|The first mover in a signaling game observes a randomly determined
state of nature (e.g. their "type") and chooses a signal.
The other other player sees the signal but not the state, and makes a response.
For example, the "beer/quiche" interpretation is that the proposer wakes up feeling either strong
or weak, and then decides whether to drink beer or eat quiche for
breakfast. The responder sees the breakfast chocie and decides whether to
fight or flee. The payoff structure may yield equilibria that yield
"separation" (signals reveals types) or "pooling" (both types send the
same signal). One extension involves price signaling by a seller with a randomly determined product quality (high or low) that cannot be directly observed by a buyer unless a verification cost is incurred.|
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There is an alternative "stripped down poker" in which one player
draws a card, high or low, and either raises or folds. If the proposer
raises, the responder can fold or call. The Nash equilibrium involves
randomization in which players sometimes bluff with a low card.
This is an excellent game to teach the notion of
randomized strategies in a context where being unpredictable has
Vecon Lab - December 4, 2023