Game Theory: Zero-sum Games

This is part 3 of our series on Game Theory, previous segments are available in our archives.

Winners and Losers

In order to pick a winning strategy, first we need to define the game. That means you need to be confident and correct in the payoffs you assign to each outcome of your game model. Game Theory has a few different kinds of well-known types of games that make understanding payoffs a lot easier.

Zero-Sum Games. In some games, every time one player gains, another loses. These are called zero-sum games because the sum of the outcomes for each player are always zero. A great example is playing poker, since every time one player wins money in a hand, all the other players lose that same amount (in total). Zero-sum games are naturally very competitive as working together has no benefit.  

Non-Zero-Sum Games. In these games there is no limit to the payoff any player can earn, so there are strategies where everyone wins together. At the same time, there will be other strategies where one player gains and others lose, so players will need to choose between collaborative strategies and competitive strategies. A great example is hiring employees, since the choice to hire a person and their acceptance of that offer benefits both parties.

After you have your payoffs in place, it’s time to start analyzing! One of the first things to look for is a strategy that, no matter what the other player does, provides a better payoff to you. These are called dominant strategies and make choosing your strategy easy. For example, take the following game model:

3 Game Model - Dominant Strategy

No matter what Player 2 does, strategy B always has a higher payout for Player 1. Likewise, no matter what Player 1 does strategy D has a higher payout for Player 2. Hence, B and D are dominant strategies and the players will almost always choose those strategies [1].

Unfortunately, most games lack dominant strategies so you will need to look carefully at the payoff distribution to choose a strategy. But, what if you aren’t sure which strategy your opponent will choose? What if you don’t even know their payoffs? Well, then you have incomplete information and we’ll discuss how to deal with that tomorrow.
[1] But not always. You may have noticed that this is actually a famous game called the Prisoner’s Dilemma. It is a well- studied game type because there are clear dominant strategies (B and D) but the total outcome for both players would be best if they both choose to cooperate and choose the non-dominant strategy (A and C). It’s really fascinating and I suggest reading more if you are interested.

Quote of the Day: “A delayed game is eventually good, a bad game is bad forever.” Shigeru Miyamoto