Game Theory and Aldon Smith

49er fans woke up Sunday to learn that one of their defensive ends, Ray McDonald, was arrested for domestic violence early Sunday morning. Shortly thereafter, San Jose Mercury News columnist, Tim Kawakami, argued that this was ultimately the 49ers fault because "they have no standard of behavior as long as the player can produce for them in the times when he is not otherwise banished from the league, and what we're seeing is  bunch of players who have absolutely gotten the unspoken message and continue to do whatever the hell they want."

Kawakami has a point, but he fails to recognize that NFL teams have absolutely no incentive punishing bad behavior (presumably by releasing players), and until the incentives change, they will continue to tolerate such behavior whether they want to or not (although as I noted a couple of weeks ago, NFL players behave better compared to other men in the same age range -- "NFL Players Aren't As Bad As You Probably Think").

To illustrate why, let us turn to the insights that game theory offer us. Economists, political scientists, sociologists, and other social scientists use game theory in order to model real-world situations that involve cooperation between two or more parties. The best known game is probably the "prisoner's dilemma," which shows how two "rational" individuals might not cooperate, even if it's in their best interests to do so. Imagine a situation in which the police have two people in prison, but they don't have enough evidence to convict them on the principal charge. They do, however, have enough to sentence both to a year in prison on a lesser charge. Each prisoner is in solitary confinement and cannot communicate with the other. The police decide to offer each prisoner the opportunity to get off scot free if they testify against the other.

The various outcomes are captured in the matrix above, which lists the "payoffs" to each of the prisoners (the payoffs for Prisoner #1 appear below each of the diagonals, while the payoffs for Prisoner #2 appear above the diagonals). The best option is for both prisoners to keep their mouth shut. If they do, they will only serve 1 year in prison on the lesser charge (note the "1s" above and below the diagonal in the upper left cell of the table below). However, the rational thing for each individual prisoner to do is to betray the other. For example, if Prisoner #1 betrays Prisoner #2 and the latter remains silent, then he'll go free, while Prisoner #2 will serve 3 years in prison. The opposite is true if Prisoner #2 betrays Prisoner #1 and Prisoner #1 remains silent. However, since both prisoners are "rational," they'll both betray the other, and both will serve prison terms of 2 years.

Now consider what I'm calling the Aldon Smith dilemma or game (see the payoff matrix below). As 49er (and NFL) fans know, the 49ers' defensive end, Aldon Smith, is a talented but troubled young man, who has had several brushes with the law, which (finally) earned him a 9-game suspension from the NFL. Many (e.g., Tim Kawakami) have repeatedly called on the 49ers to get tough with Smith, to release him, but currently there's no incentive to do so. To illustrate, consider the following payoff matrix. Assume that having Smith on one's team brings expected benefits (e.g., wins) of "8" and costs (e.g., salary, disruptive behavior) of "4" for a net gain of "4". Thus, if the 49ers release him, the only way they don't "lose" is if no other team (e.g., the Seahawks) signs him. However, if another team picks him up, then the Niners pay the price. Thus, the rational thing for them to do is to keep him regardless of what other teams plan to do.

Of course, the Niners aren't alone. No individual NFL team has the incentive to release talented but troubled players as long as their rivals will sign them. In fact, unless it becomes more costly to keep such players than to release them (e.g., "cost" of paying a player who spends half of every season suspended), teams will not be willing to do so. To illustrate assume that the costs of keeping Smith are increased from "4" to "10;" this produces a new payoff matrix (see below), which shows that if neither the 49ers nor the Seahawks sign Smith, then neither one comes out ahead. More importantly, it shows that there's no incentive for either team to sign Smith because the costs of doing so outweigh the benefits (-2). Thus, the rational thing for both teams is not to sign him.

Incentives seldom change by themselves, however, which is why it's up to the NFL to do so. In short, they have to make the costs of keeping players such as Smith (and Ray McDonald) greater than expected benefits. And that is exactly what it is (finally) starting to do. By suspending players for big chunks of a season (and for repeated offenders, for life), the NFL is changing the incentive structure for teams like the NFL, which should allow them to start making choices with which everyone, including Tim Kawakami, is more comfortable.