PLAYING TENNIS WITH A GORILLA

Two more points about game theory to lead us back to Mr Rust. First, some games, including war (and blind man's b[l]uff) have infinitely many strategies, and that in itself is no obstacle to finding a solution. However, the difficulty of formulating the infinitely many strategies of war (or blind man's b[l]uff) as a neat mathematical pattern prevents obtaining a solution in practice. As we have seen, not even chess, with a finite, albeit large, number of strategies, allows the optimum strategy to be derived. That means that for games like war, computer simulations using game theory are merely limited models on which one can study certain tendencies; but game theory cannot be used for war directly. [I am reminded of Gerard Philippe's film Fanfan La Tulipe in the 1950s. A group of 18^th-century French generals carefully plan the battle to be fought the next day, but when the actual battle begins, the chief planner exclaims in horror "Mon Dieu! The enemy has betrayed us!"]

But it is the second point that is supremely important. All of game theory is founded on the premise of a rational opponent, i.e., one who is able to discern his self-interest and plays accordingly. There is, for example, no optimum strategy for playing blackjack with an infant or tennis with a gorilla. Imagine a battle with tactical nuclear weapons and computer-carrying rockets. The commander of one side goes insane and decides to throw in a battalion of archers with crossbows. It is theoretically possible that he could win the battle, though hardly the war, because his opponent could not have expected such insanity.

Therefore, if Soviet air defenses were built strictly by game theory (which they are not), they could not be expected to stand up to a youthful prankster flying into them, for had he been rational, he should have expected to be shot down long before he crossed the coast; and game theory may fail when a player acts against his own interest.

There is a lesson in all this which I have mentioned before. You can play games, even deadly games, with the Mafia, for it is a rational opponent that knows where its self-interest lies. The Soviets, to the contrary, have often shown that they lack this ability, and it is this aspect, not just their treachery, that makes them in-capable of being partners to any treaty.