Revenue Maximization with an Uncertainty-Averse Buyer

Chawla, Shuchi; Goldner, Kira; Miller, J. Benjamin; Pountourakis, Emmanouil

doi:10.1137/1.9781611975031.134

Cited by 7 publications

(5 citation statements)

References 14 publications

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Section: Our Results and Techniquesmentioning

confidence: 99%

“…Fu et al[2013] consider the design of prior-independent mechanisms (that have no access to the buyers' private value distributions) for risk-averse buyers. Finally, Chawla et al [2018] study the design of robust mechanisms under the cumulative prospect theory model.To the best our knowledge, the only work on mechanism design under risk-loving behavior is by Hinnosaar [2017], who shows that in the absence of regulations, the seller can extract infinite revenue from the buyer with asymptotically risk-loving behavior under both the expected utility theory and prospect theory models.Recently, the duality theory framework has drawn attention in the mechanism design community for understanding optimal mechanisms for selling multiple items. For example, Daskalakis et al [2017Daskalakis et al [ , 2013 and Koutsoupias [2014, 2015] discovered the connection between the dual problem and the optimal transport (bipartite matching) problem.…”

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confidence: 99%

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Optimal Mechanism Design with Risk-Loving Agents

Nikolova

Pountourakis

Yang

2018

Web and Internet Economics

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One of the most celebrated results in mechanism design is Myerson's characterization of the revenue optimal auction for selling a single item. However, this result relies heavily on the assumption that buyers are indifferent to risk. In this paper we investigate the case where the buyers are risk-loving, i.e. they prefer gambling to being rewarded deterministically. We use the standard model for risk from expected utility theory, where risk-loving behavior is represented by a convex utility function. We focus our attention on the special case of exponential utility functions. We characterize the optimal auction and show that randomization can be used to extract more revenue than when buyers are riskneutral. Most importantly, we show that the optimal auction is simple: the optimal revenue can be extracted using a randomized take-it-or-leave-it price for a single buyer and using a loser-pay auction, a variant of the all-pay auction, for multiple buyers. Finally, we show that these results no longer hold for convex utility functions beyond exponential. Related WorkMost work on optimal mechanism design beyond the risk-neutral setting has focused on riskaverse preferences. The classic results of Maskin and Riley [1984] and Matthews [1983] provide a characterization of the optimal mechanism with concave utility functions. A recent result in this area by Dughmi and Peres [2012] is that any mechanism designed for risk-neutral buyers can be adjusted to also align the incentives of risk-averse buyers and obtain similar guarantees. Fu et al.[2013] consider the design of prior-independent mechanisms (that have no access to the buyers' private value distributions) for risk-averse buyers. Finally, Chawla et al. [2018] study the design of robust mechanisms under the cumulative prospect theory model.To the best our knowledge, the only work on mechanism design under risk-loving behavior is by Hinnosaar [2017], who shows that in the absence of regulations, the seller can extract infinite revenue from the buyer with asymptotically risk-loving behavior under both the expected utility theory and prospect theory models.Recently, the duality theory framework has drawn attention in the mechanism design community for understanding optimal mechanisms for selling multiple items. For example, Daskalakis et al. [2017Daskalakis et al. [ , 2013 and Koutsoupias [2014, 2015] discovered the connection between the dual problem and the optimal transport (bipartite matching) problem. Cai et al. [2016] consider a duality framework via linear programming, and identify a connection between the virtual valuations and the dual variables. In our setting, the problem results in a different form of dual problem than in the multi-item setting, hence we seek to establish a new duality framework that diverges from the multi-item setting to different behavior models.

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Section: Our Results and Techniquesmentioning

confidence: 99%

mentioning

confidence: 99%

Optimal Mechanism Design with Risk-Loving Agents

Nikolova

Pountourakis

Yang

2018

Web and Internet Economics

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“…Behavioral mechanism design (Easley and Ghosh, 2015) study how departures from standard economic models of agent behavior affect mechanism design. Chawla et al (2018) study the revenue-maximization when the buyer's behavioral model is beyond expected utility theory and characterize mechanism that is robust to the buyer's risk attitude. Other related works in mechanism design include Fu et al (2013); Chawla et al (2022); Dughmi and Peres (2012).…”

Section: Related Workmentioning

confidence: 99%

Rationality-Robust Information Design: Bayesian Persuasion under Quantal Response

Feng¹,

Ho²,

Tang³

2022

Preprint

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Bayesian persuasion in information design studies how an information-advantaged sender can influence a receiver to take the sender's preferred action by designing an information disclosure policy, a.k.a., a signaling scheme. Most works in Bayesian persuasion assume that the receiver is fully rational, i.e., she always selects the action that maximizes her expected utility. Yet empirical evidence suggests that human decisions may deviate from this expected utility theory. In this work, we relax the full rationality assumption and consider a boundedly rational receiver. In particular, we formulate the boundedly rationality of the receiver by adopting the classical model of quantal response, which captures the receiver's possible deviation from full rationality through incorporating noises in the receiver's process of utility estimation during decision making. Focusing on a fundamental persuasion model with binary receiver action, we seek to understand how the receiver's boundedly rational behavior impacts the design of optimal signaling schemes, and whether there exists robust signaling scheme when the receiver's boundedly rational behavior remains unknown.For both questions, we provide both positive and negative answers. At a high-level, a crucial condition which governs our answers is whether the sender's utility depends on the realized state. For the first question, in contrast to the setting with a fully rational receiver where censorship signaling scheme is always optimal (Renault et al., 2017), we show that for a boundedly rational receiver, the censorship signaling scheme remains optimal in state independent sender utility (SISU) environments, but is no longer optimal in state dependent sender utility (SDSU) environments. Nonetheless, we show that censorship signaling scheme is Θ(m)-approximation in SDSU environments, where m denotes the number of states. En route, we characterize the optimal signaling scheme in SDSU environments, in which the sender's signal either reveals the true state, or randomizes the receiver's uncertainty on only two states. For the second question, we introduce rationality-robust information design -a framework in which a signaling scheme is designed for a receiver with unknown boundedly rational behavior. We show that in SISU environments, up to a 2-approximation factor, implementing optimal censorship signaling scheme of a fully rational receiver is rationality-robust for any boundedly rational receiver. In marked contrast to this positive result, in SDSU environments, there exists no robust signaling scheme that has any bounded approximation. Nonetheless, for any problem instance with binary state, under a reasonable multiplicative boundedness condition on the receiver's behavior, the sender is able to design a signaling scheme whose approximation ratio depends linearly on the multiplicative error.

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“…The concept of risk aversion has been extensively investigated in the literature in the context of stochastic optimization and finance (e.g, [Rockafellar andUryasev, 2002, Swamy, 2011]), algorithm design (e.g., [Leonardi et al, 2001]) and especially auctions (e.g., [Chawla et al, 2018, Fu et al, 2013, Maskin and Riley, 1984, Sundararajan and Yan, 2020). These papers use different approaches to model risk and often try to explain better phenomena that arise in practice.…”

Section: Risk Aversionmentioning

confidence: 99%

Prophet Inequalities via the Expected Competitive Ratio

Ezra¹,

Leonardi²,

Rebecca³

et al. 2022

Preprint

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We consider prophet inequalities under general downward-closed constraints. In a prophet inequality problem, a decision-maker sees a series of online elements and needs to decide immediately and irrevocably whether or not to select each element upon its arrival, subject to an underlying feasibility constraint. Traditionally, the decision-maker's expected performance has been compared to the expected performance of the prophet, i.e., the expected offline optimum. We refer to this measure as the Ratio of Expectations (or, in short, RoE). However, a major limitation of the RoE measure is that it only gives a guarantee against what the optimum would be on average, while, in theory, algorithms still might perform poorly compared to the realized ex-post optimal value.Hence, we study alternative performance measures. In particular, we suggest the Expected Ratio (or, in short, EoR), which is the expectation of the ratio between the value of the algorithm and the value of the prophet. This measure yields desirable guarantees, e.g., a constant EoR implies achieving a constant fraction of the ex-post offline optimum with constant probability. Moreover, in the single-choice setting, we show that the EoR is equivalent (in the worst case) to the probability of selecting the maximum, a well-studied measure in the literature. This is no longer the case for combinatorial constraints (beyond single-choice), which is the main focus of this paper.Our main goal is to understand the relation between RoE and EoR in combinatorial settings. Specifically, we establish a two-way black-box reduction: for every feasibility constraint, the RoE and the EoR are at most a constant factor apart. This implies a wealth of EoR results in multiple settings where RoE results are known.

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Revenue Maximization with an Uncertainty-Averse Buyer

Cited by 7 publications

References 14 publications

Optimal Mechanism Design with Risk-Loving Agents

Optimal Mechanism Design with Risk-Loving Agents

Rationality-Robust Information Design: Bayesian Persuasion under Quantal Response

Prophet Inequalities via the Expected Competitive Ratio

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