Consider a many-person game of car commuters and bus commuters. Suppose that whe

Question

Consider a many-person game of car commuters and bus commuters. Suppose that when there are no car commuters on the road, the payoff to bus commuters is 20 and the payoff to people who decide to start driving is 80. As the proportion of car commuters increases, the payoffs of both car and bus commuters decrease. Assume that the payoff to car commuters is greater than the payoff to bus commuters until the proportion of population who drives a car reaches 70%, when more than 70% of the population drives, people find that congestion would become so bad that commuting with buses that have privileges to drive in bus-only lanes would be much faster than driving their own cars, when 70% of the population drives, the payoffs to both car and bus commuters equal-40. On the following graph, use the blue line (circle symbols) to plot the payoff to car commuters. Then, use the green ine (triangle symbols) to plot the payoff to bus commuters. For simplicity, assume the payoff functions are linear. PAYOFF 100 80 60 40 20 Car Commuters Bus Commuters -20 40 -60 80 -100 0 10 20 30 40 50 60 70 80 90 100 PERCENTAGE OF POPULATION WHO DRIVES Help Clear ALl

Explanation / Answer

The graph would be:-

1). Car commuters payoff line: starting from 80 on y axis ( as when 0% are driving then payoff for any new driver is 80), it will be downward sloping straight line ( as % of drivers increase, payoff will decrease due to more congestion and straight line because linear function has been assumed in the question).

2).Bus commuters payoff line: starting from 20 on y axis ( as when 0% drivers are there then payoff is 20 for bus commuters), downward sloping straight line (  as % of drivers increase, payoff will decrease due to more congestion and straight line because linear function has been assumed in the question).

Now make both the lines in a way that they intersect at the ( 70%, -40) on the graph ,i.e., 70% point on x axis and -40 point on y axis. This is so because it is given that when 70% drivers are there then both car and bus commuters will have -40 payoff.

Conclusion : As we can see that final graph would show steeper line for car commuter and relatively flatter for bus commuters.This means as more cars come on roads , the payoff of car commuters reduce much faster. But it temains higher than bus payoff until we reach 70% driver mark. Here the two payoffs are equal while beyond 70%, bus payoff would be higher due to less congested bus- only lanes.

Second Part

The above scenario reflects prisoner dilemma where each one would have dominant strategy to choose car over bus as it is giving more individual payoff initially. thus, all would choose car and the society will end up with congested road where all will be worse off.Similar thing happens in prisoner dilemma where there was a possibility for both to get higher payoff, yet they act selfishly and both end up in worse nash equilibrium. Here if all had chosen bus in first place then all would have got 20 payoff. Now if we say all people have purchasing power and all will choose simultaneously, then all will choose car and all will get negative payoff in this case and end with worse nash equilibrium.

so first two points should be correct.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.