" Gorbachev and Reagan were at each other during the cold war. They both knew their fate lied in nuclear armament/disarmament:

1. If Russia decided to disarm, and the US didnt, then Russia would be at the mercy of the US, and if the US decided to disarm and Russia didnt, then the US would be at the mercy of Russia.

2. If both decided to go ahead with arming themselves, there would be war.

3. If both decided to disarm, then there would be n war and everyone would be hale n hearty.

Assuming both countries wanted to be on the safer side, i.e., not be at the mercy of the other, and that both Gorbachev and Reagan were rational. Then Gorbachev would, rationally speaking, NOT disarm. Because, if Gorbachev disarms, then Reagan would probably NOT disarm, and Russia would be at the mercy of the US, i.e., if Reagan were to NOT disarm, Gorbachev would be much better off with war, than be at the mercy of the US. The same logic would hold for Reagan as well, which means that neither would disarm, and hence there will always be war! "

We can construct the following table from Russia's perspective:

(i)If America doesnt disarm:

(a) Russia disarms ----> Worst case scenario (Russia at US's mercy)
(b) Russia doesnt disarm ----> War (3rd best option)

(ii)If America disarms
(a) Russia disarms ----> 2 nd best option : No war
(b) Russia doesnt disarm ----> Best case scenario (Russia dominates)

From the outside, as a rational observer, it makes sense for us to claim that the best option is if both disarm and there is no war. However, from the two countries point of view, they will try to minimize their losses, hence will end up on option i (b) , which is only the third best option over all.

This kind of scenario is very common in game theory problems. The reason for this non optimal result is the fact that there is no clearcut saddle point. A saddle point is a result that is optimal to both parties, given that the choice of the other party is obvious. One very simple example of a saddle point is the case where two people play a game.

Consider the matrix

1 2
2 3

Player A chooses the ROW, and player B chooses the COLUMN. Player A is trying to minimize the number chosen and player B is trying to maximise it. Without knowing what the other person's choice is, Player A will definitely choose the first row. Again, player B will choose the second column, irrespective of the choice of playerA. Therefore, everytime the game is played, we will hit the same number, i.e., the number on the 1 st row and second column = 2. This is, indeed the optimal solution of the game. This is a direct fallout of the saddle point of the matrix.

Such scenarios are quite common in many economics problems too, and in fact Nash Equilibria (of the John F Nash fame) actually deal with the existance of such saddle points in a multiplayer game. Close