In the game show Friend or Foe, two aspects of this class show up. In the beginning of the show, six players are separated into two sets, those who choose their partner for the game and those who get chosen. Before this, however, all six players have a very small biography containing good and bad points read about them, giving each player an idea of who these other five strangers are. Based on this, we can construct a graph of buyers and sellers, where those who are choosing their partner are the buyers, and the three getting chosen are the sellers. The product here is the sellers, and the values the buyers place on each “product” is based on the appearance of the sellers and their biographies. From this, each buyer constructs their “value” for each seller, based on how much each buyer would like to be paired each seller. The buyers then vote on who they would like (vote for the highest value in their graph), and are then paired with that person. If there is no competition over a seller, then the market already has a set of market clearing prices. When competition occurs, this becomes flipped. The seller that has been chosen by 2 or 3 buyers then becomes the buyer, with either 2 or 3 sellers. The same scenario applies, where the seller has a value for the buyers, but they get their pick of the highest value without worrying about ties.
The game then continues with the three pairs for three rounds, where each pair must answer trivia questions correctly to build up their bank. At the end of each round, the pair with the lowest bank (or in the case of a tie, the pair that took the longest to answer their questions), must then come to a vote. Each player can vote either “friend” or “foe.” In the case of two friend votes, they split the money. In the case of a friend and a foe vote, the person who voted foe takes all of the money. In the case of two foe votes, no one gets any money. Before they vote, both players are given a small chance to tell the other why they should vote friend. From this, you can construct the same graph used for the prisoner’s dilemma. Assuming n dollars are paid out, the graph looks like:
|
Friend |
Foe |
|
|
Friend |
(n/2),(n/2) |
0, n |
|
Foe |
n,0 |
0,0 |
From this graph, we can determine that if one player votes Friend, the best response is to vote foe, and if one player votes foe, the best response would be to vote foe (provided you didn’t want the other player to take all of your money and leave you with nothing, otherwise there is no best response). This makes (Foe, Foe) a Nash equilibrium, as both choices are best responses to each other.
http://www.youtube.com/watch?v=r0nsJWA_PDc
-SV John Wayne