The Complexity of the Homotopy Method, Equilibrium Selection, and Lemke-Howson Solutions

@article{Goldberg2011TheCO,
  title={The Complexity of the Homotopy Method, Equilibrium Selection, and Lemke-Howson Solutions},
  author={P. Goldberg and C. Papadimitriou and Rahul Savani},
  journal={2011 IEEE 52nd Annual Symposium on Foundations of Computer Science},
  year={2011},
  pages={67-76}
}
We show that the widely used homotopy method for solving fix point problems, as well as the Harsanyi-Selten equilibrium selection process for games, are PSPACE-complete to implement. Extending our result for the Harsanyi-Selten process, we show that several other homotopy-based algorithms for finding equilibria of games are also PSPACE-complete to implement. A further application of our techniques yields the result that it is PSPACE-complete to compute any of the equilibria that could be found… Expand
The Complexity of Hex and the Jordan Curve Theorem
How Do You Like Your Equilibrium Selection Problems? Hard, or Very Hard?
An Empirical Study of Finding Approximate Equilibria in Bimatrix Games
The Complexity of Computing Equilibria
The Complexity of the Simplex Method
Unit Vector Games
The Simplex Algorithm Is NP-Mighty
The curse of simultaneity
...
1
2
3
4
...

References

SHOWING 1-10 OF 11 REFERENCES
Homotopy Methods to Compute Equilibria in Game Theory
A Differentiable Homotopy to Compute Nash Equilibria of N-Person Games
Computation of the Nash Equilibrium Selected by the Tracing Procedure in N-Person Games
Settling the complexity of computing two-player Nash equilibria
On the Complexity of Nash Equilibria and Other Fixed Points
The tracing procedure: A Bayesian approach to defining a solution forn-person noncooperative games
Nash Equilibrium and the History of Economic Theory
Homotopies for computation of fixed points
  • B. Eaves
  • Mathematics, Computer Science
  • Math. Program.
  • 1972
Graphical Models for Game Theory
...
1
2
...