There were still pirates in the 1980s, although they tended to appear in corporate boardrooms rather than the open seas. These swashbuckling financiers would engage in a “hostile takeover” by acquiring a company through the purchase of shares on the open market and against the will of the target company’s existing management (thus making the takeover “hostile”). Such investors were known as “raiders” and included people such as T. Boone Pickens, Sir James Goldsmith, Henry Kravis, and Victor Posner. All this was fictionalized in the movie Wall Street, with Michael Douglas portraying the raider Gordon Gekko, who famously espoused “Greed is good.” The time was full of jocular jargon, as management could consume a “poison pill” by taking on a costly financial structure that would make it difficult to consummate a hostile takeover. In some cases, a raid could be fought against by buying a raider’s shares back at a premium; this tack became known as “greenmail,” a takeoff on blackmail. To get a gist of the strategizing that occurred between a raider and management, consider the figure below. The raider makes an initial stock purchase, in response to which management decides whether to buy the shares back at a premium (pay greenmail) or not. If no greenmail is paid, then the raider decides whether to purchase additional shares in order to take control of the target company.
a. Find all subgame perfect Nash equilibria.
b. Find a Nash equilibrium that is not an SPNE, and explain why it is not
a SPNE.
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