Stability and perfection of Nash equilibria
Stability and perfection of Nash equilibria
Homotopies exploiting Newton polytopes for solving sparse polynomial systems
SIAM Journal on Numerical Analysis
A polyhedral method for solving sparse polynomial systems
Mathematics of Computation
Sparse elimination and applications in kinematics
Sparse elimination and applications in kinematics
Efficient incremental algorithms for the sparse resultant and the mixed volume
Journal of Symbolic Computation
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
A new algorithm for discussing Gröbner bases with parameters
Journal of Symbolic Computation
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Universality of Nash Equilibria
Mathematics of Operations Research
Lane-Exchange Mechanisms for Truckload Carrier Collaboration
Transportation Science
Lane-Exchange Mechanisms for Truckload Carrier Collaboration
Transportation Science
Discounted Robust Stochastic Games and an Application to Queueing Control
Operations Research
An algebraic approach for the unsatisfiability of nonlinear constraints
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Computing equilibria using interval constraints
CSCLP'04 Proceedings of the 2004 joint ERCIM/CoLOGNET international conference on Recent Advances in Constraints
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A central concern of game theory is the computation of Nash equilibria. These are characterized by systems of polynomial equations and inequalities. We survey the use of currently available software to solve these systems, and conclude that polyhedral homotopy continuation appears to scale best with increasing problem size.