Improspectives

This series of posts talks about game theory and applications of the classic 2 x 2 games to improv and business. I’d previously discussed Chicken and Battle of the Sexes–next up is the Stag Hunt.

The Stag Hunt game is also called the Assurance Game or the Coordination Game. The basic idea behind the Stag Hunt is that the players can increase their payoff by cooperating. Following one traditional way to state the game’s conditions, I’ll define cooperation as a situation in which two individuals can increase their immediate payoffs by working together.

In its traditional form, the Stag Hunt posits that there are two hunters. The hunters can either choose to hunt for a stag, which has a very high but uncertain payoff, or a hare, which has a small and reliable payoff. Every time you hunt for a hare you will catch one and get a small payoff. On the other hand, if you hunt for stag and the other hunter goes after a hare, you will get nothing, and the other hunter will get the hare. You get a stag only if both of you decide to go after it. That’s why this game is also called the Coordination Game: You must coordinate your efforts to get the highest possible return.

The following matrix displays the payoffs for the Stag Hunt.

As with most of the other classic 2 x 2 games, we assume that the two hunters can’t communicate. At least, not so that they can coordinate their efforts before they choose which strategy to follow on a given day. What they can see, however, are the payoffs both for themselves and for the other hunter after they play a round of the game.

Obviously the best possible outcome is for you and the other player to go for the stag every round, but adopting that strategy is difficult when you don’t know the payoffs in advance and can’t communicate during the game. The best solution, both in business and in improv, is to find a way to communicate, even if it means making taking several moves to try different choices and observe the payoffs. Then, if you make a choice that leads to the big payoff, you trust that the other player will cooperate and repeat the move.

Next time: Do humans play this game better than chimpanzees?