Spouse A (henceforth “she”, the driver) prefers the air inside the vehicle to be a little warmer than the preferred temperature of Spouse B (“he”, the navigator, not because he is a worse driver –quite the contrary– but because he is an even better passenger.) In their regular confrontation with this dilemma they are seemingly blessed with the optional dual-zone climate control in their decked out Volvo SUV.
And indeed there is an equilibrium of the dual climate-zone game in which each spouse enjoys his/her temperature bliss point. This equilibrium is unfortunately highly unstable. Because of the exchange of heat across the thermal gradient the only way each can maintain the constant target temperature is to adjust their controllers so that the air blown out their respective vents deviates slightly from that target further in the direction of the extreme. Hers must be set somewhat warmer and his somewhat cooler.
Now from that starting point, the slightest perturbation upsets the delicate balance and can set off a dangerous chain reaction. Consider for example what happens when, due to random alterations in air flow she begins to feel a bit on the cool side of her comfort zone. Her response is to adjust her controller one peg toward the red. This restores her comfort level but very soon as a result he will begin to feel the discomfort of unexpectedly hot and dry air blowing into his zone and he will react by moving his controller one peg toward the blue.
This is not likely to end well.
16 comments
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April 10, 2013 at 2:54 am
Jacob AG
One of them writes this blog post. Then a Cournot process of negotiation begins. They bargain their way towards a temperature that is set exactly halfway between their ideal temperatures. That temperature is the equilibrium, and it is static. Nobody ever touches the dials ever again.
April 10, 2013 at 6:10 am
Joshua Gans
In equilibrium you’ll establish a cold front right down the middle of your car.
April 10, 2013 at 7:03 am
twicker
That sounds awesome!
April 10, 2013 at 8:01 am
jamesoswald
Therefore, market monetarism.
April 10, 2013 at 11:27 am
Kevin
That… is… an awesome comment. I’m sure Scott Sumner would find it funny too.
April 10, 2013 at 12:36 pm
Enrique
In some respects, this situation is like the “toilet seat game” … up or down?
April 10, 2013 at 12:38 pm
Enrique
Except that in the toilet seat game, the moves of A and B are sequential instead of simultaneous …
April 16, 2013 at 4:23 am
Jeremy Chen
… in a particularly acrimonious version, the toilet seat game can be simultaneous move. The strategy space is then a bounded set in R including the origin….
June 10, 2013 at 10:20 pm
Jhon
If you re-add the discouraged worekrs that the Clinton and Bush 1 administrations removed from the U-6 unemployment rate (like ), “real” unemployment and underemployment is nearly 18%. I think this reflects the reality of the economy much more than the artificial 7% of the official U-3.”Once a decade” items and luxuries (toasters, iPods, etc.) cost less than ever before (post-inflation), but essentials (food, gas, etc.) are curving away from their “forever” bottoms and increasing 25% to 50% (or more, in some cases) from their prices of 1-2 years ago. This squeezes the monthly budgets of people who have placed themselves on the edge with overbought houses, cars, and other big-ticket items.
June 12, 2013 at 8:09 pm
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October 17, 2013 at 7:53 am
Ines
The Love of a Game Between me and my husband we have owned atiaddonil MP3 players over the years than I can count, like Sansas, iRivers, iPods (common & touch), the Ibiza Rhapsody, etc. But, the last few many years I’ve settled down to one line of gamers .
April 11, 2013 at 9:57 am
Florian
There is a nice paper by Adam and Ehud on such strategic polarization:
Click to access 1266.pdf
April 21, 2013 at 5:03 pm
Philip Ngai
You seem to be assuming adjustment 1A by A would require adjustment 1B by B that would completely negate the effect of A’s adjustment as felt by A (or perhaps even more than undo A’s initial adjustment). Then you imagine a larger adjustment 2A by A forcing even larger adjustment 2B and so on.
But in fact, an adjustment by B has a larger effect on the temperature felt by B than the temperature felt by A. That is the point of a dual-zone system.
Therefore, adjustment 1A would result in 1B which is smaller than 1A and the response 2A is smaller than 1B, etc and the system is stable, not unstable.
April 24, 2013 at 9:26 am
Insuk Cheong
Suppose A’s bliss point is a, B’s is b where a>b. Also assume that temperature felt by A is sx+(1-s)y and B’s is sy+(1-s)x where x is the level A chooses, y is the level B chooses, and s>0.5. Their response functions are sx+(1-s)y=a and sy+(1-s)x=b. You’ll see this is exactly the same as Cournot game with stable Nash equilibrium.
April 10, 2016 at 6:33 pm
Andrea Matranga
Eventually, the freezing air from the passenger side will meet the scorching air from the driver side. If the air is set to recirculate, the lack of a external humidity source will prevent precipitation, but strong wind shear will result. If external air is allowed in, given sufficient humidity levels, I predict it will start hailing on the gearshift lever.
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