Discrete Strategies in Keyword Auctions and Their Inefficiency for Locally Aware Bidders

We study formally two simple discrete bidding strategies in the context of iterative best response procedures, for the game induced by the Generalized Second Price keyword auction mechanism. These strategies have seen experimental evaluation in the recent literature as parts of best response procedures, which have been shown not to converge. Here we give a detailed definition of iterative best response under these strategies and, under appropriate discretization of the players’ strategy spaces we find that the best response state space contains socially optimum pure Nash equilibrium states of the game. We cast the strategies under a new light, arguing that they constitute natural choices for conservative myopic bidders that need to act based only on local information. For this case we provide bounds for the worst-case ratio of the social welfare of the reached locally stable states relative to the socially optimum welfare. Our work aims at providing a reference description for the strategies under study and their properties, thus filling a gap in the recent literature. We make several interesting observations experimentally, that give rise to challenging open problems. ∗Department of Informatics, Athens University of Economics & Business, Greece ([email protected]) †Department of Computer Science, University of Liverpool, United Kingdom ([email protected])