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

Authors: Nick Dotzenrod and Matt Kweon (ChE 345 Spring 2014)

Steward: Dajun Yue, Fengqi You

Date Presented: Apr. 10, 2014

Linear programming (LP) is a simple yet powerful tool that can be used as an aid in decision making under certainty - that is, the objective, constraints, and any other relevant information about the problem are known. A highly practical application of LP lies in its use in game theory. This page specifically explores how LP can be used to solve a finite two-person zero-sum game, also known as the matrix game, which is one of the simplest form of decision making games.

## Introduction

The objective of game theory is to analyze the relationship between decision-making situations in order to achieve a desirable outcome. The theory can be applied to a wide range of applications, including, but not limited to, economics, politics and even the biological sciences. In essence, game theory serves as means to create a model to represent certain scenarios that have a variety of variables and potential outcomes. With these models developed from game theory, one can determine if assumptions made for a certain scenario are valid or whether additional models should be created that could more accurately assess the current problem. Game theory can be broken into a variety of different "games," each analyzing different situations in which a decision is to be made by one player with other players potentially affecting the process.

## History

Many mathematicians would agree that John von Neumann can be considered the Father of Game Theory. John was born in Hungary in 1903 and grew up having a love for math and the sciences. In college, he received degree a degree in chemical engineering and later, a Ph.D. in mathematics from the University of Budapest.

### Matrix Game

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## Minimax Theorem

content coming soon!

## Example

example coming soon!

## References

1. S. Tadelis, Game Theory: an Introduction, Princeton University Press, 2013.

2. R. J. Vanderbei, Linear Programming: Foundations and Extensions, Springer, 2008.

3. M. J. Osborne, An Introduction to Game Theory, Oxford University Press, 2004.