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Please solved this problem I don't have more than this information ( this is game theory ) 3) This question illustrates the difference between truthful

Please solved this problem I don't have more than this information ( this is game theory )

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3) This question illustrates the difference between "truthful voting" and "strategic voting" There are two competing legislative bills in front of a committee in Congress. The committee has three legislators. Let us call the two bills, A and B and the three legislators, 1, 2 and 3. The decision of which bill to pass or whether to pass the bill or not is considered in two stages. Stage 1: In the first stage, members simultaneously vote between the two bills. The bill that gets the most votes then moves to the second stage. Stage 2: In the second stage, the legislators, after observing the outcome of Stage 1, simultaneously vote between passing the bill under consideration or maintain status quo (N). Each legislator has her own ranking over the three possible outcomes of the voting process, A, B and N. The Table below shows the preferences of the legislators: Legislator Best Outcome Next Best Outcome Worst Outcome A N B B A N W N N A B The payoff to a legislator from each outcome is as follows. She gets 1 if the best outcome is achieved; she gets 1 if her next best outcome is achieved and she gets -1 if her worst outcome occurs. a. List the players of the game (who) and the actions that each player can take (what). b. How many information sets are there in the game? c. List all possible strategies for a legislator. d. State the "truthful voting" strategy profile where the legislator votes for her more preferred outcome in each stage. e. What would be the outcome of all legislators adopted a truthful voting strategy? f. Can any of the legislators "game" the process to achieve their best outcome

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