Truthfulness in advertising? Approximation mechanisms for knapsack bidders

Quasilinear utility functions are a standard assumption in auction theory allowing for truthful and welfare-maximizing auction mechanisms. However, the literature on advertising markets suggests that the utility model of bidders rather resembles a knapsack problem, where advertisers try to maximize the sum of item values subject to a budget for a marketing campaign. Non-quasilinear environments rarely allow for truthful mechanisms. Nonetheless, some characteristics of the market environment might allow for positive results. In particular, markets are large and bidders typically consider prices as exogenous. We introduce a model of advertising markets, and study whether truthful and prior-free approximation mechanisms with good approximation ratios of the maximal welfare are possible. We analyze the offline mechanism design problem and find a truthful and randomized mechanism with an approximation ratio of only 4. This mechanism draws on a fractional deferred acceptance algorithm and randomized rounding, and it illustrates how the relax-and-round principle can be implemented in this non-quasilinear environment. The article highlights the types of assumptions necessary for truthful mechanisms with good approximation ratios in an important class of non-quasilinear utility functions.