We need to explore infinite horizon games. However, if you add up an infinite string of a positive payoff, they all equal infinity regardless of the base value. Discount factors rescue us. Recognizing that consumption today is better than consumption tomorrow and the possibility that an interaction might not continue due to unforeseen circumstances, we use the discount factor to make tomorrow’s payoffs smaller than today’s.
Although we still end up with an infinite string of payoffs, they form something known as a geometric series. In the next lecture, we will see how geometric series have a clean closed-form solution that avoids the infinity problem.
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