Game theory, vehicle weight and safety

April 22nd was Earth Day and this prompted a good deal of reflection in the mainstream media about the problem of climate change and curbing emissions. One of the readily identifiable culprits for carbon emission is transportation. In the US it makes up for 25% of all CO2 emissions. This is also by far the easiest one to inspire ranting and hand-wringing because it is at least partially a direct reflection of individual choice. (Strangely enough the amount of energy used to warm the McMansion through a cold Northeast winter is somehow considered a fixed variable while SUVs continue to inspire wrath for their inefficiency.) There is increased focus on fuel efficiency and vehicle choice. For the first time, the issue has moved beyond moral overtones of saving the environment to simple economics: when gasoline is pushing $4/gallon fuel economy suddenly begins to make sense. US automobile manufacturers have been trying to outdo one another in green-washing their mediocre track records by embracing the language of virtue. Congress recently weighed in and decided to up the CAFE standards frozen since the 1980– a change the said manufacturers vehemently opposed.

Fuel economy is just one factor determining vehicle choice. (In fact it is also just one factor determining carbon emissions: the gas guzzler driven 5K miles a year still emits less than the hybrid driven 30K miles. The Earth does not care about the efficiency of pollution, only the total amount of carbon emitted.) New York Times had an interesting article in the April 13 Sunday paper titled Tiny saves gas, but big can save lives looking at the relationship between weight and safety. One of the standard arguments reliably trotted out by talking heads against CAFE standards is that any “artificial” increase in fuel economy beyond what the market itself has generated will force consumers into driving tiny, unsafe death traps. This argument is clearly bogus for a number of reasons– vehicles with the same weight drastically differ in fuel economy, so even if weight was the only factor determining safety, improvements in aerodynamics, engine and transmission would increase MPG while keeping the weight constant.

Nevertheless the NYT article does look at the underlying premise (“weight equals safety”) and confirms that it is for the most part correct, with some exceptions. It also dispels some of the misconceptions around comparison across categories. Commercials often feature glowing results from crash-tests run by the Insurance Institute for Highway Safety. Small cars such as the Smart Fortwo and Honda Fit do very well here, often getting five-star rating. But as the article points out:

“In frontal crash tests the vehicles can be compared only against other vehicles of similar size and weight. That’s because in a frontal crash test the vehicle hitting a barrier provides the amount of striking force.”

In other words a 5-star rated small car is not necessarily better than a 3-star rated heavy one. This is basic physics: when two objects collide, the lighter one experiences greater acceleration forces. Side impact is a different story however:

“The impact comes from a ram that strikes the car. Because the striking force is the same for each test it is possible to compare vehicles of different sizes.”

In this case the Honda Fit with the “good” rating is a true improvement over the much heavier Ford Crown Victoria getting the “marginal” rating.

Because the safety against frontal impact remains a function of weight, this leads to a simple game-theory problem. If everyone had a vehicle of the same weight, then fuel economy could be tackled independently of safety. And arguably reducing that weight would improve safety because lighter vehicles are less likely to damage each other in a collision. But this is not a stable situation: anyone with a heavier vehicle will gain a competitive advantage over other drivers. The advantage is short-lived because others will reason the same way and opt for heavier automobiles. This is the prisoner’s dilemma on a large scale: if everyone “cooperated” by opting for low-weight, they would be better off in terms of safety. But avoiding the sucker payoff (namely being disadvantaged by having a lighter vehicle than the neighbors) creates an incentive for going with the heavy-weight option and when everyone does that they are all worse off collectively. The result is that any equilibrium state likely to emerge will be one where everyone is driving the heaviest possible vehicle they could have– assuming safety is the only criteria. It is not, and the increasing price of fuel is now pulling the market to a different equilibrium point. When most vehicles on the road become lighter simply as a result of high oil prices, the false dichotomy between fuel efficiency and safety may finally disappear from the repertoire of excuses for inaction.


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