GAMES THEORY WORKSHOP.

In the mathematics workshop, several practical activities are proposed in which they will have to make decisions and learn different strategies applicable to real life.

Activity number 1: The prisoner's dilemma. Games theory.

This workshop can give a lot of play, because we can do it easily, based on the television program "Steal or Split".

Game that is based on the prisoner's dilemma.

It consists of being able to steal or cooperate. If we both steal, we won't get any reward tokens. If one player steals and the other shares, the one who stole will receive ten coins (chocolate, candy...) and the opponent nothing. If both players share, they will receive a little less, for example two out of 10 or some other smaller amount.

There is a lot of competition.

Activity number 2: Nim.

In this activity, 12 chopsticks are placed alternately on a table, each player will take one or two chopsticks in his turn, as he prefers.

Whoever manages to take the last toothpick wins the game.

Strategy:

As a strategy, look for the sequence of winning numbers from back to front as a numerical pattern, and make it a general rule.

A 3-stick ending is wanted for my opponent (he'll take one or two at most, allowing me to win); 6 toothpicks, for my opponent to play. Whatever I do, I will be able to leave 3. To leave 6, I should have left 9 before and 12 before.

Sequence: Leave 3-6-9-12. Multiple of 3.

With 23 chopsticks: Alternatively, each player will take, 1, 2 or 3 chopsticks, in his turn, as he prefers. The player who is forced to take the last one loses.

Sequence: Leave 5-9-13-21-23. Or multiple of 4 plus 1.

With 16 as follows: Whoever takes the last one wins. You can take as many as you want but in a row.

Strategy: Go to decimal code and let everything add up to zero.

Activity number 3: Auction one euro.

   The game consists of auctioning €1. The minimum increase in the bid will be 5 cents. If two or more participants make the same bid, only the first will have won the bid, and the others must raise it if they want to win it.

The peculiarity of this auction is that not only the one who makes the highest bid pays, but also those who make the second and third highest bids.

Strategy: Don't play.

Example: Spiral of gun violence.

Activity number 4.- Three in a row.

It is drawn by lot which player starts. Each player places one of his chips alternately. The player who manages to place his three pieces in a straight line wins: horizontally, vertically or diagonally.

If all the squares are covered and no player has placed three tiles in a row, the game is considered a draw.

Strategy: Center and corners. Always tie.