra system.J. Phys. Soc. Japan 57,25882590.

[51] G. Weiss (1962).On certain redundant systems which operate at discrete times.Technometrics 4,6974.

[52] J. G. Wendel (1962).A problem in geometric probability.Math. Scand. 11,109111.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 14 *
Loading metrics...

Abstract views

Total abstract views: 45 *
Loading metrics...

* Views captured on Cambridge Core between 4th April 2017 - 16th August 2017. This data will be updated every 24 hours.