Game Theory -- Perfect Equilibria

Question

All right, so we have an Entrant and an Incumbent playing an entry deterrence game infinitely many times with a negligible discount rate. The Entrant first chooses whether to Enter or Stay Out (in which case the game ends, the Entrant receives 0, and the Incumbent receives 300).

After observing the Entrant's action, the Incumbent must decide to Collude (resulting in payouts of 40 for the Entrant and 50 for the Incumbent) or Fight (resulting in -10 for the Entrant and 0 for the Incumbent).

I can understand why {Stay Out, Fight} would not be a perfect equilibrium, but evidently there ARE perfect equilibria where the Entrant would never enter, and I can't wrap my head around it. Any ideas out there?

Answer 1

Hi,

yes, there can definitely be situations where the entrant would never want to enter.

For example, when the threat of fight is credible.

Since in the particular example, the resulting outcome for the entrant is -10 if it chooses to enter and faces a fight, this is of course worse than stay out (0). Therefore, if the entrant knows for sure that the incumbent will retaliate rather than cooperate, then it certainly wouldn't enter.