User Satisfaction in Competitive Sponsored Search

We present a model of competition between web search algorithms, and study the impact of such competition on user welfare. In our model, search providers compete for customers by strategically selecting which search results to display in response to user queries. Customers, in turn, have private preferences over search results and will tend to use search engines that are more likely to display pages satisfying their demands. Our main question is whether competition between search engines increases the overall welfare of the users (i.e., the likelihood that a user finds a page of interest). When search engines derive utility only from customers to whom they show relevant results, we show that they differentiate their results, and every equilibrium of the resulting game achieves at least half of the welfare that could be obtained by a social planner. This bound also applies whenever the likelihood of selecting a given engine is a convex function of the probability that a user's demand will be satisfied, which includes natural Markovian models of user behavior. On the other hand, when search engines derive utility from all customers (independent of search result relevance) and the customer demand functions are not convex, there are instances in which the (unique) equilibrium involves no differentiation between engines and a high degree of randomness in search results. This can degrade social welfare by a factor of the square root of N relative to the social optimum, where N is the number of webpages. These bad equilibria persist even when search engines can extract only small (but non-zero) expected revenue from dissatisfied users, and much higher revenue from satisfied ones

Reducing Inefficiency in Carbon Auctions with Imperfect Competition

We study auctions for carbon licenses, a policy tool used to control the social cost of pollution. Each identical license grants the right to produce a unit of pollution. Each buyer (i.e., firm that pollutes during the manufacturing process) enjoys a decreasing marginal value for licenses, but society suffers an increasing marginal cost for each license distributed. The seller (i.e., the government) can choose a number of licenses to put up for auction, and wishes to maximize the societal welfare: the total economic value of the buyers minus the social cost. Motivated by emission license markets deployed in practice, we focus on uniform price auctions with a price floor and/or price ceiling. The seller has distributional information about the market, and their goal is to tune the auction parameters to maximize expected welfare. The target benchmark is the maximum expected welfare achievable by any such auction under truth-telling behavior. Unfortunately, the uniform price auction is not truthful, and strategic behavior can significantly reduce (even below zero) the welfare of a given auction configuration. We describe a subclass of "safe-price" auctions for which the welfare at any Bayes-Nash equilibrium will approximate the welfare under truth-telling behavior. We then show that the better of a safe-price auction, or a truthful auction that allocates licenses to only a single buyer, will approximate the target benchmark. In particular, we show how to choose a number of licenses and a price floor so that the worst-case welfare, at any equilibrium, is a constant approximation to the best achievable welfare under truth-telling after excluding the welfare contribution of a single buyer