The Final Exam will take place in on Thursday, March 19, at 8:30
am in Savery 245. PLEASE BRING ONE OR MORE BLANK BLUE BOOKS (WITH
NO PAGES MISSING) AND A PEN OR LEGIBLE PENCIL TO THE EXAM. The
exam will consist of selections of questions and parts of questions
from the list below. To complete the exam, you must be prepared
to answer the questions completely but concisely. Final Exams
will be graded and final grades will be posted outside my office
(Savery 252) on Tuesday, March 24. Final Exams will be available
for pick-up during Spring Quarter in the Philosophy Department
Office, Savery 345. If you would like your Final Exam mailed to
you, please bring a sufficiently large, stamped, self-addressed
envelope to the Final Exam and insert it inside your blue book.
1. Explain/Distinguish the following terms:
(a) RST Nash equilibrium/evolutionary Nash equilibrium
(b) emergence/persistence of a norm
(d) behavior-based/attitude-based derivation of a norm
(e) pathological/non-pathological Nash equilibrium
(f) internalist/externalist interpretations of RST
(g) uniform/polymorphic Nash equilibrium combinations
2. Is the N-Person PD Supergame an N-Person PD? Explain your answer.
3. If you can successfully answer this question, then you can
explain what Taylor meant when he said that there are Chickens
nesting in the N-Person PD Supergame. (a) Draw a Schelling Diagram
of an N-Person Prisoner's Dilemma, where L = D and R = C
and where n = 10 and k = 5. (b) Consider the N-Person Prisoner's
Dilemma Supergame in which each of the sub-games is defined by
the Schelling diagram in (a). Draw a Schelling diagram for a partial
representation of the supergame, showing the two strategies L
= D-infinity and R = B(7). (It is not necessary to make precise
numerical assignments of utility to each of the possible outcomes,
but if you do so, assume each player's discount factor is .99.)
(c) On the Schelling diagram in (b) indicate two Nash equilibrium
combinations of strategies. (d) Is the partial representation
of the N-Person Prisoner's Dilemma Supergame in (b) itself an
N-Person Prisoner's Dilemma? Explain your answer. (e) In the Schelling
diagram from part (b), consider the NE outcome in which not everyone
chooses D-infinity. Call that outcome the cooperative NE outcome.
In the cooperative NE outcome, how many agents choose B(7) and
how many agents choose D-infinity? (f) Explain why this one outcome
on the Shelling diagram from (b) actually represents more than
one possible strategy combination. [Hint: Does it specify which
agents choose B(7) and which agents choose D-infinity?] (g) Explain
why the cooperative NE strategy combinations in the N-Person PD
Supergame are analogous to the NE strategy combinations in the
Two-Person Chicken Game.
4. At the beginning of this course, we considered an example involving
a Potato Farmer and a Broccoli Farmer to illustrate Buchanan's
Many Collective Action Problems. We identified three collective
action problems: (i) respecting property rights; (ii) obtaining
the benefits of exchange; (iii) production of public goods. Though
we started from the 2-person case, these are typically N-Person
Collective Action Problems. Explain how conditions in a small
town in Alaska would make it possible for purely IR agents to
solve all three of Buchanan's N-Person Collective Action Problems.
Pay particular attention to the empirical assumptions that are
required for the solutions to be stable.
5. Why is there no need to distinguish between selective and non-selective
sanctioning of defectors in a 2-Person PD Supergame?
6. Consider an N-Person Supergame where each subgame has two stages:
the first stage is an N-Person PD; the second stage is a choice
about whether to sanction other players in the supergame. It is
possible to define a sequence of conditionally cooperative strategies
with selective sanctioning: (a) Define C-CC(x)w/SS(0). [Assume
that x > k.] (b) Consider the strategy combination in which
all agents choose C-CC(x)w/SS(0). Is this an NE combination? Explain.
(c) Is there a strategy that weakly dominates C-CC(x)w/SS(0)?
If so, identify it and explain why it weakly dominates C-CC(x)w/SS(0).
If not, explain why not. (c) Define CCC(x)w/SS(1).
(d) Consider the strategy combination in which all agents choose
C-CC(x)w/SS(1). Is this an NE combination? (e) Is there a strategy
that weakly dominates C-CC(x)w/SS(1)? If so, identify it and explain
why it weakly dominates C-CC(x)w/SS(1). If not, explain why not.
(f) Is there a selective sanctioning strategy based on C-CC(x)
that is not weakly dominated by any other strategy? If so, identify
it and explain why it is not weakly dominated by any other strategy.
If not, explain why not.
7. Two gold miners strike gold in California. They try to keep the discovery secret, but soon the word spreads and 98 other miners descend on the site. Suppose that there is enough gold for all 100 miners working independently to do quite well. But the miners must find a solution to the problem of who is entitled to mine which part of the site. If there are no generally agreed upon property rights, the miners will spend so much time and energy defending their claims (whatever they may be) that they will not have time to do much actual gold mining. Consider three potential systems of property rights: (1) The two miners who discovered the gold own the entire site; no one else owns any. However, the other 98 miners can contract to work the claim and be paid an hourly wage. (2) Each miner gets a claim, but they are not equal in size. Each miner's claim is proportional to his/her size and strength. The bigger, stronger miners get a larger claim. When there is a dispute over claim size, the miners fight it out, and the winner gets the larger claim. (3) Each miner gets an equal size claim.
Which of the three systems of property rights is closest to the
practices reported by Anderson and Zerbe? Assuming that the miners
were RST agents, discuss the factors (including non-rational (but
not irrational) factors) that might have led the miners to adopt
the system described by Anderson and Zerbe rather than one of
the other two systems described above.
8. Elster argues that some sanctioning must be performed
for motives other than fear of being sanctioned. Elster refers
to agents who sanction from a motive other than fear of sanctioning
as unmoved movers. (a) Which of the premises of Elster's
argument does Pettit deny? Why? (b) How, on Pettit's view, could
a system of sanctioning be stable without any unmoved movers?
9. A complete explanation of the existence of a norm would explain
both its emergence and its persistence. (a) Is it reasonable to
expect a purely game theoretic explanation of both emergence and
persistence of a C-norm? Explain your answer with a hypothetical
example of the explanation of the emergence and persistence of
a C-norm that uses Non-Cooperative Game Theory in at least part
of the explanation. [This answer can be brief.] (b) Is it reasonable
to expect a purely game theoretic explanation of both emergence
and persistence of an S-norm? Explain your answer with a hypothetical
example of the explanation of the emergence and persistence of
an S-norm that uses Non-Cooperative Game Theory in at least part
of the explanation. [This answer can be brief.]
10. (a) What does it mean to say that joint conditional cooperation
in an N-Person PD Supergame is a coordination equilibrium? (b)
What does Pettit mean by an attitude-based derivation of norms?
(c) How does the fact that joint conditional cooperation is a
coordination equilibrium play a role in Pettit's attitude-based
derivation of norms of conditional cooperation in an N-Person
11. In class, we dramatized an N-Person PD Supergame, by pretending
that we were farmers with an indefinite number of opportunities
for mutual cooperation in the future. Explain why were we unable
to obtain agreement on any strategy combination that would have
sustained stable cooperation over time, when we confined our attention
to strategies that did not provide for selective sanctioning of
defectors? Why were we quickly able to obtain agreement to universal
conditional cooperation when we included strategies with selective
sanctioning of defectors? Explain your answers and use one or
more Schelling diagrams to illustrate the results of introducing
strategies with selective sanctioning into the supergame.
12. (a) In laboratory experiments, many subjects, but not all
subjects, Cooperate in one-shot PDs, even if it is explained to
them in advance that Defecting dominates Cooperation. Suppose
that the fact that some agents in one-shot PDs Cooperate and some
Defect is explained in terms of two types of agents, FC ("Frankian
Cooperators") and IR ("Individualistically Rational").
FC agents Cooperate if they expect the other agent to Cooperate.
Otherwise, they defect. IR agents always Defect. Briefly explain
the role of the emotions in Frank's explanation of the Cooperation
of FC agents in one-shot PDs.
(b) In Passions Within Reason, Frank reported some preliminary data which he claims support his theory. In the table above, I have reproduced his final data which were reported after the book was published. Frank claims the final data support his theory. Why does Frank claim that the final data support his theory? [Hint: For the same reason that he claimed that the preliminary data supported his theory.]
(c) In Passions Within Reason, Frank claimed that FC agents must necessarily do worse in his experimental one-shot PDs than IR agents, because they did not get to choose whom to interact with in the one-shot PD in his experiment. Is it true that FC agents must necessarily do worse than IR agents in his experiment? Explain your answer.
(d) In Passions Within Reason, Frank claimed that one advantage of FC agents in the real-world PD would be due to the fact that they could seek out others whom they believed to be FC also, and then could selectively interact with the agents they believed to be FC in a one-shot PD, rather than simply interacting with other agents at random. Thus, Frank has suggested a two-stage game. Making reasonable simplifying assumptions, use Frank's final data from the table above to calculate the Average Utility to FC and to IR agents in the two-stage game suggested by Frank. Do the calculations support Frank's theory?
(e) How might Frank defend his theory in the light of the results
of the calculation in part (d)?
13. In class we made one modification to the four gambles in Savage's discussion of the Allais Paradox: We changed the $500,000 amount to $1.5 million. Answer this question with respect to our modified Allais example.
(a) What are Gambles 1, 2, 3, and 4?
(b) In the choice between Gambles 1 and 2, which choice maximizes expected monetary return? Explain.
(c) In the choice between Gambles 3 and 4, which choice maximizes expected monetary return? Explain.
(d) If given a choice between Gambles 1 and 2, which would you choose? Explain.
(e) If given a choice between Gambles 3 and 4, which would you choose? Explain.
(f) In our modification of the Allais Paradox, what combination of choices would show that (at least in this one case) an agent favors sure gains over maximizing expected utility?
(g) In life, most people face many situations in which they favor sure gains over maximizing subjective expected utility. Call these situations Allais situations. Let us say that when people make choices consistent with maximizing subjective expected utility that they use the Subjective Expected Utility (SEU) Rule; and when they make choices that favor sure gains over maximizing subjective expected utility, that they use the Sure Gain (SG) Rule. Suppose that every one of us knew exactly the number of times in our life that we would face an Allais situation. Let that number be n. Why would we expect that, on reflection, the appeal of the SG Rule would tend to diminish for most people as n gets very large?
(h) If people's tendency to use the SG Rule rather than the SEU Rule is a psychological tendency that is subject to selection in a POS on the basis of its average success in achieving self-interested goals (SIGs), under what circumstances would we expect such a POS to select against the SG Rule and to select for the SEU Rule? Explain.
(j) Do you believe that the SG Rule is being selected against
in the real world? Explain.
14. (a) Use an example (not necessarily from the readings) to
explain how publicizing a false theory of human behavior could
make it true. (b) Use an example from the readings to explain
how publicizing a true theory of human behavior could make it
false. (c) Why do these examples raise a special problem concerning
the projectibility of theories in the human social sciences? (d)
Why is there no corresponding problem concerning the projectibility
of theories in the natural sciences?
15. (a) According to Talbott, what makes a group of individuals
a community? (b) Make the strongest argument you can for the one
of the following two positions that you regard as most likely
to be true: (i) Talbott's criterion for a community is not necessary
for a group of individuals to be a community; (ii) Talbott's criterion
for a community is not sufficient for a group of individuals to
be a community.
16. In this course, we have considered several different interpretations of Rational Self-Interest Theory as a descriptive theory of human behavior. The two main parts of RST are the theory of IR and the theory of SIGs.
(a) What do 'IR' and 'SIG' stand for?
(b) There are two parts of the RST theory of IR: a theory of parametric rationality and a theory of strategic rationality? What are these two parts of the RST theory of IR? [Just say what they are. Do not explain them here.]
In this course we have considered a variety of empirical evidence that has been thought to bear on the empirical adequacy of RST as applied to human behavior. In the remainder of this question, you will be asked to consider how this evidence bears on various interpretations of RST.
(c) What is the universal interpretation of RST?
(d) What is the idealization interpretation of RST? Explain why Simon's view fits this interpretation.
(e) What is the IRE interpretation of RST? Explain why Savage's view fits this interpretation.
(f) Give an example of evidence that conflicts with the universal interpretation but supports the IRE interpretation of:
(i) the RST theory of parametric rationality. Explain.
(ii) the RST theory of strategic rationality. Explain. [Note: If we do not get to this in class, I will not ask it on the Final Exam.]
(g) Arthur claims that there is lots of empirical evidence that conflicts with the universal interpretation of the RST theory of strategic rationality, because there is lots of cooperation in real world PDs. Explain what is wrong with Arthur's argument. [Hint: Is a PD Supergame itself a PD?]
(h) What is the Allais phenomenon? Give evidence from the readings of the Allais phenomenon. [You must refer to at least one of the readings.] Explain how the Allais phenomenon provides evidence against the IRE interpretation of the RST theory of parametric rationality;
(j) What is the one-shot PD phenomenon? Give evidence from the readings of the one-shot PD phenomenon. [You must refer to at least one of the readings.]
(k) What is the unsanctioned sanctioner phenomenon? Give evidence from the readings of the unsanctioned sanctioner phenomenon. [You must refer to at least one of the readings.]
(l) Explain how the one-shot PD phenomenon provides evidence against the IRE interpretation of the RST theory of strategic rationality.
(m) Explain how the unsanctioned sanctioner phenomenon provides evidence against the IRE interpretation of the RST theory of strategic rationality.
(n) What is a POS interpretation of RST? Explain why the views of Ferejohn and Satz fit this interpretation.
(o) What does it mean to say that a POS is selecting for a certain trait? What does it mean to say that a POS is selecting against a certain trait?
(p) Historically, there have been religious communities with norms prohibiting all sexual activity. Suppose that the choices of the members of such communities to refrain from sexual activity were in IRE. Would this be evidence against a POS interpretation of RST, where the relevant POS was either Natural Selection or some process of cultural selection? Explain.
(q) How might a defender of IRE use a POS interpretation to defend
the RST against the evidence of
(i) the Allais phenomenon;
(ii) the one-shot PD phenomenon;
(iii) the unsanctioned sanctioner phenomenon.
(r) What is Frank's main challenge to the POS interpretation of RST, where the relevant POS is Natural Selection? Explain your answer.
(s) How can group selection as explained by Wilson and Sober pose a challenge to the POS interpretation of RST? Explain your answer. [Hint: How does the example of the Hutterites illustrate the possibility of selection for traits that favor IRE choices that conflict with RST?]
(t) Suppose there were conclusive empirical evidence that right now in the actual world, the processes of Natural Selection and of cultural selection are selecting against any trait that produces IRE choices in favor of reciprocating cooperation in an anonymous sequential one-shot PD and selecting for people whose IRE choices in such situations match RST (i.e., Unconditional Defection); and selecting against people whose IRE choices favor unsanctioned sanctioning and in favor of IRE choices that match RST. Explain why it does not follow from this supposition that traits that produce IRE choices in favor of reciprocating cooperation in an anonymous sequential one-shot PD or that favor unsanctioned sanctioning will become extinct.
(u) Do you think that the POSs in which human beings are involved are selecting against traits that favor reciprocating cooperation in an anonymous sequential one-shot PD and against traits that favor unsanctioned sanctioning? Explain.
(v) EXIT POLL. You are in an anonymous sequential one-shot PD with the following choices: Button A = "I get $20" and Button B = "The other person gets $50". The other person has already chosen Button B, so you have already received $50. The other person also sent a note which says: "I assumed that if I cooperated, I could count on you to reciprocate." What would you do? Explain.