Border's theorem

In auction theory and mechanism design, Border's theorem gives a necessary and sufficient condition for interim allocation rules (or reduced form auctions) to be implementable via an auction.

It was first proven by Kim Border in 1991,[1] expanding on work from Steven Matthews,[2] Eric Maskin and John Riley.[3] A similar version with different hypotheses was proven by Border in 2007.[4]

  1. ^ Border, Kim C. (1991). "Implementation of Reduced Form Auctions: A Geometric Approach". Econometrica. 59 (4): 1175–1187. doi:10.2307/2938181. ISSN 0012-9682. JSTOR 2938181. Retrieved 3 April 2021.
  2. ^ Matthews, Steven (1984). "On the Implementability of Reduced Form Auctions". Econometrica. 52 (6): 1519–1522. doi:10.2307/1913517.
  3. ^ Maskin, Eric; Riley, John (1984). "Optimal Auctions with Risk Averse Buyers". Econometrica. 52 (6): 1473–1518. doi:10.2307/1913516.
  4. ^ Border, Kim (2007). "Reduced form auctions revisited". Economic Theory. 31 (1): 167–181. doi:10.1007/s00199-006-0080-z.