(e) Let's tweak question 1d to make it more realistic. Suppose again that before the players play Hawk-Dove, nature randomly assigns player 1 to arrive first with probability M. But, now suppose that when a player arrives second, there is a probability e that this player mistakenly believes she arrived first. Formally, we let the states of the world be: 1 ={both players believe player 1 arrived first, player 1 believes player 1 arrived first but player 2 believes player 2 arrived first, player 1 believes player 2 arrived first but player 2 believes player 1 arrived first, both players believe player 2 arrived first} Answer the following. i. Calculate the priors. ii. Write down both players' partitions. iii. Formally specify the bourgeois strategy in this context