Economic Analysis of Social Issues 1st Edition by Alan Grant

Exercise 10

Consider the traffic congestion game in problem. Find all Nash equilibria in this game, and explain your reasoning. Then, classify this game as one of our archetypes.
problem:
Commuting to work can be difficult in big cities. Suppose you and 1 million other commuters are driving downtown to work. You can either take the freeway or take surface streets. Your payoff depends on how quickly you get downtown. All else equal, the freeway is faster than surface streets. But both get slower the more people there are driving on them; if every commuter chooses the same option, traffic will come to a standstill and commuters will get a payoff of zero. Draw the graph that represents this million-player game. Let the horizontal axis represent the number of commuters on the freeway, and the vertical axes represent the payoffs to choosing a particular roadway.