ps3(404)-1 - v increases Interpret Problem 2 Public good...

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ECON 404 - Pr. Juan D. Carrillo Assignment 3 Problem 1. Mating . In certain species of birds, males can choose to be faithful ( F ) or philanderers ( P ); females can choose to be coy ( C ) or loose ( L ). Coy females insist on a long courtship before copulating, while loose females do not. Faithful males tolerate a long courtship and help rear their young (sharing equally the cost of rearing), while philanderers do not wait and do not help. The value of having an o±spring is v ( > 0) for the male and also v for the female. The total cost of rearing an o±spring is 2 r> 0. The cost of prolonged courtship is w ( > 0) for the male and also w for the female. Finally, we assume that v>r + w . (a) Interpret the condition v>r + w . (b) Write down the Normal form of the game. (c) Find the set of (pure and mixed) Nash Equilibria if v> 2 r . What happens as v increases? Interpret. (d) Find the set of (pure and mixed) Nash equilibria if v< 2 r . What happens as
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Unformatted text preview: v increases? Interpret. Problem 2. Public good provision Two players have to simultaneously decide how much to contribute to the provision of a public good. If player 1 contributes x and player 2 contributes y , then the value of the public good is 2( x + y + xy ), which they each receive. They can choose any non-negative number as their contribution. The cost of contributing x for player 1 is x 2 . The cost of contributing y for player 2 is ty 2 , where the value of t is private information for player 2. Player 1 believes that t = 1 with probability p and t = 2 with probability 1 − p . This belief is common knowledge. (a) What are the set of actions, types and beliefs of both players? (b) Find the Bayesian Nash equilibrium of the game. (c) Compare the quantities chosen by both players. Interpret (important). (d) What happens as p → 1? 1...
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