Game theory and traffic court
I got jaywalking ticket about a month ago. I considered contesting is (what a dumb ticket!) but the fine wasn't big enough to make it worth taking a morning off work. Nevertheless, it spawned a very interesting idea. I was talking about the ticket with one of my co-workers yesterday. He described fighting a moving violation he'd received (much more expensive). One strategy is to re-schedule your court appearance at the last minute. In fact, you can re-schedule twice! This is a rich situation for game theoretic analysis.
To formalize things about... let's call the contester Player 1 and the policeman (or woman) Player 2 (although I prefer Hero and Darth Vader, respectively). Assume that Player 1 can reschedule at the absolute last minute with no personal cost, after Player 2 has committed to showing up. If Player 1 and 2 both show up at court, Player 1 has a probability p of succesfully contesting the ticket. Otherwise, Player 1 must pay Player 2 (e.g., the county) X dollars. The cost of showing up at court is Y dollars for both players, whether or not the other player shows up (travel, inconvenience, etc. -- actually, there's no good reason the cost must be Y to both; in fact, the opportunity costs may be relatively high for some contesters... such as lawyers and doctors).
If Player 1 shows up the case will be resolved one way or another. Therefore, Player 1 has three pure strategies: (A) show up on the first court date, (B) reschedule once and show up on the second court date, or (C) reschedule twice and show up on the third and final court date. Player 2 has eight potential pure strategies, since Player 2 can show up on any, all, or none of the court dates. I will number Player 2 strategies from zero to seven (think of it in binary)
Decimal Third Date Second Date First Date
0 0 0 0
1 0 0 1
2 0 1 0
3 0 1 1
4 1 0 0
5 1 0 1
6 1 1 0
7 1 1 1
This is enough of a framework to set up the optimization problem and solve for the optimal mixed strategies. I shall leave that as an exercise for the reader (OK, OK, I'm lazy :) ). I reall, really wonder how many academics have written papers on the game theoretic aspects of fighting traffic tickets. There must be a rich body of data to test models.
MHP
To formalize things about... let's call the contester Player 1 and the policeman (or woman) Player 2 (although I prefer Hero and Darth Vader, respectively). Assume that Player 1 can reschedule at the absolute last minute with no personal cost, after Player 2 has committed to showing up. If Player 1 and 2 both show up at court, Player 1 has a probability p of succesfully contesting the ticket. Otherwise, Player 1 must pay Player 2 (e.g., the county) X dollars. The cost of showing up at court is Y dollars for both players, whether or not the other player shows up (travel, inconvenience, etc. -- actually, there's no good reason the cost must be Y to both; in fact, the opportunity costs may be relatively high for some contesters... such as lawyers and doctors).
If Player 1 shows up the case will be resolved one way or another. Therefore, Player 1 has three pure strategies: (A) show up on the first court date, (B) reschedule once and show up on the second court date, or (C) reschedule twice and show up on the third and final court date. Player 2 has eight potential pure strategies, since Player 2 can show up on any, all, or none of the court dates. I will number Player 2 strategies from zero to seven (think of it in binary)
Decimal Third Date Second Date First Date
0 0 0 0
1 0 0 1
2 0 1 0
3 0 1 1
4 1 0 0
5 1 0 1
6 1 1 0
7 1 1 1
This is enough of a framework to set up the optimization problem and solve for the optimal mixed strategies. I shall leave that as an exercise for the reader (OK, OK, I'm lazy :) ). I reall, really wonder how many academics have written papers on the game theoretic aspects of fighting traffic tickets. There must be a rich body of data to test models.
MHP
posted by MHP at
6:41 PM
1 Comments:
Player 1 should actually have a fourth pure strategy, D. In strategy D Player 1 simply pays the ticket. Otherwise, the opportunity cost to Player 1 is irrelavent; no matter what, Player 1 must visit the court exactly once in strategies A, B, and C.
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