Consider () , where is a standard 2-firm Bertrand competition. In each period, firms 1 and 2 choose prices 1 [0,1] and 2 [0,1] simultaneously, and firm sells (1 , 2 ) = { 1 if < (1 )/2 if = 0 if > units at price . The production cost is zero. The discount factor (0,1). Each firm uses the following Grim Trigger strategy: Charge = 1/2 in the first period. In period > 1 , charge = 1/2 if the outcome (1/2, 1/2) was observed in all previous periods; otherwise, charge = 0. Intuitively, this strategy has both players playing the monopoly price and splitting the monopoly profits evenly until one of them deviates. Once a deviation is detected, both players will revert to the Nash Equilibrium of the stage game, earning zero profit forever thereafter. (a) [25 points] Find the range of such that the Grim Trigger strategy constitutes a SPNE. (b) [25 points] Now suppose it takes > 1 periods to detect and respond to a deviation from (1/2, 1/2). Find the relationship between and such that the strategy profile is a SPNE