Most real world situations are not zero sum games with a clear optimal choice in a zero sum game.
Both parties have a preferred outcome.
They want to win and there are no doubts.
In reality things are different.
There typically isn't two universally accepted solution or a dominant winning strategy.
A non zero sum game is different because it allows participants to choose whether they want to cooperate
or to compete.
Remember the two players can have common and opposing interest at the same time.
The most classic example of a non-zero sum game is the prisoner's dilemma here.
Two players must decide what they will do and the outcome for both depends on their own actions.
So we have two criminals arrested suspected in a robbery.
Police officers hold the two criminals in different interrogation rooms and offer them the following
options.
If one of them confesses the crime and the other one doesn't.
The one who's confessed walks away free while the other one receives a 10 year sentence.
If both confess they will receive a five year sentence each and if neither one confesses they will both
walk away free.
OK so this is how the typical non-zero sum game with two players looks like at first sight.
It appears the situation in which the two prisoners cooperate and do not confess is a clear optimal
strategy right.
However please remember the two prisoners are held separately so they wouldn't know the decision of
the other party until they make their own.
It becomes very dangerous trusting the person in the next room with five or 10 years of your life.
If a prisoner confesses then the worst that can happen is being sentenced to five years.
But if he doesn't confess he may end up in jail for 10 years or even better if he confesses and the
other prisoner doesn't.
He walks away free communication is not allowed.
What do you think ought to happen.
John Nash the famous Nobel Prize winner portrayed in the movie A Beautiful Mind came up with a solution
known as Nash's equilibrium.
He proved that if a player in the context we described earlier has chosen a strategy and other players
can't benefit by changing their strategies then we would have an equilibrium in the prisoner's dilemma.
If one of the prisoners confesses he would face a zero or a five year sentence that's much better than
facing zero or 10 years of prison right.
Yes the optimal global solution is to deny confessing.
However given that prisoners cannot communicate they will choose a solution.
Optimizing their own utility in our next lesson will provide an example of how Game Theory and Nash's
equilibrium can be used when analyzing a business case.
Thanks for watching.