Day 22

Today I read about the Nash Equilibrium.  This is what Wikipedia explained about it:

Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy. pIf each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitutes a Nash equilibrium. The reality of the Nash equilibrium of a game can be tested using experimental economics method.

Stated simply, Amy and Will are in Nash equilibrium if Amy is making the best decision she can, taking into account Will's decision while Will's decision remains unchanged, and Will is making the best decision he can, taking into account Amy's decision while Amy's decision remains unchanged. Likewise, a group of players are in Nash equilibrium if each one is making the best decision possible, taking into account the decisions of the others in the game as long the other party's decision remains unchanged.

Basically, my book keeps reinforcing that Nash equilibrium only works with two rational, self-interested people. That presents a problem in a game like Survivor, because people are cast to make good television (i.e. the majority of them are nor rational players). 

To better break down the game I have to assume everyone is playing like a rational player. I have to say if they are rational than what they should do when given the situation they were put in. In my paper I will be assuming the same people and tribes won immunity, but what vote should have been made instead in an effort to win - not simply advance 3 more days. I have to clearly make that distinction because a lot of times people will make decisions just to last a little longer, but a completely rational player (given the false assumption that the only person winning nay monetary compensation is the winner with a 1 million dollar grand prize) would only position themselves to win. The amount that someone is willing to risk of their utility (as discussed in previous blog post) is how badly a person wants to win. You can predict the actions a person should make to win in risky situations based on what will give them the highest utility.