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Respond to the question: Death and Discount Rates in Repeated Gam?

09/14/2006 10:07 AM by name withheld; discount rate or discount factor?
First of all, it might be better to distinguish discount rate from discount factor. Discount rate = 1 - Discount factor.

If the probability of death were 0 and the discount rate were d, the present value is x = p + x*( 1 - d ). This implies x = p/d.

If the probability of death were s at the end of each period and the discount rate were d, the present value is x = p + ( 1 -s )*x*( 1 - d ). This implies x = p/[1-( 1 -s )*( 1 - d )] = p/[s + d - s*d]. If s*d is small enough, then approximately we have x = p/[s + d].

This proves the orgininal problem. [Manage messages]

09/13/2006 05:23 PM by MEK; Death and Discount Rates in Repeated Games
Problem: Suppose an agent plays a repeated game in which the payoff in each period is p, the agent's discount rate is d, and the probability that the agent dies at the end of each period is s > 0. Prove that the present value of the [View full text and thread]