Two rival firms -- Firm 1 (Playerl) and Firm 2 (Player 2) are deciding simultaneously on the location to launch their latest products

Two rival firms -- Firm 1 (Playerl) and Firm 2 (Player 2) are deciding simultaneously on the location to launch their latest products. Each of them can choose to launch their product in either the Red State (action R) or the Blue State (action B). A new initiative of boosting the economy in the Red State may take place, which will change the payoffs to the firms. Firm 2 only knows that there is a probability of 1/2 that the initiative will be carried out. Firm 1, on the other hand, has insider information and knows exactly whether there will be an initiative. The payoffs are as follows: RB R0.00.4 B 4.0 2.2 No Initiative, probability 1/2 RB R 6.6 6.4 B 4.6 2.2 Boost in red State, probability 1/2 A. Which of the following statements is false? There is no Bayesian-Nash equilibrium in which Player 1 chooses BB with positive probability B. There is a Bayesian-Nash equilibrium of this game in which Player 2 randomizes between R and B (.e. puts positive probability on both) (BR, R) is a Bayesian-Nash equilibrium of this game D. (RB, R) is a Bayesian-Nash equilibrium of this game
Two rival firms -- Firm 1 (Playerl) and Firm 2 (Player 2) are deciding simultaneously on the location to launch their latest products. Each of them can choose to launch their product in either the Red State action R) or the Blue State (action B). A new initiative of boosting the economy in the Red State may take place, which will change the payoffs to the firms, Firm 2 only knows that there is a probability of 1/2 that the initiative will be carried out. Firm 1, on the other hand, has insider information and knows exactly whether there will be an initiative. The payoffs are as follows: RB |R0,0 0,4 B 4.0 2.2 No Initiative, probability 1/2 RB R 6,6 6,4 B4,6 2.2 Boost in red State, probability 1/2 How much would Firm 2 be willing to pay to discover whether there is or there isn't an initiative in the Red state? [Give an answer with at most 3 decimal points, like 9.999.)
Consider a first price auction for a single item with two bidders. Suppose the bidders have independent private values, uniformly drawn in the interval (0.1). Suppose the seller sets a reserve price p=0.4, that is only bids above p=0.4 can win. If a bidder bids above p and the other bids below p, then the first bidder wins and pays a price p. If both bid above p, then the highest bidder wins and pays the second highest price. In the Bayesian equilibrium in undominated strategies, what is the probability that the item will be sold at price p=0.4? [Give an answer with at most 3 decimal points, like 9.999.]