Differences among Prisoners’ Dilemma, Stag Hunt, and Chicken Game

Question

And can you please explain how rational choice and Nash equilibrium are different in those three Game theories?

In: Economics

Answer 1

All of these “coordination games” can be boiled down to the rankings of 4 different payoffs. They are:

Coordinate: Both players do the helpful thing. In the prisoner’s dilemma, this is staying quiet. In stag hunt, this is going after the stag. In the chicken game, this is swerving.

Chaos: Both players do the unhelpful thing. In the prisoner’s dilemma, this is talking. In the stag hunt, this is going after the hare. In the chicken game, this is going straight.

Betrayed: You do the helpful thing, but I betray you and do the unhelpful thing. In the prisoner’s dilemma, this is staying quiet while the other player talks. In the stag hunt, this is hunting the stag while the other player hunts the hare. In the chicken game, this is swerving while the other player goes straight.

Betrayal: You do the unhelpful thing, betraying me because I did the helpful thing. In the prisoner’s dilemma, this is talking while the other player stays quiet. In the stag hunt, this is hunting the hare while the other player hunts the stag. In the chicken game, this is going straight while the other player swerves.

The **prisoner’s dilemma** ranks these payoffs:

Betrayal>Coordination>Chaos>Betrayed

This leads to just one (pure strategy) Nash equilibrium. If your opponent is going to be helpful, you can improve your payout by being unhelpful (Betrayal>Coordination). If your opponent is going to be unhelpful, you can improve your payout by being unhelpful (Chaos>Betrayed). Thus, both players always opt to be unhelpful and talk.

The **stag hunt** ranks these payoffs:

Coordination>Betrayal>Chaos>Betrayed

This leads to TWO Nash equilibria. If your opponent is going to be helpful, you can improve your payout by also being helpful (Coordination>Betrayal). If your opponent is going to be unhelpful, you can improve your payout by also being unhelpful (Chaos>Betrayal). Thus, you could observe a pair of rational players both hunting the stag, or both hunting the hare, but they should never go separate ways.

Finally, the **chicken game** ranks these payoffs:

Betrayal>Coordination>Betrayed>Chaos

This leads to the reverse of the stag hunt. If your opponent is going to be helpful, you want to be unhelpful (Betrayal>Coordination). If your opponent is going to be unhelpful, you want to be helpful (Betrayed>Chaos). Thus, the two rational outcomes are the two where one player swerves and the other goes straight.