Consider the following binary route choice game with 12 play…

Consider the following binary route choice game with 12 players. Each player simultaneously decides whether to take the main road or the side road. Let x define the number of commuters that take the main road. The payoff for taking the main road is UM=10+2(8-x) and the payoff for taking the side road is US=10+3. In the pure strategy equilibrium there are ________ drivers in the main road.

Consider the following volunteer-dilemma game among 3 player…

Consider the following volunteer-dilemma game among 3 players. A benefit B=5 can be enjoyed if at least one of the 3 players decides to help. More than one person helping is redundant. The player that chooses to help incurs a cost, C=1 (note: B>C>0). If no one helps, all players’ utility is 0. In the symmetric mixed-strategy equilibrium, the probability that at least one person helps is _______ (round your answer to the nearest second decimal).

Consider the following binary route choice game with 12 play…

Consider the following binary route choice game with 12 players. Let x define the number of commuters that take the main road. The payoff for taking the main road is UM=10+2(8-x) and the payoff for taking the side road is US=10+3. Suppose there is 5 drivers in the main road and 6 drivers in the side road, and you are deciding between the main road and the side road. If you choose to take the main road your imposed externality is _________.

Consider voting for the college football’s Heisman Trophy aw…

Consider voting for the college football’s Heisman Trophy award. The trophy is awarded by means of a Borda-count voting system. Each voter submits first-, second-, and third-place votes, worth 3 points, 2 points, and 1 point, respectively. Assume there are 500 Heisman voters. Under this voting system, what is the minimum integer number of first-place votes that it would have taken to guarantee victory (without any help from second or third-place votes)?