A parametric family of two ranked objects auctions: equilibria and associated risk

Mixed Mechanisms for Auctioning Ranked Items

“…Although the relevance of the GSP is evident both from its simplicity and from its applicability, nevertheless, the GSP is not actually an extension of the second price auction and, moreover, it has not, in general, an efficient symmetric Bayesian Nash equilibrium [6]. Furthermore, we do not find in the literature a parametric analysis of auction mechanisms for ranked objects that attempts to extend and encompass the best-known auction mechanisms, except for the case of 1 or 2 objects [10,11], but the latter is completely insufficient for a more complete and general analysis of the problem in hand. Finally, although variance is a reasonable measure for the variability of a random variable, perhaps it is not suitable for comparing auction mechanisms, because variance does not indicate the sign of the revenue deviations with respect to the expected revenue.…”

“…She determines the optimal allocation and payment rules for four different situations of valuations. Alonso, Sanchez-Soriano and Tejada [11] study two ranked objects auctions, propose a parametric family of mechanisms, determine the unique Bayesian-Nash equilibrium of each member of the family, and analyze the risk of the auctioneer for each auction. Liu, Chen and Whinston [58] study the design of ranked object auctions when bids are weighted and there are minimum bids.…”

“…In order to address all the issues mentioned above, we introduce a parametric family of auction mechanisms for ranked objects auctions extending the ideas in Alonso and Tejada [10], and Alonso, Sanchez-Soriano and Tejada [11]. These auction mechanisms would not be difficult to implement and apply in real situations, such as keywords auctions in search engines on the Internet, although they have a more complex structure than, for example, the GSP.…”

“…Second, we show that all members of the family satisfy the properties of fairness, no over-payment, optimality and efficiency, and all have the same expected revenue. In addition, the symmetric Bayesian Nash equilibria ] for all auctions in the family are determined, which is more difficult to obtain than in the cases of 1 or 2 objects [10,11] because as the number of objects to be auctioned increases, this calculation is increasingly complex. Moreover, when analyzing a parametric family of auctions, instead of just one, the proofs have an added difficulty due to the number of parameters increases with the number of objects.…”

Allocating revenues in a Smart TV ecosystem

“…Furthermore, game theory has been also utilized to analyze engineering problems in the broadest sense (Sanchez‐Soriano, ). Continuing with the examples given in the foregoing paragraph, the market design to adjudicate the best positions in the search‐result lists of a keyword in the business of sponsored search advertisements is based on auctions, and we can find many papers in game theory literature on this subject (see, among others, Aggarwal et al., ; Lim and Tang, ; Edelman et al., ; Feng et al., ; Varian, ; Aparicio et al., ; Alonso et al., ). However, in the case of video‐sharing web platforms or TV on the Internet we can find a number of papers in the literature in which game theory is used to analyze several technologically related problems, but very few using game theory to analyze the market design or economic aspects of the different business models related to them (see, e.g., Bonastre et al.…”