answseven - Economics 206 Spring 2007 (Prof. G. Loury)...

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Economics 206 Spring 2007 (Prof. G. Loury) Solution of Racing Problem in Assignment 7 [Racing Game] Let V be the value of the prize, and let C ( x ) be the cost to a player of taking asteptowardthe f nish line of size x . A player gets to move every second period, so if δ is the per-period discount factor, then β = δ 2 is the discount factor that applies to any value which a player expects to receive on his next turn. Consider the single-player problem of optimally approaching the f nish line from distance X : φ ( X )= Max ( x n ,N ) { β N V N X n =0 β n C ( x n ) | N X n =0 x n X } , where N 0 is an integer, and n { 0 , 1 ,...,N } The expression above embodies a player’s choice of how many steps to take to reach the f nish line ( N +1 ) ,ando fhowb igtomake each step ( x n ). The value function φ ( X ) gives the net return to either player of having a
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This note was uploaded on 07/06/2009 for the course ECON 206 taught by Professor G.loury during the Spring '07 term at Brown.

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