Game+Theory+4

=Hundred Dollar Triads=

General Description
Two players will make choices which will lead to higher individual pay-offs if they don't choose the societally optimal strategy.

Rules of the Game
There are groups of three, three rounds per game. Each player starts with an "account" of $100.

One player will be the banker, the other two will play. Position of banker will rotate so that each player will be the banker once in three rounds. The two players will choose an integer between 1 and 10, inclusive (so //not// 0). If they both pick the same number, the banker will pay each of them that amount of money from his or her "account." If one of the players guesses lower than the other, the banker will pay him or her $5 more than that amount, and the other player will get $5 less than the lower choice.

At the end of three rounds, three groups of three will play: The players with the three highest scores, the players with the three //lowest// scores, and the players with the //next// three lowest scores. (If, for some reason, there is a tie for one of the nine relevant positions, then play rock, paper, scissors (best two out of three) to break the tie. The loser of RPS will subtract one dollar from his or her score.) The players will start with their final scores from the first game.

The three winners from each of the three groups will be combined into one final group of three, and the winner from that game will be the winner. (The same tie-breaking rules apply). The players will start with their final scores from the second game.

Materials Required
Each player needs to keep score. Each player needs to write down the the numbers 1 through 10 on slips of paper and use them to make their choice.

Predicted Results
Players are expected to choose lower numbers because it is the only way they can ensure that they won't get negative scores. The strategy of choosing the higher scores is always going to be dominated. Choosing ten is going to be dominated by choosing nine because there is no way that the player can get a higher score (the highest payoff for the player is ten, and that is only possible if the other player chooses ten also. If the other player chooses ten, however, then it is in the first player's interest to choose nine, since it yields a pay-off of 14). According to the logic of game theory, this means that neither player can reasonably expect the other to choose ten, the dominated strategy. Thus nine becomes dominated by eight, and eight by seven, and so on. Thus the Nash Equilibrium can be found in both players choosing **one**. However, people are irrational, so who knows what could happen?!