Nash equilibria in random games

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn 2005, Issue , 2005, Pages 123-131

  Bárány, Imre ^a,b   Vempala, Santosh ^c   Vetta, Adrian ^d  

^a INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

LAS VEGAS ALGORITHM; NASH EQUILIBRIA; POLYTYPE FORMATION; RANDOM GAMES;

ALGORITHMS; COMBINATORIAL MATHEMATICS; MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS;

GAME THEORY;

EID: 33645030644     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SFCS.2005.52     Document Type: Conference Paper

References (39)

1. F. Affentranger and J. Wieacker, "On the convex hull of a uniform random points in a simple d-polytope", Discrete and Computational Geometry, 6, pp291-305, 1991.
2. N. Alon and J. Spencer, The Probabilistic Method, 2nd edition, Wiley, 2000.
3. D. Avis and K. Fukuda, "A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra", Discrete Computational Geometry, 8, pp295-313, 1992.
4. I. Bárány, "Intrinsic volumes and f-vectors of random polytopes", Math. Ann. 285, pp671-699, 1989.
5. I. Bárány and L. Dalla, "Few points to generate a random polytope", Mathematika 44, pp325-331, 1997.
6. I. Bárány and D. Larman, "Convex bodies, economic cap coverings, random polytopes", Mathematika 35, pp274-291, 1988.
7. K. Borgwardt, The Simplex Method: a probabilistic analysis, Springer-Verlag, 1987.
8. C. Buchta, "On the average number of maxima in a set of vectors", Information Processing Letters, 33, pp63-65, 1989.
9. C. Buchta, "A remark on random approximations of simple polytopes", Anz. sterreich. Akad. Wiss. Math.-Natur. Kl, 126, pp17-20, 1989.
10. V. Conitzer and T. Sandholm, "Complexity results about Nash equilibria", Proceedings of IJCAI, pp765-771, 2003.
11. L. Devroye, "A note on finding convex hulls via maximal vectors", Information Processing Letters, 11(1), pp53-56, 1980.
12. R. Dwyer, "On the convex hull of random points in a polytope", Journal of Applied Probability, 25, pp688-699, 1988.
13. R. Dwyer, "Convex hulls of samples from spherically symmetric distributions", Discrete Applied Mathematics, 31, pp 113-132, 1991.
14. A. Fabrikant, C. Papadimitriou and K. Talwar, "The complexity of pure-strategy Nash Equilibria", Proceedings of 36th STOC, pp604-612, 2004.
15. W. Feller, An Introduction to Probability Theory and it Applications (Vol. I), Wiley, 1950.
16. H. Groemer, "Limit theorems for the convex hull of random points in higher dimensions", Pacific Journal of Mathematics, 45(2), pp525-533, 1973.
17. I. Heuter, "Limit theorems for the convex hull of random points in higher dimensions", Transactions of the American Mathematical Society, 351, pp4337-4363, 1999.
18. S. Janson, "Poisson approximation for large deviations", Random Structures and Algorithms, 1, pp221-230, 1990.
19. A. Kalai, personal communication, 2005.
20. J. Kingman, "Random secants of a convex body", Journal of Applied Probability, 6, pp66-672, 1969.
21. D. Kirkpatrick and R. Seidel, "The ultimate planar convex hull algorithm", SIAM J. Comp., 15, pp287-299, 1988.
22. R. Lipton, E. Markakis and A. Mehta, "Playing large games using simple strategies", Proceedings of E-Commerce, pp36-41, 2003.
23. A. McLennan, "The expected number of Nash equilibria in a normal form game", to appear in Econometrica.
24. A. McLennan and J. Berg, "The asymptotic expected number of Nash equilibria of two player normal form games", to appear in Games and Economic Behavior.
25. N. Megiddo, "Improved asymptotic analysis of the average number of steps performed by the self-dual sim-plex algorithm", Mathematical Programming, 35(2), pp140-172, 1986.
26. N. Megiddo and C. H. Papadimitriou, "On total functions, existence theorems and computational complexity", Theoret. Comput. Sci., 81(2), pp317-324, 1991.
27. C. H. Papadimitriou, "On the complexity of the parity argument and other inefficient proofs of existence", Journal of Computer and System Sciences, 48(3), pp498-532, 1994.
28. C. H. Papadimitriou, "Algorithms, games and the internet", Proceedings of 33rd STOC, pp749-753, 2001.
29. C. H. Papadimitriou, "Computing correlated equilibria in multiplayer game", Proceedings of 37th STOC, pp49-56, 2005.
30. C. Papadimitriou and T. Roughgarden, "Computing equilibria in multi-player games", Proceedings of 16th SODA, pp82-91, 2005.
31. n. I.", Journal of Applied Probability, 7, pp35-48, 1970.
32. R. Savani and B. von Stengel, "Exponentially Many Steps for Finding a Nash Equilibrium in a Bimatrix Game", Proceedings of 45th FOCS, pp258-267, 2004.
33. R. Schneider, "Discrete aspects of stochastic geometry", in eds. J. Goodman and J. O'Rourke, Handbook of Discrete and Computational Geometry, Boca Raton, CRC Press, pp255-278, 2004.
34. S. Smale, "On the average number of steps in the sim-plex method of linear programming", Mathematical Programming, 27, pp241-262, 1983.
35. D. A. Spielman, S. Teng, "Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time", Journal of the ACM, 51(3), pp385-463, 2004.
36. B. von Stengel, "New maximal numbers of equilibria in bimatrix games", Discrete and Computational Geometry, 21, pp557-568, 1999.
37. B. von Stengel, "Computing equilibria for two-person games", in eds. R. Aumann and S. Hart, Handbook of Game Theory, Vol. 3, North-Holland, Amsterdam, pp1723-1759, 2002.
38. B. van Wel, "The convex hull of a uniform sample from the interior of a simple d-polytope", Journal of Applied Probability, 26, pp259-273, 1989.
39. W. Weil and J. Wieacker, "Stochastic geometry", In Handbook of convex geometry, North-Holland, Amsterdam, pp1391-1438, 1993.