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To Wait or Not to Wait

Imagine a scenario where you’re just arriving at a bus stop to catch the bus but you see no bus in the distance and you have no way to determine when the next one will arrive. You have the option to walk to your destination but a debate ensues in determining what course of action to take. Eventually you may ask yourself, sit and wait or walk?

Throughout my freshman year here at Cornell, I found myself facing this issue almost weekly.  Taking the TCAT was most certainly the lazy way out, but who ever knew what time the buses were actually supposed to come? It seemed to me that there was no best strategy apparent, but then again, I never did stop and think.

Scott Kominers, Justin Chen and Robert Sinnott, undergraduate students at Harvard and Cal Tech, took it upon themselves to derive a dominant strategy after all too frequently finding themselves facing this dilemma.  Playing out this debate mentally had basically become tiresome and frustrating. After number-crunching, the three concluded that the best choice was to in fact be lazy wait for the bus.

Clearly, however; the strategy does not hold true in all cases.  If the player does know for a fact that the wait will be longer than the walk itself, then walking would be the best choice.

Game Theory is evident in countless facets of everyday living. The bus-wait game mentioned previously easily fits within the constraints of game theory. Although success is not based off the behavior of other players, it is based off an outside factor – the bus.   The commute time serves as the payout – the shorter the commute, the higher the payout. As players, we will seek a strategy – to wait or not to wait, that will consistently award us the highest payout possible (best response). By breaking down every possible course of action, it becomes clear why waiting is the best response to an empty bus stop. Buses run on schedules and are always punctual, and chances are a bus will arrive soon. Plus, if you were to arrive at an empty bus stop, you could do something productive during this lazy period.  If the bus were to whiz by while you after you chose to walk, this would only infuriate you and ensure a negative payout due to the fact that you could have been on the bus. In addition, as Kominers explains, a person who is walking along the bus route tends to unconsciously stop at each bus stop and momentarily look for a bus coming.  Although unconscious, these pauses can add up time to the walking choice.  On the other hand, the best response to a bus at the bus stop would be to take it.  Due to long journeys and rather punctual buses that exist when such a scenario is frequently faced, taking the bus will serve as a best response.  In essence, the lazy way out here is essentially your best path to take.

Source: http://www.nytimes.com/2008/12/14/magazine/14ideas-section01-t-008.html

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