Consider the following game. Nature selects "leff" with p - 0.5 and "right" with p - 0.5. If nature selects "left," then players 1 and 2 interact according to the game on the left If nature selects "right" then the players interact according to the game on the right V W V W 6.0 4.1 TOTO 0.0 0.1 6.0 4.1 Z 5,1 3.0 5.1 210 . Suppose that, when the players choose their actions, the players do not know which matrix they are playing That is, they think that with probability 1/2 the payoffs are as in the left and with probability 1/2 the payoffs are as in the right. Write the normal-form matrix that describes the Bayesian game. What is the strategy profile that is played? . Now suppose that before the players select their actions, only player 1 observes Na- ture's choice. Represent this game in the extensive form and in the Bayesian normal form. Using dominance, what is player I's optimal strategy in this game? What is the set of rationalizable strategies in the game? In this example, is the statement "A player benefits from having more information" true or false