Calculate probability of fiona and matt ending up at theater

Reference no: EM13201124

The value for F must make Matt simi- larly indifferent: Solving this equation yields Thus, the strategy profile presented is a subgame perfect Nash equilibrium when and Given this equilibrium, let's calculate the probability of Fiona and Matt ending up at the same theater. That'll happen if either they send the same text message (and thereby coordinate at the message stage) or they send different messages but luck out by going to the same theater. The former event occurs with probability or Even if their text messages do not match, which occurs with probability or when they come to actu- ally choose where to go, the probability that they end up in the same place is (which we derived earlier). The probability that they send different mes- sages but still go to the same theater is then or The total prob- ability that they end up watching the same film is the sum of these two prob- abilities, or When there was no opportunity to engage in preplay communication, the probability that Fiona and Matt go to the same theater was .42. Allowing them to first text message each other raises the probability to .66. In this way, pre- play communication can be useful even when there is no private information. It provides players with an opportunity to signal their intentions, and that can help players to coordinate their actions. It is important that this is a setting in which players do have a certain degree of commonality of interest; that way, there is a basis for wanting to coordinate. If, however, Fiona was trying to break up with Matt, then her text message would end up being uninformative.

Reference no: EM13201124

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