(d) Now, to more closely tie the model to territoriality and rights, we'll allow one player to arrive before the other, and also allow players to condition their choice of action on who arrived first. For now, we assume players always agree on who arrived first. Formally, we model this as a Bayesian game, where: . The states of the world are 2 = {player 1 arrived first, player 2 arrived first} . . The prior is some constant, u(player 1 arrived first) = 1-u(player 2 arrived first) = . Player's partitions are II 1 = II2 = { {player 1 arrived first}, {player 2 arrived first} }. We use mi to denote an arbitrary element of IIi. Return to the payoffs from question la and answer the following questions. i. We define the 'bourgeois' strategy, s, as follows: s; (player i arrived first) = H, s, (player -i arrived first) = D. Suppose players are playing according to $1, $2. Let's see when this strategy profile is a Bayesian Nash Equilibrium (BNE) by con- sidering whether player i can benefit by deviating at any element of her partition. . In this strategy profile, what action does player i take when she arrives first? What is her payoff? Can she benefit by taking the alternative action in this element of her partition? . What action does player i's take when she arrives second? What is her payoff? Can she benefit by taking the alternative action in this element of her partition? . How do these results depend on u? ii. Define the strategy in which player i always plays hawk as s, (mi) = H for all mi Elli, and the strategy in which player i always plays dove as s (mi) = D for all m E II; Show that s, s. and si, s2 are also equilibria of this Bayesian game