Partial Answers to PD/ToC Problems

The matrices below only include values for one player. In all the problems here each agent faces the same situation. Here is a link to the two-person matrices as drawn on the board.

1a. As discussed in class, I think there are two plausible entries for the top square to the left. I'll include both alternatives, listed as a and b. Note that only the b-version leads to a ToC. With the a-version there is no dominant strategy so introducing probabilities would change the strategy that RCT prescribes to the agent.

	More than half adopt	Less than half adopt
Single agent adopts	a) (2/3 - 5%) C or b) 2/3(1.35 C)	1.35 C
Single agent doesn't adopt	2/3 C	C

Common errors: Making both of the bottom boxes equal to C. (I don't understand why this was a tempting answer.) Some forgot to include the 5% cost factor. Some didn't understand that the 1/3 was the fraction of decrease, not the new net value.

1b. Here you could just invoke a central authority but it would be good to review some of the "cute" solutions described in the Tragedy of the Commons reading on the web.

2.

	Other person feeds	Other doesn't feed
Agent feeds	2nd	3rd
Agent doesn't feed	1st	4th

This is not a Prisoner's Dilemma situation because there is no "best" or dominant action so one could gamble or play-it-safe. Note, however, that if each player goes for their first choice, everyone ends up with their worst choice! This is a typical Clash of Wills case. Whether the agent should decide to feed or not could also be affected by what s/he takes to be the probability that the other person will feed. That probability assignment might depend on promises (perhaps they could agree to take turns) and the agent's past experience with the other party.

3.

	Other person feeds	Other doesn't feed
Agent feeds	2nd	4th
Agent doesn't feed	1st	3rd

Now we do have a classic PD situation and if both agents follow the advice of this RCT analysis, the poor mule will certainly starve! Note that even if they make promises and even if the agent has had good experiences with the other keeping promises faithfully such that there is a high probability that the other will be cooperative, the simple matrix above nevertheless dictates that the agent should always defect! Arrgh!

Common errors in 2 and 3: Not recognizing the difference between a Clash of Wills situation and a true PD situation. Also some difficulties in going from the verbal description to the rankings. The rankings in these problems are often composites of more than one factor. For example, possible positive factors for the agent in both problems are a) that the mule gets fed b) that the agent gets to stay home. Possible negative factors are c) the effort of feeding and d) the extra effort of feeding alone. So then the puzzle becomes to figure out from the wording the relative weighting of these factors so that one ends up with a unique ranking and this can be puzzling. It's worth mentioning that the same difficulty arises in real life decision making. It's often easy to list all the pros and cons of a certain course of action but not so easy to figure out which are weightier.

4. Another PD situation. However, the game of chicken cannot be repeated so tit-for-tat strategies can't be applied. (Google provides lots of discussion but few creative solutions.)