qgames-10-tragedy.txt

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The Tragedy of the Commons is a classic game
which we illustrate here using an example from McCain's
book on game theory.
Consider the question of whether an individual, among many,
would be better off commuting by car or by bus.
Both must share the same roads, and the reward to an individual
is a faster commute.
This scenario can be described by a proportional game
model where the payoff, for example, the speed of commute,
is a continuous variable related proportionally
to the proportion of commuters by car.
When everyone commutes by car, the roads are clogged,
making for a lower payoff per individual,
versus when nobody commutes by car.
Say the same proportionality also holds for buses.
However, buses travel slower than cars.
And thus we observe in this simple model
that car commuters always see a higher payoff, that is a faster
commute, than bus commuters.
The dominant strategy is thus to commute by car.
Unfortunately, this leaves all the roads congested, causing
a negative payoff for everyone.
This model is not very realistic since each bus
carries more people than a car.
And since a single bus is perhaps
less impacted by congestion than many individual cars,
we may thus improve our model by having
the slope of a car commuter line be steeper
than that for bus commuters.
In this more realistic scenario, there is no longer
a dominant strategy.
Instead what we find is a Nash equilibrium at the point Q
where the two lines intersect.
This is a Nash equilibrium point because no one
can be individually better off switching at that point.
If a bus commuter switched to a car, for example,
he would have a slower commute.
Observe though that the payoff for each person
would be higher if everyone were to commute by bus, relieving
the roads of all congestion.
However, as long as individuals act
to maximize their individual payoff,
such global system optimums are not attained.
For example, in the scenario, if nearly everyone
commuted by bus, an individual could
switch to commuting by car for an even faster commute.
This is thus an example of the Tragedy of the Commons,
illustrating how all common-property resources,
roads in this case, tend to be over exploited and thus
degraded.
The traditional approach to avoid such tragedy
is to involve a trusted third-party regulator,
such as governments, who restrain over use.
Such solutions bring their own issues.
Could perhaps trusted third parties
be supplemented or replaced by trust
in quantum mechanics, or at least in apparatuses governed by quantum mechanics?