A global Newton method to compute Nash equilibria

Journal of Economic Theory

Volumn 110, Issue 1, 2003, Pages 65-86

  Govindan, Srihari ^a   Wilson, Robert ^b  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Algorithm; Global Newton method; Homotopy; Nash equilibrium; Noncooperative game

Indexed keywords

EID: 0038009937     PISSN: 00220531     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0531(03)00005-X     Document Type: Article

References (34)

1. Y. Balasko, Foundations of the Theory of General Equilibrium, Academic Press, Orlando, FL, 1988.
2. A. Dold, Lectures on Algebraic Topology, Springer, New York, 1972.
3. B. Eaves, The linear complementarity problem, Management Sci. 17 (1971) 612-634.
4. B. Eaves, Homotopies for the computation of fixed points, Math. Program. 3 (1972) 25-237.
5. B. Eaves, A Course in Triangulations for Solving Equations with Deformations, Springer, Berlin, 1984.
6. B. Eaves, H. Scarf, Equivalence of LCPs and PLS, Math. Methods Oper. Res. 6 (1981) 475-494.
7. B. Eaves, K. Schmedders, General equilibrium models and homotopy methods, J. Econom. Dyn. Control 23 (1999) 1249-1279.
8. S. Govindan, R. Wilson, Equivalence and invariance of degree and index of Nash equilibria, Games Econom. Behav. 26 (1997) 56-61.
9. S. Govindan, R. Wilson, Direct proofs of generic finiteness of Nash equilibrium outcomes, Econometrica 69 (2001) 765-769.
10. S. Govindan, R. Wilson, Computing Nash equilibria by iterated polymatrix approximation, J. Econom. Dyn. Control 27 (2003), to appear.
11. S. Govindan, R. Wilson, Structure theorems for game trees, Proc. Natl. Acad. Sci. 99 (2002) 9077-9080 Available online at www.pnas.org.
12. F. Gül, D. Pearce, E. Stacchetti, A bound on the proportion of pure strategy equilibria in generic games, Math. Methods Oper. Res. 18 (1993) 548-552.
13. J. Harsanyi, R. Selten, A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge, MA, 1988.
14. P. Herings, R. Peeters, A differentiable homotopy to compute Nash equilibria of n-person games, Econom. Theory 18 (2001) 159-185.
15. M. Hirsch, A proof of the non-retractability of a cell onto its boundary, Proc. Amer. Math. Soc. 14 (1963) 364-365.
16. M. Hirsch, S. Smale, On algorithms for solving. f (x) = 0, Commun. Pure Appl. Math. 32 (1979) 281-312.
17. J. Howson, R. Rosenthal, Bayesian equilibria of finite two-person games with incomplete information, Management Sci. 21 (1974) 313-315.
18. D. Keenan, Further remarks on the global Newton method, J. Math. Econom. 8 (1981) 159-165.
19. E. Kohlberg, J.-F. Mertens, On the strategic stability of equilibria, Econometrica 54 (1986) 1003-1039.
20. C. Lemke, Bimatrix equilibrium points and mathematical programming, Management Sci. 11 (1965) 681-689.
21. C. Lemke, J. Howson, Equilibrium points of bimatrix games, J. Soc. Ind. Appl. Math. 12 (1964) 413-423.
22. J. Mertens, Stable equilibria - a reformulation, Part I: definition and basic properties, Math. Methods Oper. Res. 14 (1989) 575-625.
23. J. Rosenmüller, On a generalization of the Lemke-Howson algorithm to noncooperative N-person games, SIAM J. Appl. Math. 21 (1971) 73-79.
24. H. Scarf, T. Hansen, The Computation of Economic Equilibrium, Yale University Press, New Haven, CT, 1973.
25. L. Shapley, A note on the Lemke-Howson algorithm, Math. Program. Stud. 1 (1974) 175-189.
26. S. Smale, A convergent process of price adjustment and global Newton methods, J. Math. Econom. 3 (1976) 107-120.
27. J. Tomlin, Robust implementation of Lemke's method for the linear complementarity problem, Math. Program. Stud. 7 (1978) 55-60.
28. B. von Stengel, Computing equilibria for two-person games, in: R. Aumann, S. Hart (Eds.), Handbook of Game Theory, Vol. 3, Chapter 45, pp. 1723-1759, North-Holland, Amsterdam, 2002.
29. B. von Stengel, New lower bounds for the number of equilibria in bimatrix games, Technical Report 264, Institut für Theoretische Informatik, Eidgenössische Technische Hochschule, Zürich, 1997.
30. R. Wilson, Computing equilibria of n-person games, SIAM J. Appl. Math. 21 (1971) 80-87.
31. R. Wilson, Computing equilibria of two-person games from the extensive form, Management Sci. 18 (1972) 448-460.
32. R. Wilson, Computing simply stable equilibria, Econometrica 60 (1972) 1039-1070.
33. R. Wilson, The bilinear complementarity problem and competitive equilibria of piecewise-linear economic models, Econometrica 46 (1978) 87-103.
34. Y. Yamamoto, A path-following procedure to find a proper equilibrium of finite games, Int. J. Game Theory 22 (1993) 249-259.