2. (10 pts) As head of the Traffic Department you are planning a new system of traffic

lights. Your experts are divided into two groups. One believes in theory A and one in

theory B (A or B is true, not both). At present you consider the two theories equally

plausible. You have two options for your light system - systems X and Y.

If theory A is true and you adopt system X, then your payoff will be 1 with probability

0.8 and 0 with probability 0.2. If theory B is true and you adopt system X, then your

payoff will be 1 with probability 0.1, and 0 with probability 0.9. Your payoff under

system Y is 0.5.

You have a two-period time horizon. You can choose system Y now for the two periods

or you can experiment for the first period (i.e., use system X) and then choose a system

for the second period depending on your payoff in period 1.

Assuming that you wish to maximize the expected value of payoff, what strategy should

you follow.