Corporate lawsuits may sometimes be signalling games. Here is one example: In 2003, AT&T (a large US telephone company) filed a suit against eBay, alleging that its electronic payment systems (PayPal etc) infringed on AT&T’s 1994 patent on “mediation of transactions by communications system”. When the suit was filed, 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 court. Suppose that AT&T is suing for $300 million (the exact number was not publicly available), also assume that if the case goes to trial, the two parties will incur court costs 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 case. 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 found innocent (i). Finally, let’s suppose that eBay can offer AT&T either a generous settlement (G) of $200 million or a stingy one (S) of $20 million. AT&T would accept the generous settlement offer (thus avoiding a costly trial), but if eBay’s offer is stingy (S), then AT&T must decide whether to accept (A) and avoid a trial or to reject the offer and take the case to court (C). In the trial, if eBay is found guilty, it must pay $300 million to AT&T in addition to paying all the court costs. If eBay is found innocent, it will pay AT&T nothing, and AT&T will pay all the court costs. Show the game in extensive form (where Nature moves first with the probabilities indicated above). Be careful to label information sets correctly. Which of the two players has an incentive to bluff (that is, to give a false signal, make an incredible threat) in this game? What would bluffing consist of? Briefly explain your reasoning. Draw the payoff matrix for this game. Eliminate any dominated strategy and then solve the remaining 2x2 game for all Nash equilibria. What are the expected payoffs to each player in equilibrium?
Corporate lawsuits may sometimes be signalling games. Here is one example: In 2003, AT&T (a large US telephone company) filed a suit against eBay, alleging that its electronic payment systems (PayPal etc) infringed on AT&T’s 1994 patent on “mediation of transactions by communications system”.
When the suit was filed, 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 court.
Suppose that AT&T is suing for $300 million (the exact number was not publicly available), also assume that if the case goes to trial, the two parties will incur court costs 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 case. 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 found innocent (i).
Finally, let’s suppose that eBay can offer AT&T either a generous settlement (G) of $200 million or a stingy one (S) of $20 million. AT&T would accept the generous settlement offer (thus avoiding a costly trial), but if eBay’s offer is stingy (S), then AT&T must decide whether to accept (A) and avoid a trial or to reject the offer and take the case to court (C).
In the trial, if eBay is found guilty, it must pay $300 million to AT&T in addition to paying all the court costs. If eBay is found innocent, it will pay AT&T nothing, and AT&T will pay all the court costs.
- Show the game in extensive form (where Nature moves first with the probabilities indicated above). Be careful to label information sets correctly.
- Which of the two players has an incentive to bluff (that is, to give a false signal, make an incredible threat) in this game? What would bluffing consist of? Briefly explain your reasoning.
- Draw the payoff matrix for this game. Eliminate any dominated strategy and then solve the remaining 2x2 game for all Nash equilibria. What are the expected payoffs to each player in equilibrium?
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