We have seen in the earlier post that the chain store has an optimal solution when it goes for acquiesce, followed by acquiesce, and the second rival enters the market.
The chain store, however, can dump the backward induction results of optimal payoff and show its strength by going to war in the first town itself. The purpose is to signal the rival that it would do the same if it entered town 2.
If that worked and deterred the rival from entering town 2, the chain store would receive a payoff = 3, which is more than what the cooperation route brings, as we saw earlier.
This is the paradox: the induction strategy should be the equilibrium choice per game theory, yet the chain store would choose a deterrence strategy as the optimal.
