(Adapted from Dixit and Nalebuff, Thinking Strategically.) Auric, a corporate raider, is attempting to gain control of a major corporation, "Aglets R Us," by buying the stock from shareholders. Suppose that before Auric makes her move, share prices are $100 per share. Suppose further that there are 99 shares outstanding and that there are 99 shareholders, each with one share. Auric makes a two-tiered bid for the shares, which I will describe in a moment. Each shareholder decides independently and simultaneously whether to tender (sell) their share to Auric. Shareholders are thus engaged in a simultaneous move game with payoffs as follows. REMARK. "Two-tiered" here means something different than in the twopart tariff that we studied as part of non-linear pricing in monopoly. If 50 shares or fewer are tendered to her, Auric commits to purchase the tendered shares for $105 each. If X>50 shares are tendered, she commits to pay a weighted average of the first tier price of $105 and a second tier price of $90. Specifically, she will pay per tendered share: X50105+XX5090=90+X750. Note that Auric buys all tendered shares, even if fewer than 50 are tendered (in which case Auric fails to get control). If Auric does get 50 or more shares, and gains control, then by law (this is in fact the case in the US) she can buy the remaining shares at a "fair price." Assume that the second tier price of $90 a share passes the legal definition of "fair price." Assume also that, given the opportunity to buy these untendered shares, Auric will in fact do so. Finally, assume that if Auric fails to get at least 50 shares, then the stock price for those who do not tender remains at $100 (this last assumption is a bit obnoxious but it makes the question simpler). (a) Show that it is a strictly dominant strategy for each shareholder to tender their share. What, then is the equilibrium price per share received by shareholders? Is it more or less than the current market price? HINT. This game is too big for a game box. The good news is that shareholder i doesn't care exactly who, by name, has tendered; i cares only about how many other people have tendered. Therefore, break your analysis into cases. Suppose that 49 or fewer shareholders, other than i, have tendered. What is i 's best response? And so on. (b) Suppose that after Auric has made her proposal, but before any shares have been tendered, a "White Knight" comes along and says that he will purchase shares for $102 a share provided at least 50 shares are tendered to him. If fewer than 50 shares are tendered, the deal is off. 1 Shareholders thus must decide whether to tender to Auric, to the White Knight, or not at all. Given this competing offer, is it still a strictly dominant strategy for each shareholder to tender to Auric? (Adapted from Dixit and Nalebuff, Thinking Strategically.) Auric, a corporate raider, is attempting to gain control of a major corporation, "Aglets R Us," by buying the stock from shareholders. Suppose that before Auric makes her move, share prices are $100 per share. Suppose further that there are 99 shares outstanding and that there are 99 shareholders, each with one share. Auric makes a two-tiered bid for the shares, which I will describe in a moment. Each shareholder decides independently and simultaneously whether to tender (sell) their share to Auric. Shareholders are thus engaged in a simultaneous move game with payoffs as follows. REMARK. "Two-tiered" here means something different than in the twopart tariff that we studied as part of non-linear pricing in monopoly. If 50 shares or fewer are tendered to her, Auric commits to purchase the tendered shares for $105 each. If X>50 shares are tendered, she commits to pay a weighted average of the first tier price of $105 and a second tier price of $90. Specifically, she will pay per tendered share: X50105+XX5090=90+X750. Note that Auric buys all tendered shares, even if fewer than 50 are tendered (in which case Auric fails to get control). If Auric does get 50 or more shares, and gains control, then by law (this is in fact the case in the US) she can buy the remaining shares at a "fair price." Assume that the second tier price of $90 a share passes the legal definition of "fair price." Assume also that, given the opportunity to buy these untendered shares, Auric will in fact do so. Finally, assume that if Auric fails to get at least 50 shares, then the stock price for those who do not tender remains at $100 (this last assumption is a bit obnoxious but it makes the question simpler). (a) Show that it is a strictly dominant strategy for each shareholder to tender their share. What, then is the equilibrium price per share received by shareholders? Is it more or less than the current market price? HINT. This game is too big for a game box. The good news is that shareholder i doesn't care exactly who, by name, has tendered; i cares only about how many other people have tendered. Therefore, break your analysis into cases. Suppose that 49 or fewer shareholders, other than i, have tendered. What is i 's best response? And so on. (b) Suppose that after Auric has made her proposal, but before any shares have been tendered, a "White Knight" comes along and says that he will purchase shares for $102 a share provided at least 50 shares are tendered to him. If fewer than 50 shares are tendered, the deal is off. 1 Shareholders thus must decide whether to tender to Auric, to the White Knight, or not at all. Given this competing offer, is it still a strictly dominant strategy for each shareholder to tender to Auric