Prisoner's Dilemma in Sports

Professional sports, particularly ones in which athletes are competing directly against one another individually (i.e sprinting and cycling), can become a setting for a prisoner's dilemma. With the presence of performance-enhancing drugs, athletes have a choice between taking these performance-enhancing drugs or not. As athletes have no information about the decisions of their competitors to take or not to take the drugs, they can decide to remain clean and avoid the risks associated with getting caught doping (typically bans from the sport) or take the drugs to gain a potential competitive advantage. The prisoner's dilemma analysis allows us to tease out why an athlete might decide to dope despite its irrationality given the steep consequences.

In a scenario with two athletes who have no information on the drug-taking habits of the other, both athletes are better off if they both remain clean. However, the dominant strategy is taking performance-enhancing drugs to gain an advantage over your opponent as neither athlete can trust the other. Taking the drugs gives you the best chance of winning given either decision by the other athlete. In theory, the addition of an "inspector" who tests the athletes and punishes the cheaters would correct this inefficiency and move the equilibrium to Pareto Optimality. However, in current practice, athletes do not fear the inspection process enough to refrain from using performance-enhancing drugs as shown by the continued reveal of cheaters in sports.

The Prisoner's Dilemma of Golden Balls

In Golden Balls, a British television show in the mid-2000’s, the players face the prisoner’s dilemma. They have two choices on their way to winning a jackpot: split or steal. If they both steal, neither gets the money. If they both split, they split the money. If one steals and the other splits, the ‘stealer’ takes the entire jackpot. The dominant strategy, then, is to steal.

In this episode, Nick achieves the Pareto optimal state despite the dominant strategy of stealing. He claims that he will steal regardless of the discussion, and offers to split the winnings informally after the show if Abraham chooses split. Otherwise, they both walk away with nothing, he claims. In the end, Nick persuades Abraham to split, and secretly splits to achieve the Pareto optimal state despite the dilemma.

Nick can avoid the trap of the dominant strategy because of the circumstances of this game. For one, the prisoners are allowed to discuss their choice before making it. However, conversation doesn’t always work: in many other episodes, discussion still leads to Pareto un-optimal states (steal-splits, or steal-steals). The second aspect is that the prize is splittable. Abraham trusts Nick enough to attribute some non-immaterial probability to actually splitting after the show. That version of the ultimatum game is something for another blog post.

Charlottesville Concert and Minimax Regret

We all know there is a lot of hype about the Charlottesville Concert coming this Sunday. I mean, tickets were FREE (+7.50 shipping and handling)! However, personally, there are aspects of the marginal cost that are not included in the price. This includes my Econometrics test on Tuesday. As a risk adverse individual (which in this case means that I am a 4th year and have FOMO, fear of missing out), whether I attend the concert will be based on where I can minimax regret.

The two states of the world are that the concert are S1= worth it (aka awesome) or S2= not worth it (aka lame). The two alternatives I will choose from are A1=to attend, or A2= to stay home and study instead. My marginal cost for attending the concert is $7.50 (assuming I could sell my ticket for this amount otherwise), plus the opportunity cost of studying for econometrics, perhaps 10 points on a test, which I value at $100. My marginal cost is therefore $107.50. My marginal benefit of attending the concert, given that it is awesome (therefore P=1), is $1,000,000. I will have the best night of my college career, have priceless memories with friends, and tell my grandkids about it. It will be like winning the lottery to me.

My regret table looks something like this:

	S1 Concert is AWESOME	S2 Concert is lame
A1 Attend Concert	0, no regret	Marginal Cost= $107.50
A2 Don’t Attend	Marginal Benefit ($1,000,000)-Marginal Cost ($107.50)= $999,892.50	0, no regret

I am going to choose the Ai which minimizes my maximum regret. Since $107.50 < $999,892.50, I will attend the concert!

Voter Registration

Reverend Jesse Jackson, a national religious, political, and civil rights leader, recently spoke on Grounds this past Thursday about a host of issues. Charlottesville was one of Jackson's first stops on his "voter registration bus tour;" 70 people registered to vote after his speech in Old Cabell Hall. My first inclination after reading this article was to think, "Wow, that's great! 70 more people will vote in this November's gubernatorial election in Virginia." However, the decision of those 70 people may have been more emotionally-charged than rational, and not all of those 70 may actually end up voting in this November's election.

Around 5 million voters are registered in Virginia, but less than half of that number will probably turn out to vote this November to decide the next governor. Some may be discouraged by this statistic, but Johnson would say it makes total sense, that it's a rational way to behave. Your vote isn't likely to break the tie in an election, and the costs normally outweigh the benefits of voting (if you assign a dollar amount to each candidate winning). A purely "rational" person would never vote in a Virginia state election. Because the costs of voting outweigh the benefits, those who have registered are only a quarter of the way there; they still need to get off work, become informed on the issues, and take time to think about their decision. Odds are all 70 newly-registered people won't vote. Rev. Jackson's efforts to register people to vote are valiant and patriotic, but they probably won't solve the problem of low voter turnout, especially in minority demographics. For voter turnout to truly rise, the benefits of voting need to outweigh the costs.

Disaster Relief as a Public Good

Following hurricanes Harvey and Irma millions of dollars of private donations have been made to support disaster relief efforts in Houston and Florida.  In three weeks, more than $350 million were raised by private charities to support Hurricane Harvey relief and the federal government approved $7.9 billion in initial relief. Disaster relief is a form of redistribution of wealth on a national level, with money going from people all around the country to people who have been hurt by a natural disaster—and this redistribution can be explained by Mueller’s three justifications of redistribution of wealth.

First, the federal government’s funding of disaster relief is justified as insurance because a disaster like a hurricane is a random event that cannot be controlled.  Though some areas are obviously much more likely to suffer a disaster, there is a chance anywhere could be struck by some sort of disaster, so because of the unknown risk that everyone is under, everyone’s utility is maximized if our government will help people when they are a victim of natural disaster. Second, the millions of dollars given privately to Harvey relief show that Americans have interdependent utility, meaning the utility of Americans depends to some extent upon the utility of other Americans, or at least those who are suffering as the result of a natural disaster.  Third, redistribution through disaster relief is a way of satisfying fairness norms.  People would rather live in a society that is fair and helps people when their lives are torn apart by a storm, so we gain utility knowing we live in a society that complies with our fairness norm of helping people in need.

Parking in Charlottesville

Outside of my house on 15^th Street, residential parking on weekends is a nightmare.  At the beginning of the past two school years, I purchased a parking permit for my block.  The permit enables the exclusion of parking to non-residents, while permitting limited rivalry between residents to find an ideal parking spot on the block.  The city of Charlottesville maintains ‘permit only’ parking Monday through Friday by ticketing individuals without permits, thereby discouraging non-residents from acting as rivals to those who purchased permits and in theory, reminding them of their exclusion from using the spaces.  However, if you were to run an errand on Friday evening and return around 6PM, you might as well have left your vehicle over by Barracks—there is no hope of parking on your block. 

During the weekend, parking becomes non-excludable and incredibly rivalrous, as many more car owners try to squeeze into the temporarily free-of-charge parking spots.  Other individuals’ choice to park where I usually keep my car either leaves me feeling the need to invest in one of these in order to easily squeeze my behemoth of a sedan into a parking space (granted of course, that there is one feasibly large enough) or simply refusing to drive anywhere.  With limited and tremendously rivalrous street parking, these new space occupants must have their cars somewhere else during the week.  Often these cars belong to apartment residents who do not want to pay for spaces in their parking garages, so they scrounge for parking in a characteristically Pareto inefficient move – while these guests to 15^th Street may be better off by parking on my block over the weekend, my neighbors and I who have nowhere else to park, are certainly not.