Computational Complexity of Computing a Quasi-Proper Equilibrium

@inproceedings{Hansen2021ComputationalCO,
  title={Computational Complexity of Computing a Quasi-Proper Equilibrium},
  author={Kristoffer Arnsfelt Hansen and Troels Bjerre Lund},
  booktitle={FCT},
  year={2021}
}
We study the computational complexity of computing or approximating a quasi-proper equilibrium for a given finite extensive form game of perfect recall. We show that the task of computing a symbolic quasiproper equilibrium is PPAD-complete for two-player games. For the case of zero-sum games we obtain a polynomial time algorithm based on Linear Programming. For general n-player games we show that computing an approximation of a quasi-proper equilibrium is FIXPa-complete. Towards our results for… 

References

SHOWING 1-10 OF 34 REFERENCES
Computational Complexity of Proper Equilibrium
TLDR
The computational complexity of proper equilibrium in finite games is studied and it is shown that the task of simply verifying the proper equilibrium conditions of a given pure Nash equilibrium is NP-complete.
The complexity of computing a (quasi-)perfect equilibrium for an n-player extensive form game
  • K. Etessami
  • Computer Science, Mathematics
    Games Econ. Behav.
  • 2021
Computing a quasi-perfect equilibrium of a two-player game
Refining an algorithm due to Koller, Megiddo and von Stengel, we show how to apply Lemke’s algorithm for solving linear complementarity programs to compute a quasi-perfect equilibrium in behavior
The Real Computational Complexity of Minmax Value and Equilibrium Refinements in Multi-player Games
We show that for several solution concepts for finite n-player games, where \(n \ge 3\), the task of simply verifying its conditions is computationally equivalent to the decision problem of the
Efficient Computation of Equilibria for Extensive Two-Person Games
Abstract The Nash equilibria of a two-person, non-zero-sum game are the solutions of a certain linear complementarity problem (LCP). In order to use this for solving a game in extensive form, the
Computing a proper equilibrium of a bimatrix game
We provide the first pivoting-type algorithm that computes an exact proper equilibrium of a bimatrix game. This is achieved by using Lemke's algorithm to solve a linear complementarity problem (LCP)
Computing Normal Form Perfect Equilibria for Extensive Two-Person Games
TLDR
This paper presents an algorithm for computing an equilibrium of an extensive two-person game with perfect recall by virtue of using the sequence form, whose size is proportional to the size of the game tree.
The Complexity of Approximating a Trembling Hand Perfect Equilibrium of a Multi-player Game in Strategic Form
TLDR
The task of computing an approximation of a trembling hand perfect equilibrium for an n-player game in strategic form, n ≥ 3, is considered and it is shown that this task is complete for the complexity class FIXP a.
Extensive-Form Perfect Equilibrium Computation in Two-Player Games
TLDR
It is shown that the sequence form can be exploited in a non-trivial way and that, for general-sum games, finding an EFPE is equivalent to solving a suitably perturbed linear complementarity problem, and Lemke's algorithm can be applied, showing that computing an E FPE is $\textsf{PPAD}$-complete.
The Real Computational Complexity of Minmax Value and Equilibrium Refinements in Multi-player Games
  • K. A. Hansen
  • Mathematics, Computer Science
    Theory of Computing Systems
  • 2018
TLDR
The results thus improve previous results of NP-hardness as well as Sqrt-Sum- hardness of the decision problems to completeness for ∃ℝ${\exists {\mathbb {R}}}$-completeness for the problem of deciding existence of a probability constrained Nash equilibrium.
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