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(5) [25 pointsl Consider Alice and Bob,two producers in a Cournot duopoly market. They both manufacture the same product at zero cost and compete in quantities. (This is similar to the question on HW3, with c-0.) There are two price forecasting agencies in town, offering two different predictions: Agency X predicts the price will be p 10-2(ga q), whereas agency Y predicts p 10 - (qa +qb) (here qi is the quantity produced by firm i and p is the price-per-item, hence for example Alice's profit equals ?,-q,p). We assume that it is common knowledge that Bob believes and uses X's prediction. However, he doesn't know which agency Alice trusts and uses. His prior is that, with probability a she also trusts agency X, while with probability 1 - a she trusts Y. (Assume for simplicity that a is common knowledge.) (a) [15 pts Formulate the above as a Bayesian game. Define (i) the agents' types, ii) their common prior over types, (iii) their utility functions. (b) [10 pts] Find a Bayes-Nash equilibrium (ga,)for the above game. Find the payoffs for both agents, for the case that Alice trusts agency Y. (5) [25 pointsl Consider Alice and Bob,two producers in a Cournot duopoly market. They both manufacture the same product at zero cost and compete in quantities. (This is similar to the question on HW3, with c-0.) There are two price forecasting agencies in town, offering two different predictions: Agency X predicts the price will be p 10-2(ga q), whereas agency Y predicts p 10 - (qa +qb) (here qi is the quantity produced by firm i and p is the price-per-item, hence for example Alice's profit equals ?,-q,p). We assume that it is common knowledge that Bob believes and uses X's prediction. However, he doesn't know which agency Alice trusts and uses. His prior is that, with probability a she also trusts agency X, while with probability 1 - a she trusts Y. (Assume for simplicity that a is common knowledge.) (a) [15 pts Formulate the above as a Bayesian game. Define (i) the agents' types, ii) their common prior over types, (iii) their utility functions. (b) [10 pts] Find a Bayes-Nash equilibrium (ga,)for the above game. Find the payoffs for both agents, for the case that Alice trusts agency Y