LOCAL interaction gave us an account of how the convention of the equal split can invade a population stuck in an inefficient and inequitable polymorphism of the bargaining game, and spread to take over the entire population. Is local interaction the key we seek for enabling the transition from the hare hunting equilibrium to the stag hunting equilibrium in the stag hunt game?

THE BAD NEWS

In 1993, Glenn Ellison investigated the dynamics of the stag hunt played with neighbors, where the players are arranged on a circle. He found limiting behavior not much different from that in the large population with random encounters. With a small chance of error, the population spends most of its time in the risk-dominant equilibrium — which in our stag hunt games is hunting hare.

The difference in the dynamics between the large population with random encounters and the small population with local interaction is that in the latter, the population approaches its long-run behavior much more rapidly. Hare hunting is contagious. The moral for us, if any, seems to be that in small groups with local interaction, the degeneration of the social contract into the state of nature can occur with great rapidity.

THE GOOD NEWS

But let us not be too hasty in swallowing that moral. Consider the dynamics of the stag hunt game played on a lattice under exactly the same assumptions as those used in the previous chapter to investigate bargaining on a lattice.