Zero Sum Games
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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 [View full text and thread]
|09/14/2006 10:07 AM by name withheld; discount rate or discount factor?|
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 game to the agent is the same as the present value of the game would be if the probability of death were zero and the discount rate were d + s.
|09/13/2006 05:23 PM by MEK; Death and Discount Rates in Repeated Games|
Answer: if the probability of death were 0 and the discount rate were d + s, the present value is x = p / ( 1 - ( d + s)).
However, I get the following:
Present value x = p + ( 1 -s ) * x / ( 1 - d).
Then x = p * ( 1 - d) / ( s - d).