h3w08 - i = 1 , 2 , 3 ,write out the strategy sets, S i ,...

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Department of Economics The Ohio State University Econ 805—Homework #3 due Thursday, February 21 Prof James Peck Winter 2008 1. Mas-Colell, exercise 7.D.1. 2. Consider the following game. The players are three voters, who must vote either YES or NO (no abstentions). The referendum will succeed if at least two of the voters vote YES, and it will fail otherwise. Suppose that player 1 receives a payo f of 2 if the referendum succeeds, and a payo f of 2 if it fails. Players 2 and 3 receive a payo f of 1 if the referendum succeeds, and a payo f of 1 if it fails. Assume that we have a private ballot, where players cannot see how the other players vote until the ballots are counted. (a) What is the normal form of this game? That is, for
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Unformatted text preview: i = 1 , 2 , 3 ,write out the strategy sets, S i , and the payo f functions, i . (b) Express the normal form game using matrices. (For a three player game, you can write it as a collection of matrices, one matrix for each strategy of player 3. Player 3 chooses the matrix, player 1 chooses the row, and player 2 chooses the column. Each box of each matrix has three numbers, corresponding to the payo f s of the three players.) (c) Represent this game in extensive form. 3. Mas-Colell, exercise 8.D.4. If the two demands sum to less than or equal to $100, they do the project, each gets his demand, and any money left over goes to charity. 4. Mas-Colell, exercise 8.D.5. 1...
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