You have created a business-to-business (B2B) Internet venture directed at an industry with exactly 50 identical firms. Your services allow these firms to do business with each other more efficiently as members of your trading network. You plan to sell access to your service for a price p per member firm. Each firm's benefit from the service is given by 2n, where n is the number of other firms joining the B2B network as a member. So, if 21 firms join your service, each places a value of 2 x 20 or 40 on membership in your network.Suppose for part (a) that you set the price, p, and then firms simultaneously and independently decide whether or not to join as members.

a. Show that, for a price greater than zero and lower than 98, there exist exactly two Nash equilibria in the simultaneous-move game played by firms deciding whether or not to join the network as members.

Suppose for part (b) that you are able to persuade 10 firms to join your network at an initial stage as "charter members." At the second stage, you set a price for the remaining 40 firms. These 40 firms then simultaneously decide (as in part (a)) whether to join your network as regular members.

b.For each price p, determine the equilibria of the game played between the remaining 40 firms in the second stage.

Finally, consider the same situation as in part (b), but suppose that, when there are multiple Nash equilibria, firms behave conservatively and conjecture that the low-adoption Nash equilibrium will be played. (Note that, by the definition of Nash equilibrium, this conjecture is self-fulfilling.)

c.How much would you be willing to pay (in total to all 10 early adopters) in order to persuade the first 10 firms to join the network as charter members?