Game Theory - Level 2

In the previous blog, we discussed about the Prisoner's Dillema and Nash Equilibrium.

We also concluded that game theory states that "It is best to take a decision which leads us better off regardless of the decision our opponent takes" .This logic was introduced so that the player is always benefitted. (Have no clue what I am talking about? Click here to read the previous blog)

Now let's play another game

In a war, the soldiers generally have two options - fight or run --- and there are two outcomes to the war, your side wins or looses. As simple as that.

Using the same procedure as the Prisoner's Dillema, let's weigh the options one by one.

Consider a soldier at the front, It may occur to him/her that if the defense is likely to be successful, then it isn’t very probable that his own personal contribution will not be essential. But if he stays, he runs the risk of being killed or wounded

On the other hand, if the enemy is going to win the battle, then his/her chances of death or injury are higher still, and now quite clearly to no point, since the line will be overwhelmed anyway.

So If the soldier has to establish Nash Equilibrium the best option is to run. He/She will benefit no matter what the outcome of the war.

If you were a soldier this would guarantee your win in the game (i.e survive) . But, obviously this writer isn't going to make things that easy for you.

In this game you are the commander of this army. So if all the soldiers decide to use game theory and establish Nash Equilibrium securing their personal victory, You will inevitably loose cause you have to surrender to the enemy. The best decisions for each individual have led to the worst result for the group as a whole and you as their head, commander

What do you do?

When you can't beat the odds, change the game.

And how do you do that?

By limiting the options for your soldiers. Altering other players’ expectations of his/her future actions, ( i.e changing their options ) and thereby induce them to take actions favorable to commander.

In other words, twist the game in such a way that what benefits the soldier's personally and establishes their Nash Equilibrium, results to the commander's victory too.

This is what the Spanish conqueror Cortez did in the Battle of Delium.

When landing in Mexico with a small force who had good reason to fear their capacity to repel attack from the far more numerous Aztecs, he used game theory to his advantage. He burnt down all the retreating ships. With retreat having thus been rendered physically impossible, the Spanish soldiers had no better course of action than to stand and fight—and, furthermore, to fight with as much determination as they could muster.

Better still, from Cortez’s point of view, his action had a discouraging effect on the motivation of the Aztecs. He took care to burn his ships very visibly, so that the Aztecs would be sure to see what he had done. They then reasoned as follows: Any commander who could be so confident as to willfully destroy his own option of escape if the battle went badly for him must have good reasons for such extreme optimism. It cannot be wise to attack an opponent who has a good reason (whatever, exactly, it might be) for being sure that he can’t lose. The Aztecs therefore retreated into the surrounding hills, and Cortez had the easiest possible victory.

Interesting right?

What seemed like an extreme measure taken by Cortez, dooming all his soldiers to fight a war they had a disadvantage in, seemed to do the exact opposite and given them an easy victory.

This can apply for present day scenarios also.

Consider countries and their treaties. Let's assume, country A and B. If a condition so occurs ( like need of more land etc) in country A that their Nash Equilibrium can be attained only by warring against B then it puts B at a loss. By placing peace treaties and policies, they limit A's possibilities, forcing A to consider only possibility which will not hurt B. This is B's method of "buring the ships"