Computer Generated Farmers: Information and Nash Equalibrium

Introduction

Economic actors in general are greedy. They will try to better their outcome using information they acquire, mimicing the strategies of anyone who is doing better than them. Our question was, given a simple economic system and actors following a simple rule: do as other who are doing better than you are doing, will this system ever reach a reasonably stable nash equalibrium? Will it ever become pareto optimal? And will the economic actors be happy? In order to answer these questions, we built a computer generated simulation program and monitored how certain factors influenced the system.

Objective

We used computer gerated farmers to simulate a special economic system, in which each farmer had a limited number of friends who they could get information from to try to better their strategic outcome.

Setup

We will generate 100 digital farmers, each having a production capacity of 1, choice of 2 crops to make (corn and rice), and a profit function. We will call the amount of corn a farmer makes alpha. Since each farmer has a production capacity of 1, naturally the amount of rice this farmer makes will be 1-alpha. Each farmer will try to maximize their profit according to the price of crops in the market and the profit function. The profit function will take the form similar to p=a/x where p is profit, a is some constant, and x is the quantity of crops the farmer is producing. with no asymptote. This follows the rule that the more units of a product produced, the less the production cost (usually) is. The price function will also be determined by a P=b/X function, this time P standing for price of the crop, b is some constant, and X is the total number of the crop being produced. Therefore, the two functions will look like the following:

File:Function.png You have to be logged into the wiki to upload a image.Gribble 15:34, 12 Apr 2006 (EDT)

When the farmer makes a decision, he will treat the price as a constant, and maximize profit according to the profit function. This can be solved using some simple calculus.

Maximize <math>a1/x1+a2/x2</math> Subject to