PD/ToC Problems

1. Cape Halibut Bay supports a fishing industry based solely on small boats that are able to navigate the shallow waters near the harbor. There are 40 independently owned boats that fish in the bay. There is a new technology that can increase a boat's catch by 40%, and only a 5% increase in a boat's catch would be needed to pay for the installation and maintenance of the new equipment. Unfortunately, if more than half of the boats adopt the new technology, the stock of fish will be depleted so quickly that every boat will experience about a 1/3 (one-third) reduction in its catch.

a. What should the individual boat owner do to maximize productivity? Include a matrix in your answer. Represent the average catch before the new technology became available as C.

b. What could the boat owners do together to avoid losses? Is there any way in which they can avail themselves of the new technology without depleting the stock of fish?

2. Lil' Abner and Daisy Mae own a mule that they both use for plowing their gardens. They have agreed to help each other feed the mule every day. The job requires moving a heavy sack of grain that the two of them can handle with ease. Each knows that the other could move the sack alone if it were absolutely necessary. Thus each thinks to himself: "It's not necessary for me to go there every day. Lil' Abner [Daisy Mae] will be there if I am not and can get the job done - I'd rather do something else." Suppose both parties would prefer that the mule be fed by someone to its not being fed at all and that both would prefer that the other do it to doing it alone or together.

a. Draw up a decision matrix using rank ordered utilities.

b. According to RCT what will happen in this situation? Is this a good solution? Is a better one possible? If so, how might it be realized?

3. Consider this variation on the Lil' Abner/Daisy Mae situation. Each would still rather that the other fellow feed the mule but now each so resents the prospect of doing it by themselves that they would prefer that the mule not be fed at all to doing it alone. However, each prefers that they feed the mule together to letting it starve.

a. Draw up a decision matrix using rank ordered utilities.

b. According to RCT what will happen in this situation? Is this a good solution? Is a better one possible? What measures could be taken to realize the better solution?

4. In the game of chicken two players race their automobile straight at each other. If neither veers, they will crash and die heroes in the eyes of their friends. If one veers and the other holds fast to the course, the one who holds fast will be regarded as a hero and the other will be branded a "chicken". If both veer, their reputations will remain unchanged. Assume that each player ranks the outcomes in this descending order; live hero, no change, dead hero, chicken.

a. According to RCT what will happen? Include a matrix in your answer.

b. How might the players arrive at a better outcome?