# Difference between revisions of "Matrix game (LP for game theory)"

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Steward: Wei-Han Chen, Fengqi You | 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 |

## Revision as of 01:21, 12 November 2020

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