?? E XERCISE 208.1 (Price competition) Extend the model in Exercise 125.2 by having the sellers…

?? EXERCISE 208.1 (Price competition) Extend the model in Exercise 125.2 by having the sellers simultaneously choose their prices before the buyers simultaneously choose which seller to approach. Assume that each seller’s preferences are repre- sented by the expected value of a Bernoulli payoff function in which the payoff  to not trading is 0 the payoff to trading at the price p is p. Formulate this model precisely as an extensive game with perfect information and simultaneous moves.

2   Show that for every p ≥ 1  the game has a subgame perfect equilibrium in  which

2   each seller announces the price p. (You may use the fact that if seller j’s price is at least 1 , seller i’s payoff in the mixed strategy equilibrium of the subgame in which the buyers choose which seller to approach is decreasing in her price pi when pi  > pj.)