Each of n people chooses whether or not to contribute a fixed amount toward the provision of a public good. The good is provided if and only if at least k people contribute where 2 ≤ k ≤ n; if it is not provided, then the contributions are not refunded. Each person ranks the outcomes from best to worst as follows: 

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(i) Any outcome in which the good is provided and he/she does not contribute. (ii) Any outcome in which the good is provided and he/she contributes. (iii) Any outcome in which the good is not provided and he/she does not contribute. (iv) Any outcome in which the good is not provided and he/she contributes. Answer the following questions. (a) Formulate this situation as a strategic (normal-from) game. (b) Find ALL pure strategy Nash equilibria of this game. Is there a Nash equilibrium in which more than k people contribute? One in which k people contribute? One in which fewer than k people contribute? (c) Provide a definition of a Pareto optimal strategy profile. Which pure strategy equi- libria of this game are Pareto optimal? Briefly explain. (i) Any outcome in which the good is provided and he/she does not contribute. (ii) Any outcome in which the good is provided and he/she contributes. (iii) Any outcome in which the good is not provided and he/she does not contribute. (iv) Any outcome in which the good is not provided and he/she contributes. Answer the following questions. (a) Formulate this situation as a strategic (normal-from) game. (b) Find ALL pure strategy Nash equilibria of this game. Is there a Nash equilibrium in which more than k people contribute? One in which k people contribute? One in which fewer than k people contribute? (c) Provide a definition of a Pareto optimal strategy profile. Which pure strategy equi- libria of this game are Pareto optimal? Briefly explain.

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Answer a There are n players with two possible strategies for each These are A Contribute or B Do not Contribute The benefits and options for each pla... View the full answer