A strongly polynomial algorithm to solve combinatorial linear programs
Operations Research
On the Complexity of Nash Equilibria and Other Fixed Points (Extended Abstract)
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Market equilibrium via a primal--dual algorithm for a convex program
Journal of the ACM (JACM)
Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
Spending Constraint Utilities with Applications to the Adwords Market
Mathematics of Operations Research
A perfect price discrimination market model with production, and a (rational) convex program for it
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
New results on rationality and strongly polynomial time solvability in eisenberg-gale markets
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
A perfect price discrimination market model with production, and a (rational) convex program for it
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Rationality and Strongly Polynomial Solvability of Eisenberg-Gale Markets with Two Agents
SIAM Journal on Discrete Mathematics
The notion of a rational convex program, and an algorithm for the Arrow-Debreu Nash bargaining game
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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The solution to a Nash or a nonsymmetric bargaining game is obtained by maximizing a concave function over a convex set, i.e., it is the solution to a convex program. We show that each 2-player game whose convex program has linear constraints, admits a rational solution and such a solution can be found in polynomial time using only an LP solver. If in addition, the game is succinct, i.e., the coefficients in its convex program are "small", then its solution can be found in strongly polynomial time. We also give non-succinct linear games whose solution can be found in strongly polynomial time.