Low-Regret Algorithms for Strategic Buyers with Unknown Valuations in Repeated Posted-Price Auctions

We study repeated posted-price auctions where a single seller repeatedly interacts with a single buyer for a number of rounds. In previous works, it is common to consider that the buyer knows his own valuation with certainty. However, in many practical situations, the buyer may have a stochastic valuation. In this paper, we study repeated posted-price auctions from the perspective of a utility maximizing buyer who does not know the probability distribution of his valuation and only observes a sample from the valuation distribution after he purchases the item. We first consider non-strategic buyers and derive algorithms with sub-linear regret bounds that hold irrespective of the observed prices offered by the seller. These algorithms are then adapted into algorithms with similar guarantees for strategic buyers. We provide a theoretical analysis of our proposed algorithms and support our findings with numerical experiments. Our experiments show that, if the seller uses a low-regret algorithm for selecting the price, then strategic buyers can obtain much higher utilities compared to non-strategic buyers. Only when the prices of the seller are not related to the choices of the buyer, it is not beneficial to be strategic, but strategic buyers can still attain utilities of about 75% of the utility of non-strategic buyers.</p

Points mechanisms and rewards programs

© 2018 Wiley Periodicals, Inc. I study points programs, such as frequent flyer and other rewards programs, as a revenue management tool. I develop a two-period contracting model where a capacity-constrained firm faces consumers who privately learn their valuations over time. The firm cannot commit to long-term contracts, but it can commit to allocate any unsold capacity through a points program. This points scheme creates an endogenous and type-dependent outside option for consumers, which generates novel incentives in the firm's pricing problem. It induces the firm to screen less ex interim, and to offer lower equilibrium prices, reversing the intuition of demand cannibalization

Multi-Unit Auctions to Allocate Water Scarcity Simulating Bidding Behaviour with Agent Based Models

Multi-unit auctions are promising mechanisms for the reallocation of water. The main advantage of such auctions is to avoid the lumpy bid issue. However, there is great uncertainty about the best auction formats when multi-unit auctions are used. The theory can only supply the structural properties of equilibrium strategies and the multiplicity of equilibria makes comparisons across auction formats difficult. Empirical studies and experiments have improved our knowledge of multi- unit auctions but they remain scarce and most experiments are restricted to two bidders and two units. Moreover, they demonstrate that bidders have limited rationality and learn through experience. This paper constructs an agent-based model of bidders to compare the performance of alternative auction formats under circumstances where bidders submit continuous bid supply functions and learn over time to adjust their bids to improve their net incomes. We demonstrate that under the generalized Vickrey, simulated bids converge towards truthful bids as predicted by the theory and that bid shading is the rule for the uniform and discriminatory auctions. Our study allows us to assess the potential gains from agent-based modelling approaches in the assessment of the dynamic performance of multi-unit procurement auctions. Some recommendations on the desirable format of water auctions are provided.Multi-unit auctions, Learning, Multi-agent models, Water allocation

Adaptive Contract Design for Crowdsourcing Markets: Bandit Algorithms for Repeated Principal-Agent Problems

Crowdsourcing markets have emerged as a popular platform for matching available workers with tasks to complete. The payment for a particular task is typically set by the task's requester, and may be adjusted based on the quality of the completed work, for example, through the use of "bonus" payments. In this paper, we study the requester's problem of dynamically adjusting quality-contingent payments for tasks. We consider a multi-round version of the well-known principal-agent model, whereby in each round a worker makes a strategic choice of the effort level which is not directly observable by the requester. In particular, our formulation significantly generalizes the budget-free online task pricing problems studied in prior work. We treat this problem as a multi-armed bandit problem, with each "arm" representing a potential contract. To cope with the large (and in fact, infinite) number of arms, we propose a new algorithm, AgnosticZooming, which discretizes the contract space into a finite number of regions, effectively treating each region as a single arm. This discretization is adaptively refined, so that more promising regions of the contract space are eventually discretized more finely. We analyze this algorithm, showing that it achieves regret sublinear in the time horizon and substantially improves over non-adaptive discretization (which is the only competing approach in the literature). Our results advance the state of art on several different topics: the theory of crowdsourcing markets, principal-agent problems, multi-armed bandits, and dynamic pricing.Comment: This is the full version of a paper in the ACM Conference on Economics and Computation (ACM-EC), 201