A differentiable homotopy to compute Nash equilibria of n-person games

Economic Theory

Volumn 18, Issue 1, 2001, Pages 159-185

  Herings, P Jean Jacques ^a   Peeters, Ronald J A P ^a  

^a MAASTRICHT UNIVERSITY   (Netherlands)

Author keywords

Computation of equilibria; Noncooperative game theory; Tracing procedure

Indexed keywords

EID: 0035533757     PISSN: 09382259     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00004129     Document Type: Article

References (26)

1. 1. Brown, D.J., DeMarzo, P.M., Eaves, B.C.: Computing equilibria when asset markets are incomplete. Econometrica 64, 1-27 (1996)
2. 2. Damme, E.E.C. van: Stability and perfection of Nash equilibria. New York: Springer 1987
3. 3. Damme, E.E.C. van: Game theory: the next stage. In: Kirman, A.P., Gérard-Varet, L.A. (eds.) Economics beyond the millenium, pp. 184-214. Oxford: Oxford University Press 1995
4. 4. Elzen, A.H. van den, Talman, A.J.J.: An algorithmic approach towards the tracing procedure of Harsanyi and Selten. Games and Economic Behavior 28, 130-145 (1999)
5. 5. Garcia, C.B., Lemke, C.E., Lüthi, H.J.: Simplicial approximation of an equilibrium point of non-cooperative N-person games. In: Hu, T.C., Robinson, S.M. (eds.) Mathematical programming, pp. 227-260. New York: Academic Press 1973
6. 6. Garcia, C.B., Zangwill, W.I.: Pathways to solutions, fixed points, and equilibria. Englewood Cliffs: Prentice Hall 1981
7. 7. Harsanyi, J.C.: Oddness of the number of equilibrium points: a new proof. International Journal of Game Theory 2, 235-250 (1973)
8. 8. Harsanyi, J.C.: The tracing procedure: a Bayesian approach to defining a solution for n-person noncooperative games. International Journal of Game Theory 4, 61-94 (1975)
9. 9. Harsanyi, J.C., Selten, R.: A general theory of equilibrium selection in games. Cambridge: MIT Press 1988
10. 10. Herings, P.J.J.: A globally and universally stable price adjustment process. Journal of Mathematical Economics 27, 163-193 (1997)
11. 11. Herings, P.J.J.: Two simple proofs of the feasibility of the linear tracing procedure. Economic Theory 15, 485-490 (2000)
12. 12. Herings, P.J.J., Elzen, A.H. van den: Computation of the Nash equilibrium selected by the tracing procedure in N-person games. Tilburg: CentER Discussion Paper, No. 9804, Tilburg University. Games and Economic Behavior (accepted) (2001)
13. 13. Herings, P.J.J., Schmedders, K.: Computing equilibria in finance economies with incomplete markets and transaction costs. Meteor Research Memorandum 00/34, University of Maastricht, Maastricht (2000)
14. n, I. Morse theory, Chebyshev approximation. Methoden und Verfahren der mathematischen Physik, vol. 29. Frankfurt: Peter Lang 1983
15. 15. Judd, K.L.: Computational economics and economic theory: substitutes and complements? Journal of Economic Dynamics and Control 21, 907-942 (1997)
16. 16. Laan, G. van der, Talman, A.J.J., Heijden L. van der: Simplicial variable dimension algorithms for Solving the nonlinear complementarity problem on a product of unit simplices using a general labelling. Mathematics of Operation Research 12, 377-397 (1987)
17. 17. Lemke, C.E., Howson J.T. Jr.: Equilibrium points of bimatrix games. SIAM Journal on Applied Mathematics 12, 413-423 (1964)
18. 18. Mas-Colell, A.: The theory of general economic equilibrium: a differentiable approach. Cambridge: Cambridge University Press 1985
19. 19. McKelvey, R.D., McLennan, A.: Computation of equilibria in finite games. In: Amman, H.M., Kendrick, D.A., Rust, J. (eds.) Handbook of computational economics, vol. I, pp. 87-142. Amsterdam: Elsevier 1996
20. 20. McLennan, A.: The expected number of Nash equilibria of a normal form game. Mimeo (1999)
21. 21. Rosenmüller, J.: On a generalization of the Lemke-Howson algorithm to noncooperative N-person games. SIAM Journal on Applied Mathematics 21, 73-79 (1971)
22. 22. Schanuel, S.H., Simon, L.K., Zame, W.R.: The algebraic geometry of games and the tracing procedure. In: Selten, R. (ed.) Game equilibrium models II, methods, morals and markets, pp. 9-43. Berlin Heidelberg New York: Springer 1991
23. 2 maps. Applied Mathematic and Computation 5, 297-311 (1979)
24. 2 maps. ACM Transactions on Mathematical Software 6, 252-260 (1980)
25. 25. Watson, L.T., Billups, S.C., Morgan, A.P.: HOMPACK: a suite of codes for globally convergent homotopy algorithms. ACM Transactions on Mathematical Software 13, 281-310 (1987)
26. 26. Wilson, R.: Computing equilibria of N-person games. SIAM Journal on Applied Mathematics 21, 80-87 (1971)