Non-discriminative algorithmic pricing: decentralized resource allocation in markets

Abstract

2) Pricing under uncertainty: Even when the seller only has access to a distribution over (submodular) buyer valuations, and items have a non-linear production cost, we show that it is possible to efficiently compute prices that result in a one-fourth approximation to the optimum for social welfare.

4) Price Competition in Networked Markets We consider a market where multiple sellers compete on price and show that the efficiency of the market at equilibrium drops linearly as the number of monopolies increases. Based on this result, we argue that monopolies are not as evil as they are made out to be.

3) Simultaneously optimizing both profit and welfare: For large markets with repeated engagement, it is understood that myopically optimizing profit while compromising on buyer welfare could hurt the long-term revenue of the marketplace. Bearing in this mind, we design the first bi-criteria pricing mechanisms that result in a simultaneous constant factor approximation to both profit and social welfare.

Despite the popularity of item pricing in various real life markets, much remains unknown about forming computationally efficient pricing algorithms with good performance guarantees. The objective of this thesis is to bridge the gap between theory and practice and understand the revenue and social welfare properties of non-discriminative pricing mechanisms in a constructive manner. This thesis will focus on nuance and attempt to dissect how various (realistic) market constraints affect revenue and social welfare. Specifically, we are interested in computing prices that simultaneously optimize multiple objectives and in studying more realistic models of buyer behavior. The main high level message of this work is a strong argument in favor of non-discriminative pricing, i.e., using arguably the simplest of pricing mechanisms, we can obtain approximation guarantees that are often comparable to more complex pricing schemes such as bundle pricing and discriminatory posted prices. The primary contributions of this work are:

Markets are the de facto way by which most economies operate, and prices lie at the core of most decentralized markets: a seller assigns prices for their goods or services, and buyers decide whether or not to pay the asked price. Moreover, although there are certainly exceptions, a seller usually cannot price discriminate, i.e., charge buyers different prices for the same good. Such a practice is not only undesirable and regulated by law, it may also be infeasible in markets with a large population of buyers. This thesis provides a rigorous theoretical analysis of the power and limitations of non-discriminative pricing schemes, also known as item pricing.

1) Static vs Dynamic Pricing: For m-good markets where buyers arrive sequentially, we provide an efficient algorithm to compute static, non-discriminatory prices whose revenue is within a O(log²m)-approximation of the optimum social welfare, thereby showing that no dynamic pricing scheme can outperform simple, static prices by a large profit margin.