• Corpus ID: 245877823

Safe Equilibrium

@article{Ganzfried2022SafeE,
  title={Safe Equilibrium},
  author={Sam Ganzfried},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.04266}
}
The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may obtain an extremely low payoff. On the other hand, a maximin strategy assumes that all opposing agents are playing to minimize our payoff (even if it is not in their best interest), and ensures the maximal possible worst-case payoff, but results in exceedingly… 

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References

SHOWING 1-10 OF 15 REFERENCES

Safe opponent exploitation

The problem of playing a finitely-repeated two-player zero-sum game safely is considered, and it is shown that profitable deviations are indeed possible---specifically, in games where certain types of 'gift' strategies exist, which is defined formally.

Mixed-Integer Programming Methods for Finding Nash Equilibria

The first mixed integer program (MIP) formulations for finding Nash equilibria in games (specifically, two-player normal form games) are presented and different design dimensions of search algorithms that are based on those formulations are studied.

Reexamination of the perfectness concept for equilibrium points in extensive games

  • R. Selten
  • Economics
    Classics in Game Theory
  • 2020
The concept of a perfect equilibrium point has been introduced in order to exclude the possibility that disequilibrium behavior is prescribed on unreached subgames. (Selten 1965 and 1973).

Safe Strategies for Agent Modelling in Games

The Safe Policy Selection algorithm (SPS) is introduced as a method to vary in a controlled fashion and it is proved in the limit that an agent using SPS is guaranteed to attain at least a safety value in the cases when the opponent modelling is ineffective.

Computing Robust Counter-Strategies

A technique for computing robust counter-strategies for adaptation in multiagent scenarios under a variety of paradigms that can take advantage of a suspected tendency in the decisions of the other agents, while bounding the worst-case performance when the tendency is not observed.

Fictitious Play Outperforms Counterfactual Regret Minimization

It is shown that fictitious play leads to improved Nash equilibrium approximation with statistical significance over a variety of game classes and sizes.

Fast Complete Algorithm for Multiplayer Nash Equilibrium

A new complete algorithm for computing Nash equilibrium in multiplayer general-sum games, based on a quadratically-constrained feasibility program formulation, that runs significantly faster than the prior fastest complete algorithm and that its runtimes even outperform the best incomplete algorithms.

AN ITERATIVE METHOD OF SOLVING A GAME

Abstract : In the paper, demonstration is made of the validity of an iterative procedure suggested by George W. Brown for a two-person game. This method corresponds to each player choosing in turn

Fictitious Play with Maximin Initialization

It is shown that the degree of equilibrium approximation error ofictitious play can be significantly reduced by carefully selecting the initial strategies, and several new procedures for strategy initialization are presented.

Regret Minimization in Games with Incomplete Information

It is shown how minimizing counterfactual regret minimizes overall regret, and therefore in self-play can be used to compute a Nash equilibrium, and is demonstrated in the domain of poker, showing it can solve abstractions of limit Texas Hold'em with as many as 1012 states, two orders of magnitude larger than previous methods.