Expected Value: Bidding for a House

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SUMMARY

The discussion centers on the expected value of bidding for a house with a uniform price distribution between 0 and 1000. Participants analyze the profit formula, P = nV - B, where n represents the resale multiplier (e.g., n = 1.5) and B is the bid amount. The consensus is that bidding should not exceed 500n to ensure a positive expected profit, leading to a maximum bid of 750 when n = 1.5. Calculations reveal that bidding 750 results in a negative expected payout, indicating that this strategy is flawed.

PREREQUISITES
  • Understanding of expected value and profit calculations
  • Familiarity with uniform distribution concepts
  • Knowledge of probability theory, particularly in relation to bidding strategies
  • Basic mathematical skills for integrating functions and evaluating expected outcomes
NEXT STEPS
  • Study the law of iterated expectations in probability theory
  • Learn about marginalization techniques in probability distributions
  • Explore advanced bidding strategies in auction theory
  • Investigate the implications of different resale multipliers on bidding outcomes
USEFUL FOR

Mathematicians, economists, real estate investors, and anyone interested in auction theory and decision-making under uncertainty.

  • #31
etotheipi said:
Ah, thanks for clarifying! That makes sense. But shouldn't we write the integral as$$\langle \text{Profit}\rangle _{\text{savvy}}= \int_0^{V_m} \frac{1}{V_m} \left( \int_{V}^{V+fV}\dfrac{(n V-B)}{2fV}dB \right) dV$$because the inner integral is not a constant (depends on ##V##) so we can't pull it out of the outer integral?
Yes we should. I got lazy. :blushing:
 
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  • #32
I can hardly complain; I think one tiny bit of laziness is quite excused, given the rest of your excellent analysis and work on Excel :wink:. Thanks for taking the time to clarify! 😁
 
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