Computational Analysis of Perfect-Information Position Auctions
  After experimentation with other designs, the major search engines converged on the weighted, generalized second-price auction (wGSP) for selling keyword advertisements. Notably, this convergence occurred before position auctions were well understood (or, indeed, widely studied) theoretically. While much progress has been made since, theoretical analysis is still not able to settle the question of why search engines found wGSP preferable to other position auctions. We approach this question in a new way, adopting a new analytical paradigm we dub "computational mechanism analysis." By sampling position auction games from a given distribution, encoding them in a computationally efficient representation language, computing their Nash equilibria, and then calculating economic quantities of interest, we can quantitatively answer questions that theoretical methods have not. We considered seven widely studied valuation models from the literature and three position auction variants (generalized first price, unweighted generalized second price, and wGSP). We found that wGSP consistently showed the best ads of any position auction, measured both by social welfare and by relevance (expected number of clicks). Even in models where wGSP was already known to have bad worse-case efficiency, we found that it almost always performed well on average. In contrast, we found that revenue was extremely variable across auction mechanisms, and was highly sensitive to equilibrium selection, the preference model, and the valuation distribution. 
David R.M Thompson, Kevin Leyton-Brown
cs.GT cs.AI