Matrix game (LP for game theory)

From Cornell University Computational Optimization Open Textbook - Optimization Wiki
Revision as of 02:21, 12 November 2020 by Dlo52 (talk | contribs) (Initial edits.)
Jump to navigation Jump to search

Author: David Oswalt (SysEn 6800 Fall 2020)

Steward: Wei-Han Chen, Fengqi You

What is the Matrix Game?

  • History and overview of Game Theory
  • Rationality, strategy, payout
  • Application to LP (minimax and duality)

Theory and Algorithmic Discussion

  • Game Theory – Prisoner’s Dilemma
  • Stochastic Vector Introduction – Prisoner’s Dilemma with different probabilities
  • How this relates to Linear Programming
  • Minimax Theorem
    • Minimize the maximum payoff of opposing player
  • Duality Theorem

Numerical Example

  • Fourth and Goal Dilemma
  • Offensive and defensive decisions and payoffs
  • Results

Other Applications of the Matrix Game

  • Economics
  • War
  • Gambling
  • Intelligence and Foreign Policy

Conclusion

  • TBD

References

  • Add later