Here is an application of game theory to political science. We will build a simple model of political platform competition. Consider an ideological"street" with people residing on it and 2 political parties choosing where to locate themselves along this street and "sell" their product to the residents in order to capture votes.Location in these types of models does not refer to geographical location, but rather ideological stand. For simplicity, assume people are uniformly distributed along this street (just as many people in the middle as there are on extremes or at any other point of the street), so capturing votes simply means capturing as high of a street segment as you can. If you wish you can draw this on a piece of paper as a line segment representing the street and then consider different possible locations for the 2 parties. The natural assumption is that the residents will vote for the party that is closer to them, as given by their street location. Let's also assume that everybody on the street will vote.

Questions:

1. What is the Nash Equilibrium of this game? Where will the 2 parties locate themselves? You won't be able to draw this as a matrix so instead you need to use the "guess and verify" method. Guess some possible locations and verify that neither party wants to deviate from there.

2. How does the game theoretic prediction from Q1 compare with the reality of the political environment? If you find some differences, can you explain how those differences can be explained? What could possibly be changed in the model described above that will lead to a closer representation of reality and a better fit between the game theoretic prediction and reality?