You have created a business-to-business Internet venture directed at an industry with 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 network as a member. So, if 21 firms join your service, each places a value of 2 × 20 or 40 on membership in your network. (a) Suppose you set the price, p, and then firms simultaneously and independently decide whether or not to join as members. Show that, for a 0
You have created a business-to-business Internet venture directed at an industry with 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 network as a member. So, if 21 firms join your service, each places a value of 2 × 20 or 40 on membership in your network.
(a) Suppose you set the price, p, and then firms simultaneously and independently decide whether or not to join as members. Show that, for a 0<p<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. At a 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.
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