I was analysing the payoff matrix of a game which is quite similar to the Prisoner's Dilemma.
The game is from a game show on TV here called Golden Balls. For those who are not familiar, it is a show which starts with a number of players and in the first few rounds players are eliminated and a cash prize is built up between them. In the final round there are only two players left, and each of them is faced with an option - split or steal...
The rules are as follows:
If both split, then the cash prize is halved between them.
If one splits and one steals, then the splitter gets nothing and the stealer gets it all.
If both steal, then both get nothing.
Clearly the best decision is to steal, as that offers the highest payoff, with no EXTRA risk of losing everything than if you split. However, what is the Nash Equilibria?
I find that all outcomes apart from the one where both split is a Nash Equilibrium. I'm using the definition that a Nash Equilibrium is an outcome such that, if either player changed their decision with the other staying the same, their payoff would not increase. Am I right?