# 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

## Conclusion

- TBD

## References

- Add later