Harvard. Reading List and Final Exam for Games and Strategy. Schelling, 1963

 

Thomas Schelling was hired by the Harvard economics department as a professor in 1958. According to the Harvard course catalogues, he taught the undergraduate course “Games and Strategy” nine times during the 1960’s.  This post provides the syllabus/reading list and final exam for that course from the first term of the 1963-64 academic year.

Materials from Schelling’s course “Economics and National Security” that he taught in 1960 and from his 1970 course “Conflict, Coalition and Strategy” have been transcribed and posted earlier here at Economics in the Rear-view Mirror.

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Course Announcement

Economics 135. Games and Strategy

Half course (fall term). M., W., F., at 10. Professor Schelling

Theories and experimental studies of rational decision in conflict, collusion, coalition, bargaining, collective decision, arbitration, and uncertainty.

Source: Official Register of Harvard University. Vol. LX, No. 21 (September 4, 1963): Faculty of Arts and Sciences. Courses of Instruction for Harvard and Radcliffe 1963-1964, p. 103.

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Economics 135
Games and Strategy
Fall, 1963

Reading Assignments

PART I. COPING WITH AN INTELLIGENT ADVERSARY

1. Rapoport, Anatol: Fights, Games and Debates, Chapters 7, 8, 9; pages 130-165. (35 pages)
2. Williams, John D.: The Compleat Strategyst, Chapters 1, 2; pages 1-85, and Chapter 3, pages 86-91 then scan rest of chapter. (91 pages)
3. Hitch, Charles J. and McKean, Roland: The Economics Defense in the Nuclear Age, Chapter 10, “Incommensurables, Uncertainty, and the Enemy,” pages 182-205. (23 pages)
4. Read, Thornton: “Strategy for Active Defense,” Papers and Proceedings of the AEA, American Economic Review, Vol. 51, No. 2, May 1961, pp. 465-471.
5. Alchian, Armen A.: “The Meaning of Utility Measurement,” American Economic Review, Vol. 43 (March 1953) pages 26-50. (25 pages)

(OPTIONAL: R. Duncan Luce and Howard Raiffa, Games and Decisions, Chapters 1-4, pp. 1-87.)

PART II. COERCION AND DETERRENCE

6. Schelling, Strategy of Conflict, Chapters 1, 2, 5, 7, 8; pages 3-52, 117-161, 175-203. (121 pages)
7. Ellsberg, Daniel: “The Theory and Practice of Blackmail,” (38 pages) mimeograph
8. Schelling: “The Threat of Violence in International Affairs,” Proceedings, 57th Annual Meeting, American Society International Law. (INT. 16.8)
9. Stevens, Carl M.: Strategy and Collective Bargaining Negotiation, chapters 3 and 5, pages 27-56 and 77-96. New York: McGraw Hill, 1963.

PART III. MUTUAL RESTRAINT

10. Kenneth: Conflict and Defense, Chapters 1, 2, 6, pp. 1-40, 105-122. (58 pages)
11. Schelling: Chapters 3, 4, 9, 10; Appendix A; pages 53-118, 207-254, 257-266. (121 pages)
12. Cassady, Ralph, Jr.: “Taxicab Rate War,” Journal of Conflict Resolution, Vol. 1, pages 364-8 (December, 1957). (5 pages)
13. Valvanis, Stephan: “The Resolution of Conflict When Utilities Interact,” Journal of Conflict Resolution, Vol. 2 (June 1958) pages 156-69. (13 pages)
14. Rapoport, Chapter 10, pp. 166-79 (14 pages)
15. Boulding, Chapters 12, 13, pp. 227-73.
16. Schelling: “War Without Pain and Other Models,” World Politics, XV, (April, 1963) pp. 465-487.

PART IV. COLLECTIVE DECISION AND ARBITRATION

17. Farguharson, Robin: “Sincerity and Strategy in Voting,” mimeograph (February 5, 1955) (7 pages)
18. Black, Duncan: “On the Rationale of Group Decision Making,” Journal of Political Economy, Vol. 56 (February, 1948), pages 23-34 (12 pages)
19. Steinhaus, Hugo: “The Problem of Fair Division,” Econometrica, Vol. 16 (January, 1948), pages 101-109. (9 pages)
20. Dahl, Robert A.: A Preface to Democratic Theory, Chapter 2, pages 34-60, with special attention to notes 9 and 12, pages 42-43 and 43-44. (26 pages)
21. Rapoport, Chapter 11, pp. 180-194. (15 pages)
22. Rapoport, Chapter 12, pages 195-212. (17 pages)

PART V. EXPERIMENTAL GAMES

23. Flood, Merrill M.: “Some Experimental Games,” Management Science, Vol. 5 (October, 1958) pages 5-26. (22 pages)
24. Kaplan, Burns, and Quandt: “Theoretical Analysis of the Balance of Power,” Behavioral Science, Vol. 5 (July, 1960), pages 240-52. (12 pages)
25. Schelling: Chapter 6, pages 162-72. (11 pages)
26. Rapoport: Chapter 13, pages 213-25. (12 pages)

READING PERIOD

27. Burns, Arthur L.: “A Graphical Approach to some Problems of the Arms Race,” Journal of Conflict Resolution, Vol. 3, pages 326-42. (16 pages)
28. Thibaut, John W. and Kelley, Harold H.: The Social Psychology of Groups, Chapter 7, pages 100-125. (26 pages)
29. Goffman, Irving: “On Face-Work,” Psychiatry: Journal for the Study of Interpersonal Processes, Vol. 18 (August 1955), pp. 213-31.
30. Twain, Mark, “The Man that Corrupted Hadleyburg,” in The Complete Short Stories of Mark Twain.

Source: Harvard University Archives. Syllabi, course outlines and reading lists in Economics, 1895-2003. Box 8, Folder “Economics, 1963-64”.

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FINAL EXAMINATION
ECONOMICS 135
January 29, 1964

ANSWER ALL FIVE QUESTIONS: The first two questions should take no more than ten or twenty minutes each, allowing at least forty-five minutes each for the last three.

1. The following entry was submitted to the PUNCH “Toby competition” calling for an “unpleasing codicil to a will,” and received a runner-up award in the issue of July 6, 1960:

To my daughter, Judith Georgina Margaret, I leave my house, land and all my worldly possessions therein on the condition that it should be run as either an hotel, a college for gardeners or a rest-house for disappointed Beatniks.

My cash and capital are to be put into a trust. My widow, three daughters and nine grandchildren will each have an equal share in the trust. No income or capital can be drawn from the trust until the will is contested by a legatee. If this happens, the contesting legatee will lose his share to the others. If the others pay compensation for this loss, all capital will go untied to a charity.

Describe and discuss in game-theoretical terms the arrangement described in the second paragraph. Draw a matrix to represent it. (For purposes of the matrix, you may reduce the number of legatees to two.) Include, with respect to the two-person matrix, any pertinent references to a “solution,” “equilibrium point,” dominant or dominated strategies, or “efficiency” of outcome.

2. It has been observed that for many people an important criterion in sending or not sending a Christmas card to someone is whether or not they expect to receive one from the person. They would be embarrassed if they received one and had not sent one, but would rather not bother sending one unless they were going to receive one. They might also not wish to embarrass the recipient by sending a card he did not expect and implying he had been negligent. It may not be going too far to suppose that some people, in deciding whether or not to send a card, recognize that the other person, in deciding whether or not to send his card, is wondering whether or not he will get a card.
   Draw a matrix corresponding to this situation, explaining your choice of numerical payoffs, and analyze the situation in familiar fashion.
3. Two companies, Vitamins, Inc. and Hormones, Inc., sell to groups of potential customers that partially overlap. Some potential consumers of vitamins can meet their needs with hormones, but not all of them; and some potential consumers of hormones can meet their needs with vitamins, but not all of them. Prices are such that the two commodities are pertinent[sic, “perfect”?] substitutes for each other within the overlapping market. Advertizing is the principle form of competition between the two companies. Advertizing also increases, for Vitamins, Inc., sales to those who have no interest in hormones, and similarly for Hormones, Inc.
   The total advertizing budgets for the two companies are fixed by long-term contracts. In the short run they can vary the content of their advertizing. Specifically, the vitamin company can emphasize those uses of vitamins that compete with hormones or those uses that do not. If it emphasizes the uses that do compete, it tends to increase its share of the common market; if it emphasizes the virtues peculiar to vitamins it will increase consumption of vitamins by those who have no interest in hormones but will tend to lose in the market common to both. And similarly for the hormone company. A good deal of research has been done by both companies, leading to advertizing policies that take the rival’s advertizing campaign into account.

V has settled on the following policy:

1. 1. 1. If H puts less than 20% of its budget into competitive advertizing, V will put none into that form;
      2. If H puts 20% or more into the competitive form, V will put the same percentage into competitive advertizing as H does.

H has arrived at the following policy:

1. 1. 1. If V puts less than 25% into competitive advertizing, H will put twice that percentage into competitive advertizing;
      2. If V puts 25% or more into competitive advertizing, H will put exactly 50% into that form.

The Problem:

1. 1. Sketch the “partial equilibrium curves,” and analyze what may happen if each of the two firms simply reacts to what it sees the other doing.
   2. If H gets sophisticated and understands V’s behavior (but V goes on just reacting to what Hdoes), what policy do you expect H to follow, with what result?
   3. If both get sophisticated and realize the nature of their interacting policies, how does your analysis change?
   4. Reinterpret this problem in terms of two countries with fixed defense budgets, allocating their military resources into “offensive” and “defensive” components.

4. A three-man board composed of A, B, and C, has held hearings on a personnel case involving an officer of the company. This officer was scheduled for promotion but, prior to final action on his promotion, he took a decision that cost the company a good deal of money. The question is whether he should be (1) promoted anyway, (2) denied the promotion, or (3) fired.
   The board has discussed the matter at length and is unable to reach unanimous agreement. In the course of discussion it has become clear to all three of them that their separate opinions are as follows:

A considers the officer to have been a victim of bad luck, not bad judgment, and wants to go ahead and promote him but, failing that, would keep him rather than fire him.
B considers the mistake serious enough to bar promotion altogether; he’d prefer to keep the officer, denying promotion, but would rather fire than promote him
C thinks the man ought to be fired but, in terms of personnel policy and morale, believes the man ought not to be kept unless he is promoted, i.e. that keeping on an officer who has been declared unfit for promotion is even worse than promoting him.

To recapitulate, their preferences among the 3 outcomes are:

	Promote	Keep	Fire
A	1st	2nd	3rd
B	3rd	1st	2nd
C	2nd	3rd	1st

They must proceed to a vote. Voting is by majority. These are the two alternative procedures for voting, and they must first vote on which procedure to use. These alternative procedures are:

1. 1. Decide first, by majority vote, whether or not he is guilty of a mistake. If (I) he is not found guilty, promote him; if (II) he is found guilty, decide by another majority vote whether to (i) fire him or (ii) to keep him.
   2. By majority vote decide first, as a matter of principle, on the proper course of action if he is guilty — (I) to fire him or (II) to keep him without promotion. Then, once the appropriate penalty has been decided, decide by another majority vote whether he is guilty or not,

(i) promoting him if not guilty, otherwise
(ii) proceeding in accordance with the penalty decided on (I or II) in the first vote.

They must first elect one of the two procedures. They do this, too, by majority vote. They first hold a majority vote to choose procedure 1 or 2; they then vote in accordance with the procedure so selected.

Assume that (a) everyone’s preferences among the three outcomes are fully evident as a result of discussion, (b) everyone is shrewd enough and willing to vote in whatever fashion will attain his own preferences, and assumes everyone else will do the same, (c) voting is silent, by simultaneous ballot, and (d) no “deals” can he made among the three voters as to how they will vote.

The question:

1. 1. 1. What happens to the officer? Promoted, just kept, or fired?
      2. Which of the two voting procedures, 1 or 2, did they elect to use?
      3. What would have happened to the officer if board-member A had preferred not to promote him?
      4. What might have happened if A and B could make a deal and vote accordingly?
      5. Describe some third majority-vote procedure which if it were used, would lead to the officer’s being kept (pursuant to the board’s preferences in the above table).

5. Goffman says, “To study face-saving is to study the traffic rules of social interaction. …By face-work I mean to designate the actions taken by a person to make whatever he is doing consistent with face. …Thus poise in one important type of face-work, for through poise the person controls his embarrassment and hence the embarrassment that he and others might have over his embarrassment.”

See how far you can go in treating “poise” and “embarrassment” by a Richardson-process interaction model along the lines of Boulding or Valavanis.

Source: Papers Printed for Midyear Examinations [in] History, History of Religions, …, Economics, …, Naval Science, Air Science (January, 196) in the bound volume Social Sciences, Final Examinations January 1964 (HUC 7000.28, no. 150).

Image Source: Harvard Kennedy School Magazine, Summer 2012.