## Nash equilibrium in duopoly with products defined by two characteristics

http://www.stern.nyu.edu/networks/Economides_Nash_Equilibrium_in_Duopoly.pdf

Nash equilibrium in duopoly with products defined by two characteristics

This is an essay written by Nicholas Economides from Columbia University in 1986. It basically discusses whether Nash equilibrium exists or not in duopoly when products have two characteristics and what could be the influence factor. Knowing that when two companies have only product with one characteristic difference distance is the factor that determined if Nash equilibrium exist. Lots of famous works have proved that when two companies are close enough, both of them would undercut their opponents and capture the whole market. Instead of doing the same work as his predecessor, Nicholas focuses on two variables and uses math to prove his assumption. Finally, he came to this conclusion: Nash equilibrium in prices exists for all symmetric varieties. This means no matter no far this two companies are, as long as their product has two difference, they can reach Nash equilibrium.

What this article related to what we have learned is definitely Nash equilibrium. However, here it more like to be result. The main idea here is how two characteristics have different effect with one characteristic. Then, I have to talk something about Nash equilibrium myself. Nash equilibrium is a very important phenomenon occurs in all kinds of economics models. Most of time, it comes out with duopoly. In an identical model, when there are only two huge company in one market, their price will fix at an certain level and this price is definitely not the best for both company. However, they have to hold this price because, whenever one company adjusts its price (it doesn’t matter whether the price is going up or down), it losses profits. Nash equilibrium is not good for the whole market but it lets the companies in market to reach a real balance.