Answer Happy

game theory econ3115
This is a bit tricky. For part (a) you need to draw the returns to A and B as a function of the fraction of population in A. The two lines cross three times; if you don't have three crosses, you have drawn it wrong. You should have five equilibrium in part b 5 points for each part S3. Consider a small geographic region with a total population of 1 million people. There are two towns, Alphaville and Betaville, in which each person can choose to live. For each person, the benefit from living in a town increases for a while with the size of the town (because larger towns have more amenities and so on), but after a point it decreases (because of congestion and so on). If x is the fraction of the population that lives in the same town as you do, your payoff is given by * if 0 5 xs 0.4 0.6 - 0.5x if 0.4 <xsl. (a) Draw a graph like Figure 11.11, showing the benefits of living in the two towns, as the fraction living in one versus the other varies con tinuously from 0 to 1. (b) Equilibrium is reached either when both towns are populated and their residents have equal payoffs or when one town-say Betaville-is totally depopulated, and the residents of the other town (Alphaville) get a higher payoff than would the very first per son who seeks to populate Betaville. Use your graph to find all such equilibria. (C) Now consider a dynamic process of adjustment whereby people gradually move toward the town whose residents currently enjoy a larger payoff than do the residents of the other town. Which of the equilibria identified in part (b) will be stable with these dynamics? Which ones will be unstable?