Embedded Files
In Demand estimation and the Roy Model economists have made assumptions about how individuals behave. However, these models limit individual's to thinking about their own behavior. In game theory based models, economists make assumptions where individual's make decisions based on interactions with decisions of other individuals.
Consider the problem of estimating the value of going for a pass or a run on 4th down in NFL. David Romer uses data on the outcomes of plays and calls made to estimate the value of going for it relative to punting or kicking on 4th down. Romer argues that his results suggest that NFL coaches do not make rational decisions, thus casting doubt on a central pillar of economics and economic policy making. The difficulty with accepting Romer's result on its face is that, to his point, NFL coaches generally don't go for it on 4th down. Romer's solution is to use success rates from runs and passes on 3rd down to estimate what those success rates would be on 4th down. To estimate the success rate from various to-go distances, Romer estimates the success rates of pass plays from those distances and the success rates of run plays from those distances. He then weights the two estimates by the probability of a run play at each to-go distance. Here lies the problem.
The issue is that a coaches choice of whether to play pass or run may be different in 4th down. One reason it may be different is that the defense will be different in 4th down. Both of these may be different because the outcomes are different on 4th down. Let's say that a pass is a high risk/high reward strategy while a run as a low risk/low reward strategy. A coach may be willing to take the risk on 3rd down, because they know they have one more chance to kick a field goal or kick the ball to the other end of the field. If they take such a risk on 4th down, they will turn the ball over downs (the opposition will get the ball at that relatively good position on the field).
Game theory provides a method for analyzing how the offense and defense will choose between run and pass on 3rd down and on 4th down. It can show how the behavior will change between the two situations. Moreover, the game provides a way for the statistician to estimate the appropriate parameters using 3rd down data, then simulate the outcomes for 4th downs. These simulated results can be then be used to estimate the value of going for it on 4th down and determine whether the estimates correspond to the actual behavior of the NFL coaches.
Google Sites
Report abuse