Arwin and Dewi are neighbors that work for the same company in the same office building....

Arwin and Dewi are neighbors that work for the same company in the same office

building. Each morning they both have the choice to commute to work by car or by bicycle. The

road to their office is narrow and in poor condition. Arwin and Dewi are the only people who

travel on this road at this particular time in the morning. If both choose to commute by car it

takes each of them 17 minutes to get to work. However, if there is just one car on the road

traveling the time is reduced to 8 minutes. Commuting by bicycle is generally quite fast: it only

takes 12 minutes if there are no cars. However the local law gives priority to the cars on the

road. As a result, it takes 22 minutes to reach the destination by bicycle if another person

decides to drive at the same time. Both Arwin and Dewi seek to minimize their commute times

each morning to reach the office in the shortest amount of time possible.

a. Using the information above, create the payoff matrix for this game.

Solutions

Expert Solution

A) There are two commuters: Arwin and Dewi. There are two modes of commute: car and bicycle.

If both of them travel by car, it takes each of them 17 minutes to get to work.

If one of them travels by car, then his commute time is reduced to 8 minutes. On the other hand the person who chooses to commute by bicycle, due to the local law giving priority to the cars on the road, it takes 22 minutes to reach the destination.

If both of them travel by bicycle, it takes each of them 12 minutes to get to work.

The payoff matrix has been depicted in table given below. The first number in parenthesis denotes the payoff of Arwin to commute and the second number denotes the payoff of Dew to commute. These are negative because each of them wants to reach the office in the shortest amount of time possible, so the less time it takes the better or the higher payoff they receive.

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Rahul Sunny answered 2 months ago

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