1. Squaretown is a small town, perfectly square in shape (see below). Residents are dis- tributed evenly across the entire town geography. On Friday night, every resident of Squaretown gets a takeout pizza. Assume that the Squaretown residents pick their pizza restaurant on the basis of which is closest, and that this is the only factor they consider. Assume that each pizza restaurant wants to have as many customers as possible and that they can locate anywhere in the town.' (a) If there are two pizza restaurants, where do they locate in equilbrium (if one exists)? (b) If there are three pizza places, where do they locate in equilibrium (if one exists)? Make sure you clearly explain your answer: why the outcome you have found is an equilibrium, why outcomes are not possible equilibria, etc. 2. Imagine an auction where the item being auctioned is a signed photograph of Dr. Trees. Assume the number of bidders (N) is at least 32 and assume that every bidder has a unique positive value of this item: no bidders place the same dollar value on this prize. If we conduct a second-price, sealed-bid auction for this item, is there any possible NE where the person who values the photograph the least wins the auction? (Make sure to explain in detail why or why not by describing how each of the various bidders could change their strategy and if that would benefit them or not.) 3. See the game below: B L R 4 T 3,2 1,1 B x,y 2, 1 (a) Find payoffs for a and y so that this game has a single equilibrium that is the same whether the game is simultaneous or sequential with Player A moving first. (b) Find payoffs for r and y so that both players have higher equilibrium payoffs when the game is played sequentially (Player A first) than when it is played simultane- ously. i. Create a backstory for this game - what situation could these payoffs (from b) describe? Including the same location as other restaurants, if desired 2In reality, thousands would bid