Corporate lawsuits may sometimes be signaling games. Here is one example. In 2003, AT&T filed suit against eBay, alleging that its Billpoint and PayPal electronic-payment systems infringed on AT&T's 1994 patent on “mediation of transactions by a communications system." Let's consider this situation from the point in time when the Suit was filed. In response to this suit, as in most patent-infringement suits, eBay can offer to settle with AT&T without going to court. If AT&T accepts eBay's settlement offer, there will be no trial. If AT&T rejects eBay's settlement offer, the outcome will be determined by the court.
The amount of damages claimed by AT&T is not publicly available. Let's assume that AT&T is suing for $300 million. In addition, let's assume that if the case goes to trial, the two parties will incur court costs (paying lawyers and consultants) of $10 million each.
Because eBay is actually in the business of processing electronic payments, we might think that eBay knows more than AT&T does about its probability of winning the trial. For simplicity, let's assume that eBay knows for sure whether it will be found innocent (i) or guilty (g) of patent infringement. From AT&T's point of view, there is a 25% chance that eBay is guilty (g) and a 75% chance that eBay is innocent (i). Let's also suppose that eBay has two possible actions: a generous settlement offer (G) of $200 million or a stingy settlement offer (S) of $20 million. If eBay offers a generous settlement, assume that AT&T will accept, thus avoiding a costly trial. If eBay offers a stingy settlement, then AT&T must decide whether to accept (A) and avoid a trial or reject and take the case to court (C). In the trial, if eBay is guilty, it must pay AT&T $300 million in addition to paying all the court costs. If eBay is found in: nocent, it will pay AT&T nothing, and AT&T will pay all the court costs.
(a) Show the game in extensive form. (Be careful to label information sets correctly.)
(b) Which of the two players has an incentive to bluff (that is, to give a false signal) in this game? What would bluffing consist of? Explain your reasoning.
(c) Write the strategic-form game matrix for this game. Find all of the Nash equilibria to this game. What are the expected payoffs to each player in equilibrium?