# Crossing norms

Categories: Yellow Pad

*The author is an associate professor of economics and dean of the College of Business and Economics of De La Salle University.*

Early one morning in late November, on my way to De La Salle University

for an important appointment, I hit a traffic jam that, hyperbole

aside, stretched for at least a mile on Zamora Bridge, that

flyover-bridge infrastructure complex that connects Valenzuela Street

in Sta. Mesa and Quirino Avenue in Pandacan. The cause of the

bumper-to-bumper snafu: gridlock at the Tejeron Street intersection,

where cars refused to give way to those going crosswise relative to

their direction. Ruing my choice of route for the day, as the minutes

ticked away I tried to make the best of a bad situation by devising an

economic model that offered an explanation for my predicament. What

follows is the game-theoretic parable that came out of my ruminations.

Consider a two-stage supergame (that is, a game that is iterated ad

infinitum) consisting of N players, where N is a fairly large number

(perhaps corresponding to the number of drivers in Metro Manila). At

the first stage of an iteration, the players each draw a card that

indicates whether or not they are in the game for that iteration, and

if so what their direction and rank in line are. For expositional

convenience, assume that there are only two directions, northbound and

eastbound, and that n, the number of players called on to play (which

varies randomly iteration by iteration) is much smaller than N. Thus,

players either draw a blank card, which means they are not playing, or

a card that says, say, 10 northbound, which means they are 10th in the

northbound line.

At the second stage of the iteration, the n players form two lines,

ordered by the direction and rank they have drawn. Players 1 northbound

and 1 eastbound then independently and secretly choose one of two

possible actions, give way or cross. Suppose that the two players

decide to give way. Then nothing happens and the players have to choose

their actions again. Suppose instead that both decide to cross. Then a

gridlock results (because only one player may cross at a time).

Finally, suppose that one of the players, say, 1 northbound, decides to

cross and the other player decides to give way. Then 1 northbound has

won the right-of-way (which is the objective of the players in each

iteration); 2 northbound moves up to take the space vacated, and play

is restarted between 1 eastbound and 2 northbound. This second stage

game is repeated over and over until one line vanishes and the players

on the other line can cross the intersection unimpeded.

To complete the description of the game, define the payoffs of the

outcomes as follows: If a player gives way, he receives 1 in terms of

some well-being index (however this may be measured). If he decides to

cross and wins the right-of-way, he receives 2. If he decides to cross

and gridlock ensues he receives -10. I assume that the payoffs are

additive over the games played so that if a player is able to cross

only after giving way once and “gridlocking” twice, he gets -19 , which

probably means that he is fuming mad as he moves away from the

intersection. Those who have studied game theory will recognize that

the structure of the game’s payoff matrix is that of prisoner’s

dilemma. The kink, however, is that a player cannot extricate himself

from an iteration until he has won the right of passage. In other

words, if the other line is long, it will not do to simply give way. At

some point, the player must risk crossing and causing a gridlock in

order to escape from the game. Indeed, the number of times that a

player may give way until he gets the gridlock-equivalent level of

well-being can be calculated from the payoff matrix. It is equal to 12,

.

On his 13th time “at bat,” so to speak, the player must win the

right-of-way if he is not to fall into a level of well-being that is

below even that at gridlock. And so when the players are left to their

own devices, i.e., when the convention is every man for himself, it is

almost inevitable that a gridlock will occur, since the cumulative cost

of repeatedly giving way will make a player increasingly insistent on

having his own turn at crossing the intersection. And unless he pairs

up with someone who is willing to give way at the very time that he

decides to cross, gridlock will occur.

‘disaster solution’

But “gridlocking” is a disaster solution, which charges a large penalty on the players. Can they do better?

In fact, institutions have been designed to improve on the gridlock

outcome. Two examples are the traffic light and the traffic cop

(whether duly authorized or not). The distinctive elements of both are

that (a) the right to assign who has the right-of-way is vested in a

device in the first case and in a person who is not himself one of the

drivers involved in the second case and (b) compliance from the drivers

is exacted by force of law or, in the case of civic-minded citizens who

direct the traffic flow without legal authority, by moral suasion.

What is unfortunate – and tragic – is that, in Metro Manila, no

institution has evolved that improves on every man for himself when

there is neither a traffic light nor a traffic cop. An example of such

an institution is the set of conventions that are in place in several

states in the US, which may be summarized as follows: (i) The first car

to arrive at an intersection has the right-of-way; (ii) In case two

cars arrive at the same time, the car on the right has the

right-of-way; and (iii) in case there is a line of cars at each of the

four points of an intersection, the right-of-way rotates among the

lines in a counterclockwise direction, with only one car allowed to

cross each time.

In the context of our game-theoretic model, the conventions have three

crucial features that allow them to solve the traffic coordination

problem. First, each player is made to bear a small cost – i.e., wait a

turn, or in our model, a well-being level of 1 , which is still way

above the payoff at gridlock – in exchange for earning the

right-of-way. Second, compliance is readily observed. (Think about how

much more difficult it would be to monitor compliance if the

right-of-way is given to, say, five cars at a time. Then it would be

more tempting for the sixth car to slip in with the other cars on the

pretext that its driver miscounted.) Third, continued compliance by

drivers is based on norms that are built on trust. This is why easy

verification of compliance is important. Because the more times drivers

observe that the conventions are complied with, the stronger the

conventions become as norms of behavior. Conversely, each time drivers

observe others crossing out of turn, trust in the conventions is eroded

and their status as norms of behavior becomes more tenuous. For these

conventions to have a chance to develop into norms in Metro Manila,

however, a crucial realization must dawn on all (N) drivers: This is

that, although the number of players, n, in a particular intersection

game is small relative to N, the intersection game is played infinitely

often. It is thus a virtual certainty that all drivers will be called

on to play the game at some point in their driving lives. Indeed, the

more often and the longer one drives (here think about drivers of

public utility vehicles), the higher is the probability of playing.

Moreover, the laws of probability ensure that a driver will win (i.e.,

cross) some and lose (i.e., gridlock) some. The problem is that the

payoff of winning is small (e.g., bragging rights), while the penalty

of losing is large (e.g., missed appointments and lost productivity).

Drivers therefore should not myopically look at the intersection game

as a one-shot deal. Instead, they should see it as it truly is: a

supergame whose penalties they can minimize with crossing norms based

on trust.

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