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. The socially optimal outcome requires that there are _________ drivers in the main road.

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).