Networks

This summer I vacationed with my two cousins Lucia and Mario who are 8 years old, and, obviously, had to entertain them. I taught them how to play tic-tac-toe, but after around 5 games, Mario came running to me in tears. They had agreed that the person who won the game had the right to go first in the next one, and he had not been able to win any of them and was not able to go first. Naturally, I thought the issue was him just not paying enough attention to the game and he just had to concentrate to beat his sister, but I was wrong.

The article linked above talks about the effects of nash equilibrium in tic-tac-toe. It argues that, despite politeness encouraged by parents (letting the other person go first); assuming both players are logical, there is no chance of winning the game for the person who does not start. The reason for this is that there is only one winner for the game and player 1 will always play their dominant strategy. The response from player 2 can then never be other than to look for the nash equilibrium to neutralize player 1’s strategy. This causes the best possible outcome for player 2 to be a tie.

Turns out that my cousin was paying attention after all, he just wanted to be the one to start!