Consider an infinitely repeated game with two symmetric firms competing on prices, i.e., the standard Bertrand model. To simplify the problem, assume zero fixed cost and constant marginal cost (c) for all firms. In every period, there is a probability u that a third firm (new entrant) will enter the market and set a price equal to marginal cost -c; with the remaining probability (1 - u) there is no new entrant and the two firms may try to collude.

(Note: a "hit and run" entry only last one period and the possibility of entry is therefore determined in every period independently.)

Both firms have a common discount factor d. Assuming that firms will punish each other using trigger (or Nash reversion) strategy, please derive the minimum discount factor (d_min) that could sustain tacit collusion in this infinitely repeated game.