pedestrian stand-off


These past few weeks I’ve been doing some reading on the Prisoner’s Dilemma. It is an interesting scenario used in game theory, especially its iterated version, on which there is a very interesting book as well, if someone is interested in an introduction to game theory. This reading is done partly because of an assignment, and partly because I think the iterated version of it might apply to certain urban phenomena (post to follow, as soon as I manage to wrap my head around the concept). However, yesterday I reached the point where I thought that I might have slightly overdone it with the reading.

As I was crossing the road, some pedestrians were crossing from the opposite side as well. Our paths and relative speeds would cause us to bump into one another, and so I paused mid-stride for a moment to let them pass. At that point, it occurred to me that just for a moment we had engaged in a quick game of chicken (which I obviously lost, because I’m such a polite person). With the recent reading still in my head, I started thinking of the rules of such a game, and I ended up with the ‘pedestrian stand-off’, a game played unknowingly by urbanites every day.

The pedestrian stand-off is a cooperative game between 2 players, played once between a pair of pedestrians whose paths meet on the street. It represents the process that takes place when two people attempt to resolve their courses, in order not to collide. Both players want to spend as less time as possible in the path negotiation, so they are playing with time as the resource to be gained. For each person individually, the best solution is to not change paths at all, a decision that will be called being aggressive (A). If a person stops to let the other pass, then he is being passive (or polite, hence P). If neither is polite (A,A), then the two collide, which, although a bit troublesome [1], resolves the interaction quickly. Worse yet, if both are polite (P,P), then they spend the most amount of time by entering into this all-known little dance, where at first they both lean to one side to let the other pass, then both lean to the other side, etc etc, until one gives up. This produces the following payoff matrix:

PedestrianStandOffMatrix

For the two players, I and II, deciding on being either aggressive (A) or passive (P), the relative payoffs are w>p>c>d, where continuing to walk (w) is the best outcome, since the other person cleared the way. Pausing one’s walk (p) is next, as it is only a momentary pause. Colliding (c) is the second-to-last, since a small amount of time will be spent readjusting course. Finally, starting the left-to-right polite dance (d) is the worst outcome, time-wise.

Interestingly enough, the best solution to the interaction is the asymmetric one, where one person needs to let the other pass. Both symmetric solutions yield worse results than the asymmetric one, as they are both more time-consuming. Furthermore, it pays better to  generally be aggressive; not as a way of being rude, but as a way of indicating one’s intentions, and letting others know and adapt to them [2].

As it turns out then, it is more rewarding, time-wise, to make one’s intentions apparent and not deviate from them, and this is done by being aggressive (A) (if one does that however, one needs to have his apologies at the ready). On the other hand, it is also good to quickly identify a person operating on said principle, and give way to them. Although by pausing momentarily, the polite person gets rewarded with (p), which is less than (w), on the whole, both individuals have done better, as both (p) and (w) are better outcomes than (c).

To conclude, after having written all this,  I found it a bit odd that I spent my whole tube ride home thinking about this, and a good indicator that it would probably be a good time to switch my reading from Robert Axelrod to Terry Pratchett. And so I did.

_________

[1] To make things easier, I’ll assume that there aren’t any unequal collisions in terms of speed or bulk (so no ‘Granny vs Skinhead’ collisions). Instead, to keep my imaginary individuals safe from harm, I’ll be using the more convenient (and highly unrealistic) assumption that all players are male, 1.83 m, 75 kg corbusianesque individuals.

[2] Incidentally, I have come to understand that this is the best course of action when driving (especially a motorbike) and interacting with other motorists as well, in the sense that a motorist needs to constantly make his presence and intentions obvious to other motorists.

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