If we assume that each player prefers shorter sentences to longer ones, and that each gets no utility out of lowering the other player's sentence, and that there are no reputation effects from a player's decision, then the prisoner's dilemma forms a non-zero-sum game in which two players may each cooperate with or defect from (i.e., betray) the other player. In this game, as in all game theory, the only concern of each individual player (prisoner) is maximizing his/her own payoff, without any concern for the other player's payoff. The unique equilibrium for this game is a Pareto-suboptimal solution—that is, rational choice leads the two players to both play defect even though each player's individual reward would be greater if they both played cooperatively.
In the classic form of this game, cooperating is strictly dominated by defecting, so that the only possible equilibrium for the game is for all players to defect. No matter what the other player does, one player will always gain a greater payoff by playing defect. Since in any situation playing defect is more beneficial than cooperating, all rational players will play defect, all things being equal.
- Numbers are concrete and easily understood - if asked to defend the selection or non-selection of a team, its difficult to argue with a formula based rank; and
- The vast majority of comparisons that occur during NCAA selections are based on the RPI (e.g. record vs the Top 25 in the RPI, record vs the the top 50, the top 100, strength of schedule, non-conference strength of schedule, etc.)
These comparisons are particularly crucial when the last at-large spots for an NCAA tournament are being selected. Typically, two types of teams compete for the last at-large spots: a) additional representatives from a conferences that already have numerous bids; or b) teams from conferences trying to get a second bid in addition to their conference automatic qualifier, who are often strong second place teams or first place teams from weaker conferences who are upset in their conference tournament.
Generally teams from "power conferences" get more at-large bids. This can happen for a number of reasons. Ideally, it will be because the team is truly better. Skeptics will argue that it is due to brand name recognition, history, tradition or politics. But another possible reason is that the committee when choosing these final teams constantly compares the criteria cited above along with information such as:
- an individual team's performance against teams already in the tournament; and
- an individual team's performance against team's under consideration for selection.
The resulting selection of "power conference teams" reflects a rational choice by selection committees because there are so many more "defensible" points of comparison on which to base a decision, and these points of comparison are often conference opponent comparisons. Weaker teams from stronger conferences compare favorably through a halo effect from their conference partners. Stronger teams from weaker conferences simply have fewer comparison points and are not able to benefit from a similar halo. Indeed the rising tide lifts all boats. So you have to make the tide rise. How?
When it comes to athletic scheduling and the RPI, there are only 2 things you can control, who you play and your team's performance (which effects winning or losing). Thus, when using a formula that weights the winning percentage of your opponent more highly than other factors, creating high winning percentages for the opponents you play most often (other conference members) makes perfect sense. And this is best achieved through collective conference efforts to win - with superior talent and/or beneficial scheduling.
Most teams will continue to struggle with the dilemma's of scheduling because there are so many other factors that influence scheduling decisions in addition to the RPI - the need to generate revenue or cut costs, maintaining traditional rivals, enhancing the student athlete experience and the like. Further, just as in the prisoner's dilemma, you have to trust your partner in crime to do the right thing or else you suffer and they benefit. The result is that most teams will continue to act independently. But there's a reason the same conferences are highly represented in the post season every year - they win games and have top teams, but when the last selections are made, some teams may appear better than they truly are. Creating the appearance of quality through independent scheduling is hard. You need help from your conference "friends" - truly a prisoner's dilemma.