Consider the same information cascade game. Remember the prior belief is 0.5, the payoff of correct choice = 1, and the payoff of wrong choice = 0; flip a coin when indifferent. The signal accuracy is p for every player, i.e., Pr(sL|L is correct) = Pr(sR|R is correct) = p. Assume that 1/2 < p < 1.

Part 1:

The signal accuracy is p = 0.92. If the private signals for the first 7 travellers are sL, sR, sR, sR, sL, sL, sR (in this particular order), what would traveller #7 do?

Part 2:

Suppose that the signal accuracy is p = 0.95. What is the unconditional probability of the following choice sequence?

LR LLR R R

When there are two possible states of the world, the unconditional probability of an event = Pr(event | state 1) * Pr(state 1) + Pr(event | state 2) * Pr(state 2).

Part 3:

Signal accuracy is p = 0.69. What is the unconditional probability of the following choice sequence?

LR R LR R R

Note: When there are two possible states of the world, the unconditional probability of an event = Pr(event | state 1) * Pr(state 1) + Pr(event | state 2) * Pr(state 2).

answers