Question

Consider the following variation on a a simultaneous move incomplete information game covered in lecture. There are two players. Each can choose to "go" to a public place of some type (a cafe or a park) or "stay" at homeIf both go, they meet. If only one goes, they end up alone and get payoff of 0. Whoever stays at home gets their outside option of 1/4. Consider the following variation on a a simultaneous move incomplete information game covered in lecture. There are two players. Each can choose to "go" to a public place of some type (a cafe or a park) or "stay" at homeIf both go,they meet. If only one goes, they end up alone and get payoff of 0. Whoever stays at home gets their outside option of 1/4If they meet, each player enjoys a payoff equal to their own type multiplied by their opponent's type Player1/ player2 go stay.Suppose Fun B, Boring B, and Boring A choose to "go" with probability .75. What is Fun A's expected payoff from playing her best response?

Answer 1

Fun A's expected payoff from playing her best response is 0.5625.

Step-by-step explanation:

In this game, Fun A's expected payoff can be calculated as the sum of the payoffs when both players go and when only one player goes. Let's calculate it step by step:

1. When both players go: The probability that Fun B goes is 0.75. So the probability that both players go is 0.75 * 0.75 = 0.5625. In this case, Fun A gets a payoff of 1.

2. When only one player goes: The probability that Fun B stays is 1 - 0.75 = 0.25. So the probability that only Fun A goes is 0.75 * 0.25 = 0.1875. In this case, Fun A gets a payoff of 0.

3. Adding up the payoffs: Fun A's expected payoff is 0.5625 * 1 + 0.1875 * 0 = 0.5625.