How do Chennai-ites quarrel over water?

Game theory and its implications is one subject that never fails to amaze me by both its simplicity and profoundness. The recent Nobel Prize in economics awarded to Robert Aumann, a mathematician based in Jerusalem and Thomas Schelling, an American economist for their work in game theory highlights the richness and diversity in this subject.

Game theory is a theory of choice, where decisions players make affect one another. Aumann’s contribution is that cooperation between players is possible if the game prolongs infinitely often, but players compete if the game goes for a finite period of time. How?

Coming from a water starved city like Chennai, let me quote a normal quarrel that happens between neighbors: the bore-well problem. Suppose our neighbor installed a bore-well and a booster pump, which sucks up water twice as fast as the normal pump. When both of us had normal pump, we got 10 liters of water each. Now that he has a booster pump and we don’t, he gets 15 liters and we get none. (Assuming 5 liters gets wasted when booster pump sucks water furiously).So we have no option but install bore-well ourselves, and now both of us end up getting 5 liters each. (5 liters wasted per pump)

In the long term, this is a suboptimal solution (5 vs. 10). So we enter into an agreement where either of us won’t switch booster pump unless the other person switches it on the previous day.

Thus, if the game goes on infinitely, the players cooperate. What if the game is for finite interval? Suppose our neighbor vacates his place next Sunday, he will switch on the last day, because he has no motivation to do otherwise. Anticipating this, I’ll switch the motor on Saturday, which he anticipates on Friday…and the entire thing unravels.

Schelling’s work is on the formal theory of deterrence and retaliation, where paradoxically, the player is better off by making his response uncertain. The Spanish general Cortez who colonized Mexico burnt his boats on arrival demoralizing his adversaries because they knew that his army could not retreat.

The works of Aumann and Schelling demonstrates the subject’s breadth and depth.