The Game Theory of deterring fare evasion on light rail

As I’ve mentioned before, if TriMet builds more light rail capacity, fare evasion will become a greater problem. Buses have a built-in fare inspector as the driver adds little additional marginal cost for inspecting passengers’ fare compliance. MAX however, does not.

Light rail requires additional labor to enforce payment. In game theory, this is a situation where a pure strategy does not exist. That is to say, there does not exist one optimal strategy for TriMet to consistently follow, given the two pure strategies of inspecting every train or not inspecting any trains. The Nash Equilibrium in this case will be a mixed strategy.

Sometimes TriMet should be inspecting fares, and other times it should not, because, at around $40 an hour, TriMet’s fare inspectors are too expensive to check every trip. TriMet would lose more money from labor costs than lost passenger revenue. However, if TriMet never inspected fares, the lost revenue would eventually exceed the cost of paying for some deterrence. The optimal mixed strategy would entail a rate of inspection such that the labor costs remain less than the increased revenue.

What is that optimal inspection rate? Assuming TriMet’s labor costs are not too high to achieve this, it would normally be the point where passengers find no expected gain from failing to pay for a ticket.

If there is complete information among riders about the penalty for fare evasion, its deterrence is a function of the probability of getting caught times the size of the penalty. Fare evasion can then be deterred if this number is greater than the price of the ticket.

(Probability of getting caught) x (the cost of the penalty) > (price of fare)

For TriMet, given its average fare price of $1.46 and $175 fine, the optimal frequency is:

(Rate of inspection) x $175 > $1.50

So the rate of inspection should be $1.50/$175 or roughly around 1% of MAX trips need to be randomly inspected. That seems doable, but it doesn’t appear to me that TriMet is doing this. The Portland area’s transit agency is probably losing more money in lost passenger revenue than it would have to spend to maintain this inspection rate.

Eric Shierman lives in Salem and is the author of A Brief History of Political Cultural Change




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Posted by at 05:00 | Posted in Public Transportation, TriMet | Tagged | 2 Comments |Email This Post Email This Post |Print This Post Print This Post
  • Bob Clark

    Wow, love this game theory. TriMet could also raise the fine with “a little help from their friends” in high places. But then you have to figure how much of the fine the commuter will actually pay back, if they lack the savings to do so. In this instance, they might be kicked off TriMet for good, but here again they probably could risk riding the light rail again; even buses since not all bus drivers are going to recognize the “dead beat.”

    For folks who were raised with many cultural norms, there is the stigma of getting caught. This would reduce the fine somewhat needed. And also, the cost of a rider’s delay by fare enforcers because he/she tried stiffing the fare probably reduces the necessary fine amount.

    Other ways would be to lower the costs of enforcement by having robocops or the mafia take over the job.

    For most people though you could drop the fare to zero, and they still wouldn’t care to ride light rail. Time is very valuable for most folks, and the ambling meandering ways of several of Max’s legs; are time sinks. Subways or elevated trains are much more useful in dense Metro settings, but they are very, very costly to build. So, we got a cute, botique little train set instead.

  • Oregon Engineer

    it is pretty obvious that trimet is not charging passengers the true cost or public transit. Based just on the fare of 1.50 this only gets you about 3 miles according to the government reimbursement rate for travel in your car at $.535 per mile and this does not pay for your time which in the real world has a value. So even at the 1.50 per fare the passengers are really riding for free as it is. The game theory here is will i ever get caught. after about 50 days of riding for free (2 times per day) it is about break even. even if you do get caught how long is it before you are banned from trimet and after that does trimet have facial recognition to catch you again? Isn’t public transit wonderful. free rides.

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