Competition and Simple Auctions

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" summary

Shows necessary conditions for a seller’s best response when competing against M−1 rivals who commit to second‑price, zero‑reserve auctions: optimality requires a modified virtual value (Myerson virtual value plus a competition correction) to be nondecreasing, recovering Myerson at M=1 and McAfee as M→∞. Uses Border’s theorem to describe feasible interim allocations, formulates the problem as an optimization with endogenous visit probabilities and MPEC constraints, discretizes types to get existence and complementary‑slackness conditions, and finds second‑price (with any reserve) fails when the condition is violated.

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" chapters (16)

1. 0:00Intro
2. 1:58McAfee
3. 7:26conjecture
4. 9:35high level intuition
5. 11:06outside options
6. 12:45the best option
7. 13:39equilibrium constraints
8. 18:03helpful observation 1
9. 18:55helpful observation 2
10. 23:41discretization
11. 25:02equilibrium conditions
12. 25:35optimization problem
13. 25:51equilibrium
14. 27:59discrete types
15. 28:51remaining steps
16. 29:25conclusion