It is the morning commute in Congestington, DC. There are 100 drivers, and each driver is… 1 answer below »

It is the morning commute in Congestington, DC. There are 100 drivers, and each driver is deciding whether to take the toll road or take the back roads. The toll for the toll road is $10, while the back roads are free. In deciding on a route, each driver cares only about income, denoted y, and his travel time, denoted t. If a driver’s final income is y and his travel time is t, then his payoff is assumed to be (where we have made the dollar value of one unit of travel time equal to 1). A driver’s income at the start of the day is $1,000. If m drivers are on the toll road, the travel time for a driver on the toll road is assumed to be m (in dollars). In contrast, if m drivers take the back roads, the travel time for those on the back roads is 2m (again, in dollars). Drivers make simultaneous decisions as to whether to take the toll road or the back roads.

a. Derive each player’s payoff function (i.e., the expression that gives us a player’s payoff as a function of her strategy profile.)

b. Find a Nash equilibrium.

 

 

 

 

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