# Introduction to game theory: Zero sum games

A zero sum game is one where whatever one person gains another person loses.

It is called a zero-sum game because each gain by one player, say +\$100, is offset by the loss of another, -\$100. The two always add up to zero.

A non-zero sum game is one in which the total amount of stuff that the players can win between them goes up or down.

Let’s take a poker game as an example:

Let’s say that there are three players, Dan, Bill and Dave each starting with \$100, a total of \$300.

They meet at Dan’s house and play for a couple of hours. At the end of the evening Dan has \$200, Bill has \$60 and Dave has \$40. The total amount of money between them is still \$300.

Dan is up \$100, Bill is down \$40 and Dave is down \$60.

The total of these three numbers is zero (100-40-60), so it is a zero-sum game.

The next week they decided to head down to their local casino to play in a tournament. There are 50 players in the tournament, each paying \$100 to enter, a total of \$5,000. The casino takes a 5% cut, or \$250, leaving \$4,750 as prize-money for the players. The players start with \$5,000 but they end up with \$4,750, the total of their gains and losses is -\$250 so this is a non-zero sum game.

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