On the complexity of nash equilibria and other fixed points

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

Volumn , Issue , 2007, Pages 113-123

  Etessami, Kousha ^a   Yannakakis, Mihalis ^b  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b Columbia University ^*

Author keywords

[No Author keywords available]

Indexed keywords

(ALGORITHMIC) COMPLEXITY; FIXE D POINTS; FIXED POINTS (FP); MIXED STRATEGIES; NASH EQUILIBRIUM (NE);

COMPUTER SCIENCE; FIBER OPTIC CHEMICAL SENSORS; TELECOMMUNICATION NETWORKS;

FOUNDATIONS;

EID: 46749089648     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2007.4389485     Document Type: Conference Paper

References (41)

1. E. Allender, P. Bürgisser, J. Kjeldgaard-Pedersen, and P. B. Miltersen. On the complexity of numerical analysis. In 21st IEEE Comp. Compl. Conf., 2006.
2. R. M. Anderson. "Almost" implies "Near". Trans. Am. Math. Soc., 296, pp. 229-237, 1986.
3. R. A. Becker and S. K. Chakrabarti. Satisficing behavior, Brouwer's fixpoint theorem and Nash equilibrium. Economic Theory, 26:63-83, 2005.
4. L. Blum, F. Cucker, M. Shub, and S. Smale. Complexity and Real Computation. Springer-Verlag, 1998.
5. V. Bubelis. On equilibria in finite games. Intl. J. Game Theory, 8(2), 65-79, 1979.
6. J. Canny. Some algebraic and geometric computations in PSPACE. In STOC, pp. 460-467, 1988.
7. X. Chen and X. Deng. Settling the complexity of two-player Nash equilibrium. FOCS, pp. 261-272, 2006.
8. X. Chen, X. Deng, and S. H. Teng. Computing Nash equilibria: approximation and smoothed complexity. In FOCS, pp. 603-612, 2006.
9. A. Condon. The complexity of stochastic games. Inf. & Comp., 96(2):203-224, 1992.
10. C. Daskalakis, P. Goldberg, and C. Papadimitriou. The complexity of computing a Nash equilibrium. In STOC, pp. 71-78, 2006.
11. C. Daskalakis, A. Fabrikant, and C. Papadimitriou. The game world is flat: The complexity of Nash equilibria in succinct games. Proc. ICALP, 2006.
12. R. S. Datta. Universality of Nash equilibria. Math. of Oper. Res., 28(3), 424-432, 2003.
13. R. Durbin, S. R. Eddy, A. Krogh, and G. Mitchison. Biological Sequence Analysis: Probabilistic models of Proteins and Nucleic Acids. Cambridge U. Press, 1999.
14. B. C. Eaves, H. Scarf. The solution of systems of piecewise linear equations. Math, of O.R., 1(1), 1-27, 1976.
15. J. Esparza, A. Kučera, and R. Mayr. Model checking probabilistic pushdown automata. In LICS, 2004.
16. K. Etessami and M. Yannakakis. Recursive Markov chains, stochastic grammars, and monotone systems of non-linear equations. In STACS, 2005. (See full expanded version from http://homepages.inf.ed.ac.uk/kousha/).
17. K. Etessami and M. Yannakakis. Recursive Concurrent Stochastic Games. In ICALP, 2006.
18. M. R. Garey, R. L. Graham, and D. S. Johnson. Some NP-complete geometric problems. In 8th ACM STOC, pp. 10-22, 1976.
19. J. Geanakoplos. Nash and Walras equilibrium via Brouwer. Economic Theory, 21:585-603, 2003.
20. I. Gilboa and E. Zemel. Nash and correlated equilibria: some complexity considerations. Games and Economic Behavior, 1:80-93, 1989.
21. P. Goldberg and C. Papadimitriou. Reducibility among equilibrium problems. In STOC, 2006.
22. F. Gul, D. Pearce, E. Stacchetti. A bound on the proportion of pure strategy equilibria in generic games. Math. 0} Oper. Res. 18, pp. 548-552, 1993.
23. P. Haccou, P. Jagers, and V. A. Vatutin. Branching Processes: Variation, Growth, and Extinction of Populations. Cambridge U. Press, 2005.
24. T. E. Harris. The Theory of Branching Processes. Springer-Verlag, 1963.
25. R. J. Horn and C. R. Johnson. Matrix Analysis. Cambridge U. Press, 1985.
26. B. Juba. On the hardness of simple stochastic games. Master's thesis, CMU, 2005.
27. M. Kimmel and D. E. Axelrod. Branching processes in biology. Springer, 2002.
28. K.-I. Ko. Computational complexity of fixed points and intersection points. J. Complexity, 11, pp. 265-292, 1995.
29. A. N. Kolmogorov and B. A. Sevastyanov. The calculation of final probabilities for branching random processes. Doklady, 56:783-786, 1947. (Russian).
30. R. Lipton and E. Markakis. Nash equilibria via polynomial equations. In LATIN'04, 2004.
31. R.J. Lipton, E. Markakis, A. Mehta. Playing large games using simple strategies. Proc. ACM Conf. Elec. Comm., 36-41, 2003.
32. C. Manning and H. Schütze. Foundations of Statistical Natural Language Processing. MIT Press, 1999.
33. J. Nash. Non-cooperative games. Annals of Mathematics, 54:289-295, 1951.
34. C. Papadimitriou. The Euclidean traveling salesman problem is NP-complete. Theor. Comp. Sci., 4:237-244, 1977.
35. C. Papadimitriou. On the complexity of the parity argument and other inefficient proofs of existence. J. Comput. Syst. Sci., 48(3):498-532, 1994.
36. J. Renegar. On the computational complexity and geometry of the first-order theory of the reals, parts I-III. J. Symb. Comp., 13(3):255-352, 1992.
37. H. Scarf. The approximation of fixed points of a continuous mapping. SIAM J. Appl. Math., 15:1328-1343, 1967.
38. H. Scarf. The Computation of Economic Equilibria. Yale University Press, 1973.
39. L.S. Shapley. Stochastic games. Proc. Nat. Acad. Sci., 39:1095-1100, 1953.
40. P. Tiwari. A problem that is easier to solve on the unit-cost algebraic RAM. Journal of Complexity, pp. 393-397, 1992.
41. H. Uzawa. Walras's existence theorem and Brouwer's fixed point theorem. Econ. Stud. Q., 13:59-62, 1962.