Econ110_Section11

Econ110_Section11 - Section XI: Signaling Games Daniel Egel...

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Section XI: Signaling Games Daniel Egel November 30, 2008 1 Beer and Quiche: The Classic Example This is the classic example for signaling games. 1 However, Matt Levy’s description of the game is just too good to not use: In one of the canonical treatments of the signaling game, we consider two gentlemen having a dispute over honor. Lord Signaler has offended the honor of Baron von Receiver, and the Baron is on his way to challenge Lord Signaler to a duel this morning. If Lord Signaler is tough, he will win the duel. If he is wimpy, he will lose. However, either way, Lord Signaler would prefer Baron von Receiver to rescind his challenge. Lord Signaler knows his own type, but Baron von Receiver only knows that there is a .1 probability of weakness and a .9 probability of strength. Sitting down to his breakfast, Lord Signaler sees the Baron coming in the distance. His Lordship must still, however, choose what to eat for breakfast. If he is weak, he would gain an extra 2 utility from quiche and 0 from a beer. Conversely, a tough Lord Signaler would get an extra 0 utility from a quiche and 1 utility from a beer. The only information that Baron von Receiver has is the following: The probability of strong vs. weak. The payoffs. Whether Lord Signaler drinks a beer or eats quiche for breakfast. 9 10 1 10 N quiche beer WEAK -→ quiche beer ←- STRONG Don t 1 , 0 Duel - 1 , 1 Don t 3 , 0 Duel 1 , - 1 Don t 3 , 0 Duel 1 , 1 Don t 2 , 0 Duel 0 , - 1 A few questions to clarify the diagram: 1 This game is to signaling games as the Prisoner’s dilemma is to strategic form games. 1
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1. How many decision nodes are there here? Label all the decision nodes with the person making the decision. 2. How many subgames does this game have?
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Econ110_Section11 - Section XI: Signaling Games Daniel Egel...

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