1. Imagine two countries, A and B, that have a disputed piece of territory between them. Tension is mounting. The ministers of country A meet in emergency session to plot their course of action. They conclude that there are really only two options open to them. One is to offer to negotiate the dispute with country B, and the other is to attack swiftly in an attempt to take the territory by force. The main uncertainty is over what country B will do. Will country B negotiate in good faith, or will it try to attack first?

The ministers of A agree that the best thing would be to attack while B is preparing to negotiate. The worst possibility would be to have B attack as they are trying to negotiate. In that case, B would get most of the territory. However, if both countries attack simultaneously, being fairly equally matched, they will probably each end up with about half the territory, after fighting a short war. If B would negotiate, they could probably end up agreeing to split the territory without a war.

A. Set up a matrix for the decision problem from the standpoint of country A. Rank the outcomes using 1st for the best and 4th for the worst.

B. Which RCT decision strategy applies (e.g., maximizing expected utility, play it safe, gamble, best option, satisfactory option)? What action does this strategy indicate? (If more than one strategy applies, discuss all of them.)

C. Country B is in exactly the same position as country A. If it applies the same decision strategy, what will the outcome be?

D. Return to question B above. Suppose country A believed that the probability that country B would decide to negotiate was 2/3. Assuming that country A is still making its decision according to the simple dictates of RCT, how would having this information affect its decision making strategy?

2. Use as the basis for the following questions the matrix for the Prisoner's Dilemma presented in Lecture 14, slides 3 and 4. (Or you can use the one in Plous on p. 247 if you change the box where Plous writes "5 years" to one saying "4 years" for each prisoner.)

A. Let's now explore the "Feel Your Pain" resolution. (As you will surmise from the last question in this section, our results will be somewhat inconclusive.) Suppose the first prisoner (Able) is so empathetic that he feels the second prisoner's pain in an amount equal to his own. (So if Baker gets a 10 year sentence, that would be just as bad as if Able himself got 10 years.)

i) Set up a new decision matrix for the perfectly empathetic Able and insert Able's new utilities. Now apply RCT. Which decision strategy now applies - or can you tell? Discuss.

ii) Suppose Baker's decision matrix remains as before (Baker is NOT empathetic) while Able is perfectly empathetic. What is likely to be the outcome after both Able and Baker make their choices (still assuming they are completely isolated from one another)? Does it matter whether or not Baker knows that Able is perfectly empathetic?

iii) What if Able and Baker are both perfectly empathetic and know that about each other?

iv) What if Able and Baker are each perfectly empathetic but mistakenly believe of the other that they are NOT at all empathetic?

v) Return to question (i) above. What does RCT dictate if Able believes that there is only a 1/3 chance that Baker would confess? What if Able believes that there is a 9/10 chance that Baker would confess?

vi) Just to think about (no need to write out an answer): Is just empathy enough to guarantee a good outcome to PD situations?

B. Let us now explore the Moral Imperative remedy for PD situations. Suppose Able has been brought up in a tightly-knit mob family where children have been told from Day 1 to NEVER tell the police anything. (Perhaps a more realistic case would be American soldiers taken as prisoners of war who are honor bound never to tell the enemy anything except their name, rank and serial number.)

i) If both Able and Baker follow the mobsters code, what will the outcome be?

ii) Suppose only Able is bound by the mobster code, what will the outcome be?

iii) Suppose Able is bound by the mobster code and Baker is not. Suppose Able is also perfectly altruistic and believes that the probability that Baker will confess is 9/10. What conflict might Able now face? Would it matter whether Able had also been brought up his mobster family to believe that he had a duty to always do what is best for himself and his partners in crime no matter what?

iv) Just to think about (no need to write out an answer): What are some limitations on solving the PD by invoking moral imperatives?

3. You have not been given any problems like the following one before. However, the web reading assignment called "Social Behavior and Kin Selection" includes a table of "coefficient of relatedness" values (which are used in "Hamilton's Rule" for the prediction of altruistic behavior). NB: This site is no longer available. Use instead: http://taumoda.com/web/PD/library/kin.html

With this information in hand you should approach this problem like an SAT question.

A. Suppose a retired biologist named Ham decides to make out her will using as a recipe for distribution the coefficients of relatedness found in Evolutionary Theory (ET). Ham has 4 surviving children and 5 cousins. If Ham's total estate is worth $550,000, how much should she leave to each of her 9 descendants?

B. Ham decides to think in more detail about her will. Of her 4 children she reckons that 2 of them will never amount to anything from a reproductive point of view because she is certain they will never have any off-spring. Of the remaining children, she believes one is 75% likely to have a nice brood of 6 kids. She reckons that the odds are two to one that her fourth child will have 3 kids. She doesn't know her cousins well enough to say but people in their general socio-economic class have on average 0.9 children each. Now how should Ham divide her estate if her goal is to use her money to support the contributions of her own genes to future generations?

C. Suppose Ham were going to give advice to Able re how empathetic he should be to Baker in the PD situation discussed in the above problem. Suppose Baker is Able's grandchild. Draw up a decision matrix for the PD situation described in Problem #2 above if one assumes that Able's degree of empathy is based on the strength of "blood ties".

4. (The presentation of the following problem is seriously over simplified but the point it makes has some validity.) A psychologist in a mental hospital is trying to decide what clinical diagnosis to attach to a patient. There are two obvious choices: one is to classify the patient as having a borderline case of Delusional Disorder; the other is to select the category of Paranoid Schizophrenic. The clinician thinks that there's a good probability (say 70%) that the less pathological diagnosis will turn out to be the correct one. However, being a good student of RCT she also has to consider the costs and benefits to her reputation in the clinic is she picks the wrong diagnosis.

If she concludes that the patient is sicker than what might first appear, then the clinic will be proud of any future progress the patient makes and not blame her for any lack of progress. If, however, she pronounces the patient less sick than might at first appear, the rest of the staff will expect progress and a failure (particularly a dramatic one such as a suicide or violent attack) could be a disaster to her career.

A. Draw up a simple two-by-two decision matrix for the psychologist and rank order the outcomes. What choice is dictated by RCT?

B. The patient is also interested in how the diagnosis turns out and has a choice as to whether to try to appear as normal as possible during the interview thereby hoping to receive the milder label of borderline delusional or whether to dramatize his erratic thought patterns, thus hoping to receive a diagnosis that reflects a more disturbed state.

The patient has a great fear (paranoia?) of being locked up in an institution even though there's nothing really much wrong with him. On the other hand, he would take a certain glee in fooling all the shrinks into thinking he was pretty much OK if he were indeed stark raving mad. He doesn't particular like the idea of being treated as mad even if he were mad, but on the other hand it would be quite boring to both be more or less and normal and also treated as being more or less normal.

Draw up a decision matrix for the patient. What choice is dictated by RCT?

C. How does the structure of the above two-person interaction compare to that of the examples of the PD we have seen?