PHIL. 466A

FINAL PROJECT: A Real-World N-Person Collective Action Problem

Due in class on Friday, March 13, 1998


Find a newspaper, magazine, or book description of a situation that you believe can be interestingly modeled as an N-Person Prisoner's Dilemma Supergame. Make a copy of your source to turn in with your analysis of it. Please keep in mind that, contrary to the impression that I may have conveyed in this course, not every situation can be interestingly modeled as an N-Person Prisoner's Dilemma Supergame. Please begin this assignment enough in advance that, if you discover that the case you have chosen does not fit the model well, you will have time to find another case to model. Also, keep in mind that the case is much less interesting if the "solution" simply involves an agent external to the game (e.g., the state) who simply enforces cooperation. (However, there are many interesting n-person collective action problems that arise in the functioning of a state.) Choose a case in which there are interesting internal factors involved, though it is not necessary to choose a case that in the real world has been "solved". There are lots of interesting real-world cases. Don't get stuck with a bad case.

Once you have chosen your case, analyze it from the point of view of symmetrically situated, IR agents with complete and perfect information. Your analysis must include, at a minimum:

(a) an analysis of the sub-game, including: (i) definitions of relevant strategies; (ii) utility assignments to the relevant outcomes (not all possible outcomes), with a rationale for the choice of utility assignments; and (iii) a Schelling diagram for the relevant sub-game strategies. What conditions are necessary for each subgame to be an N-person Prisoner's Dilemma?

(b) an analysis of the super-game, including: (i) definitions of relevant supergame strategies; (ii) calculation of expected utility of relevant combinations (not all possible combinations) of the relevant strategies (requires some assumptions concerning a reasonable discount factor); (iii) at least one Schelling diagram of relevant supergame strategies. [Note that your analysis must contain at least two Schelling diagrams, one for the subgame in part (a) and one for the supergame here.] Is there an IR solution to the supergame? Are there conditionally cooperative Nash Equlibrium combinations of strategies in the supergame? Explain your answers.

(c) a discussion and defense of the assumptions that are necessary to apply your game theoretic model to the actual situation described in your newspaper, magazine, or book source, including a discussion of all the conditions necessary to model your case as an N-Person Prisoner's Dilemma Supergame in which there are Nash equilibrium combinations of conditionally cooperative strategies.

(d) a discussion of the psychological and socio-cultural factors that play a role, or might play a role in the "solution" of the collective action problem you have selected. To show that they might lead to or support a "solution" in our sense of the word, you must show how they serve to correlate individual strategies to produce a Nash equilibrium, or how they make a Nash equilibrium combination more stable.

(e) Do you have any recommendations for how the agents involved in the case you describe could do a better job of "solving" their collective action problem, or do the agents in the case you describe provide us with any useful lessons or tools for "solving" other collective action problems? Explain your answer.