In this two part article, I will demonstrate using game theory that it is not possible for the the human race to cooperate to save the earth from global warming. No matter how dire the situation or how clearly it is demonstrated that the earth will be doomed if we all don’t stop polluting, it can never happen.
To demonstrate this however, I will need to elaborate on the concepts of the Nash equilibrium that I introduced earlier. To recap, it simply means that given the strategies that everyone else is playing, each person is happy with their own decision.
Image Credit: Onken Bio-pot
The Nash equilibrium implies stability. It’s a stable solution to the game, inasmuch that people have no incentive to change their strategy. In the movie A Beautiful Mind, despite the implication, the solution given by Russell Crowe (the actor playing John Nash) is not a Nash equilibrium!
The situation, if you remember, was that Nash and his two pals were in a bar, and four women walked in, one of whom was truly stunning. Nash proposed to his friends that if everyone hit on the beautiful babe, then the rejected men (two of them) would fail to score with even the other women who would not like being “second choice.” As a result, only one out of the three would get laid. His solution was that they all hit on the other women and thus increase their chance of collectively scoring.
The movie implies that this was what set Nash thinking and laid the path for his paper on Nash equilibriums. However, you will recognize that the above situation was not a Nash Equilibrium. If everyone has hit on the other women, then no one has hit on the stunning babe. Consequently, each man would regret not hitting on her (since no one else has) and would be dissatisfied with his choice. In a Nash equilibrium, everyone is happy with their choice, given that everyone else has made theirs.
Image Credit: John Nash
In a given game, it is possible for multiple Nash equilibriums to be present or no Nash equilibriums at all. If this is the case, then it is not possible to predict the outcome of the game. There are various types of games including coordination games, trust games, outguessing games, and chicken games. Out of these, outguessing games and chicken games have no Nash equilibriums, whereas trust games have multiple Nash equilibriums. Hence, for these games, it is not possible to predict the outcome. In coordination games, however, there is just one Nash equilibrium, and so, it is possible to predict the outcome for coordination games.
In the next article, I will demonstrate that when it comes to saving the planet, there is only one Nash equilibrium – that of everyone using carbon based fuels and is, therefore, the only stable outcome for rational beings like us! It is a completely new sort of game that deserves special attention…and one that dooms us all.