Every game theory model includes players, strategies and payoffs. The players are the decision makers whose behavior we are trying to explain and predict. Strategies are the potential choices to change prices. The pay- off is the outcome or consequence of each strategy. A zero sum game is the one in which the gain of one player comes at the expense and is exactly equal to the loss of the other player. The Nash equilibrium is a situation in which each player chooses an optimal strategy given the strategy chosen by the other player. In this game where there are 101 players and a button to push. Suppose one player is playing with the other 100 players playing whose identities are unknown to him. When he pushes one button, the first thing it does is to take $2 away from him and the same happens to every other player who pushes the button. Suppose he pushes your button, then his balance is down to $98 provided other players do not press any button. But if he does not push and others also do not push then he still has his the $100 left with him. Generally it does not happen, as the strangers will push the button due to curiosity. The results are surprising when a group of strangers push the button and the percentage vary anywhere between 30% to 70%. On an average 50% of people push the button, then the person who did not push are still having $50. So the Pareto optimal solution will be either the player pushes one button and loses $2($2,$98) and other players do not push the button. Or else all the players push the button and are left with no money($0,$0) There is also another option of one player pushing the button and the other do not push i.e. half of the players will push the button and the other half do not push then they are left with $ 50 ($50,-$50).
Player 1
Player 2
The players will always press the button and hence the Nash equilibrium will be at ($0,$0 ).
If the players have met before then after discussing they will be pressing the button in such case that they all are left with $50 in their hands. So, the optimal solution will be ($50,-$50). As the players will press the button, but even there is a possibility that when money comes in between every player will try to gain more which will be in the range of 30% to 70% and they may fight among themselves for monetary gain. So , the result is unpredictable
Works Cited
Scott, P. Stevens."Practical Application of Game Theory", Thomas Edison State University. Online Video Clip 14 December 2011.
<https://www.youtube.com/watch?v=89FrPu1UHt8>
Scott, P. Stevens."Practical Application of Game Theory", Thomas Edison State University. Online Video Clip. 14 December 2011.
<https://www.youtube.com/watch?v=GdnTv7loVt4>
Scott, P. "Stevens.” Practical Application of Game Theory", Thomas Edison State University. Online Video Clip 14 December 2011.
<https://www.youtube.com/watch?v=EPW3EzlzugU>
Scott, P."Stevens. ”Practical Application of Game Theory", Thomas Edison State
< https://www.youtube.com/watch?v=z4eYicg_S3k>
