Matrix game (LP for game theory)

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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


  • TBD


  • Add later