## Answered: - Consider the following delegation versus centralisation model of

Consider the following delegation versus centralisation model of decision making,loosely based on some of the discussion in class.A principal wishes to implement a decision that has to be a number between 0 and 1;that is, a decision d needs to be implemented where 0 1 ? d ? . The difficulty for theprincipal is that she does not know what decision is appropriate given the current stateof the economy, but she would like to implement a decision that exactly equals whatis required given the state of the economy. In other words, if the economy is in state s(where 0 1 ? ?s ) the principal would like to implement a decision d = s as theprincipal?s utility Up (or loss from the maximum possible profit) is given byU sd P ?? ? . With such a utility function, maximising utility really means makingthe loss as small as possible. For simplicity, the two possible levels of s are 0.4 and0.7, and each occurs with probability 0.5.There are two division managers A and B who each have their own biases. ManagerA always wants a decision of 0.4 to be implemented, and incurs a disutility UA that isincreasing the further from 0.4 the decision d that is actually implement, specifically,0.4 U d A ?? ? . Similarly, Manager B always wants a decision of 0.7 to beimplement, and incurs a disutility UB that is (linearly) increasing in the distancebetween 0.7 and the actually decision that is implemented - that is 0.7 U d B ?? ? .Each manager is completely informed, so that each of them knows exactly what thestate of the economy s is.(a) The principal can opt to centralise the decision but before making her decision ?given she does not know what the state of the economy is ? she asks for ECOS3003 Problem set 3 of 4recommendations from her two division managers. Centralisation means that theprincipal commits to implement a decision that is the average of the tworecommendations she received from her managers. The recommendations are sentsimultaneously and cannot be less than 0 or greater than 1.Assume that the state of the economy s = 0.7. What is the report (or recommendation)that Manager A will send if Manager B always truthfully reports s?(b) Again the principal is going to centralise the decision and will ask for arecommendation from both managers, as in the previous question. Now, however,assume that both managers strategically make their recommendations. What are therecommendations rA and rB made by the Managers A and B, respectively, in a Nashequilibrium?(c) What is the principal?s expected utility (or loss) under centralised decision making(as in part b)?(d) Can you design a contract for both of the managers that can help the principalimplement their preferred option? Why might this contract be problematic in the realworld?

Running head: DELEGATION VERSUS CENTRALIZATION MODEL OF DECISION

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Delegation versus centralization model of decision making

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DELEGATION VERSUS CENTRALIZATION MDEL OF...

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