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We consider agents with non-linear preferences given by private values and private budgets. We quantify the extent to which posted pricing approximately optimizes welfare and revenue for a single agent. We give a reduction framework that extends the approximation of multi-agent pricing-based mechanisms from linear utility to nonlinear utility. This reduction framework is broadly applicable as Alaei et al. (2012) have shown that mechanisms for linear agents can generally be interpreted as pricing-based mechanisms. We give example applications of the framework to oblivious posted pricing (e.g., Chawla et al., 2010), sequential posted pricing (e.g., Yan, 2011), and virtual surplus maximization (Myerson, 1981).
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Mechanisms with money are commonly designed under the assumption that agents are quasi-linear, meaning they have linear disutility for spending money. We study the implications when agents with non-linear (specifically, convex) disutility for payments participate in mechanisms designed for quasi-linear agents. We first show that any mechanism that is truthful for quasi-linear buyers has a simple best response function for buyers with non-linear disutility from payments, in which each bidder simply scales down her value for each potential outcome by a fixed factor, equal to her target return on investment (ROI). We call such a strategy ROI-optimal. We prove the existence of a Nash equilibrium in which agents use ROI-optimal strategies for a general class of allocation problems. Motivated by online marketplaces, we then focus on simultaneous second-price auctions for additive bidders and show that all ROI-optimal equilibria in this setting achieve constant-factor approximations to suitable welfare and revenue benchmarks.
Many facts are learned through the intermediation of individuals with special access to information, such as law enforcement officers, officials with a security clearance, or experts with specific knowledge. This paper considers whether societies can learn about such facts when information is cheap to manipulate, produced sequentially, and these individuals are devoid of ethical motive. The answer depends on an information attrition condition pertaining to the amount of evidence available which distinguishes, for example, between reproducible scientific evidence and the evidence generated in a crime. Applications to institution enforcement, social cohesion, scientific progress, and historical revisionism are discussed.
We identify the first static credible mechanism for multi-item additive auctions that achieves a constant factor of the optimal revenue. This is one instance of a more general framework for designing two-part tariff auctions, adapting the duality framework of Cai et al [CDW16]. Given a (not necessarily incentive compatible) auction format $A$ satisfying certain technical conditions, our framework augments the auction with a personalized entry fee for each bidder, which must be paid before the auction can be accessed. These entry fees depend only on the prior distribution of bidder types, and in particular are independent of realized bids. Our framework can be used with many common auction formats, such as simultaneous first-price, simultaneous second-price, and simultaneous all-pay auctions. If all-pay auctions are used, we prove that the resulting mechanism is credible in the sense that the auctioneer cannot benefit by deviating from the stated mechanism after observing agent bids. If second-price auctions are used, we obtain a truthful $O(1)$-approximate mechanism with fixed entry fees that are amenable to tuning via online learning techniques. Our results for first price and all-pay are the first revenue guarantees of non-truthful mechanisms in multi-dimensional environments; an open question in the literature [RST17].
Incentives are more likely to elicit desired outcomes when they are designed based on accurate models of agents strategic behavior. A growing literature, however, suggests that people do not quite behave like standard economic agents in a variety of environments, both online and offline. What consequences might such differences have for the optimal design of mechanisms in these environments? In this paper, we explore this question in the context of optimal contest design for simple agents---agents who strategically reason about whether or not to participate in a system, but not about the input they provide to it. Specifically, consider a contest where $n$ potential contestants with types $(q_i,c_i)$ each choose between participating and producing a submission of quality $q_i$ at cost $c_i$, versus not participating at all, to maximize their utilities. How should a principal distribute a total prize $V$ amongst the $n$ ranks to maximize some increasing function of the qualities of elicited submissions in a contest with such simple agents? We first solve the optimal contest design problem for settings with homogenous participation costs $c_i = c$. Here, the optimal contest is always a simple contest, awarding equal prizes to the top $j^*$ contestants for a suitable choice of $j^*$. (In comparable models with strategic effort choices, the optimal contest is either a winner-take-all contest or awards possibly unequal prizes, depending on the curvature of agents effort cost functions.) We next address the general case with heterogeneous costs where agents types are inherently two-dimensional, significantly complicating equilibrium analysis. Our main result here is that the winner-take-all contest is a 3-approximation of the optimal contest when the principals objective is to maximize the quality of the best elicited contribution.
The advent of machine learning tools has led to the rise of data markets. These data markets are characterized by multiple data purchasers interacting with a set of data sources. Data sources have more information about the quality of data than the data purchasers; additionally, data itself is a non-rivalrous good that can be shared with multiple parties at negligible marginal cost. In this paper, we study the multiple-principal, multiple-agent problem with non-rivalrous goods. Under the assumption that the principals payoff is quasilinear in the payments given to agents, we show that there is a fundamental degeneracy in the market of non-rivalrous goods. Specifically, for a general class of payment contracts, there will be an infinite set of generalized Nash equilibria. This multiplicity of equilibria also affects common refinements of equilibrium definitions intended to uniquely select an equilibrium: both variational equilibria and normalized equilibria will be non-unique in general. This implies that most existing equilibrium concepts cannot provide predictions on the outcomes of data markets emerging today. The results support the idea that modifications to payment contracts themselves are unlikely to yield a unique equilibrium, and either changes to the models of study or new equilibrium concepts will be required to determine unique equilibria in settings with multiple principals and a non-rivalrous good.
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