Payment Dominance

Let’s consider the following game. It is known as “stag hunt”. There are two hunters that can either cooperate and hunt a stag which would bring them a pay-off of 9 each or they could decide to work independently and hunt a rabbit which would bring them a pay-off of 1 each. The problem is that the stag can only be hunted if both hunters cooperate. If one hunter defects, the hunter who tries to hunt the stag, receives nothing.

The following pay-off matrix shows the relevant pay-offs:

For rational players, the most efficient equilibrium is {stag; stag}. And it should be the strategy of choice for every player. So, here the pay-offs help us solve the coordination problem.