Rational convex programs and efficient algorithms for 2-player Nash and nonsymmetric bargaining games

SIAM Journal on Discrete Mathematics

Volumn 26, Issue 3, 2012, Pages 896-918

  Vazirani, Vijay V ^a  

^a Georgia Institute of Technology   (United States)

Author keywords

Convex programs; Market equilibria; Nash bargaining

Indexed keywords

BARGAINING GAME; CONCAVE FUNCTION; CONVEX PROGRAMS; CONVEX SET; LINEAR CONSTRAINTS; MARKET EQUILIBRIA; NASH BARGAINING; NONSYMMETRIC; POLYNOMIAL-TIME; RATIONAL SOLUTION; STRONGLY POLYNOMIALS;

ALGORITHMS; GAME THEORY; POLYNOMIAL APPROXIMATION; SET THEORY;

CONVEX PROGRAMMING;

EID: 84860553610     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/110832021     Document Type: Article

References (19)

1. W. C. Brainard and H. E. Scarf, How to Compute Equilibrium Prices in 1891, Cowles Foundation Discussion Paper 1272, New Haven, CT, 2000.
2. X. Chen, X. Deng, and S.-H. Teng, Settling the complexity of computing two-player Nash equilibria, J. ACM, 56 (3), (2009).
3. D. Chakrabarty, N. Devanur, and V. V. Vazirani, New results on rationality and strongly polynomial solvability in Eisenberg-Gale markets, SIAM J. Discrete Math., 24 (3), pp. 1117-1136
4. C. Daskalakis, P. Goldberg, and C. Papadimitriou, The complexity of computing a Nash equilibrium, SIAM J. Comput., (2009), pp. 195-259.
5. E. Eisenberg and D. Gale, Consensus of subjective probabilities: The pari-mutuel method, Annl. Math. Statist., 30 (1959), pp. 165-168.
6. K. Etessami and M. Yannakakis, On the complexity of Nash equilibria and other fixed points, SIAM J. Comput., 39 (2010), pp. 2531-2597.
7. M. Grotschel, L. Lovasz, and A. Schirjver, Geometric Algorithms and Combinatorial Optimization, Springer-Verlag, Berlin, 1988.
8. G. Goel and V. V. Vazirani, A perfect price discrimination market model with production, and a rational convex program for it, Math. Oper. Res., 36, (2011), pp. 762-782.
9. K. Jain and V. V. Vazirani, Eisenberg-Gale markets: Algorithms and game-theoretic properties, Games Econom. Behav., 70 (2010), pp. 84-106.
10. E. Kalai, Nonsymmetric Nash solutions and replications of 2-person bargaining, Internat. J. Game Theory, 6 (1977), pp. 129-133.
11. E. Kalai, Solutions to the bargaining problem, in L. Hurwicz, D. Schmeidler, and H. Sonnenschein, eds., Social Goals and Social Organization, Cambridge University Press, Cambridge, UK, 1985, pp. 75-105.
12. F. P. Kelly, Charging and rate control for elastic traffic, European Transactions on Telecommunications, 8 (1997), pp. 33-37.
13. J. F. Nash, The bargaining problem, Econometrica, 18 (1950), pp. 155-162.
14. J. F. Nash, Equilibrium points in n-person games, Proc. Nat. Acad. Sci., USA, 36 (1950), pp. 48-49.
15. M. Osborne and A. Rubinstein, A Course in Game Theory, MIT Press, Cambridge, MA, 1994.
16. E. Tardos, A strongly polynomial algorithm to solve combinatorial linear programs, Operations Research, 34, (1986), pp. 250-256.
17. W. Thomson and T. Lensberg, Axiomatic Theory of Bargaining with a Variable Population, Cambridge University Press, Cambridge, UK, 1989.
18. V. V. Vazirani, The notion of a rational convex program, and an algorithm for the Arrow-Debreu Nash bargaining game, J. ACM, 59 (2012).
19. J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, NJ, 1944.