## Shengwu Li

### Assistant Professor of Economics, Harvard University

### shengwu_li@fas.harvard.edu

I study economic theory and behavioral economics. In particular, I often think about how we can design economic systems, in the presence of computational complexity, that are nonetheless simple and transparent for human beings.

## What's new?

New working paper: Sequential Cursed Equilibrium (with Shani Cohen).

Updated working paper: Algorithmic Mechanism Design with Investment. (Formerly titled "Investment Incentives in Truthful Approximation Mechanisms".) Results now include an application to fully polynomial-time approximation schemes for the knapsack problem.

## Working Papers

Cursed equilibrium posits that players in a Bayesian game neglect the relationship between their opponent’s actions and their opponent’s type (Eyster and Rabin, 2005). Sequential cursed equilibrium generalizes this idea to extensive games, including those with endogenous private information. It predicts that players neglect the information content of hypothetical events, but make correct inferences from observed events—as is consistent with data from experiments on hypothetical thinking.

### What's My Employee Worth? The Effects of Salary Benchmarking (with Zoë Cullen and Ricardo Perez-Truglia)

U.S. legislation prohibits employers from sharing information about their employees’ compensation with each other, but employers are allowed to use salary benchmarks; that is, aggregated data provided by third parties. We study an auction-theoretic model of salary benchmarks. We provide empirical evidence on the effects of salary benchmarks, using administrative data on 200,000 new hires.

### Fairness in Incomplete Information Bargaining: Theory and Widespread Evidence from the Field (with Daniel Keniston, Bradley J. Larsen, J.J. Prescott, Bernardo S. Silveira, and Chuan Yu)

This paper uses detailed data on sequential offers from seven vastly different real-world bargaining settings to document a robust pattern: agents favor offers that split the difference between the two most recent offers on the table. Our settings include negotiations for used cars, insurance injury claims, a TV game show, auto rickshaw rides, housing, international trade tariffs, and online retail. We demonstrate that this pattern can arise in a perfect Bayesian equilibrium of an alternating-offer game with two-sided incomplete information, but this equilibrium is far from unique. We then provide a robust-inference argument to explain why agents may view the two most recent offers as corresponding to the potential surplus. Split-the-difference offers under this weaker, robust inference can then be viewed as *fair*. We present a number of other patterns in each data setting that point to split-the-difference offers as a strong social norm, whether in high-stakes or low-stakes negotiations.

Human beings attempt to rationalize their past choices, even those that were mistakes in hindsight. We propose a formal theory of this behavior. The theory predicts that agents commit the sunk-cost fallacy. Its model primitives are identified by choice behavior and it yields tractable comparative statics.

### The Value of Excess Supply in Spatial Matching Markets (with Mohammad Akbarpour, Yeganeh Alimohammadi, and Amin Saberi)

We study dynamic matching in a spatial setting. Drivers are distributed at random on some interval. Riders arrive in some (possibly adversarial) order at randomly drawn points. The platform observes the location of the drivers, and can match newly arrived riders immediately, or can wait for more riders to arrive. Unmatched riders incur a waiting cost c per period. The platform can match riders and drivers, irrevocably. The cost of matching a driver to a rider is equal to the distance between them. We quantify the value of slightly increasing supply. We prove that when there are (1 + ε) drivers per rider (for any ε > 0), the cost of matching returned by a simple greedy algorithm which pairs each arriving rider to the closest available driver is O(log3(n)), where n is the number of riders. On the other hand, with equal number of drivers and riders, even the ex post optimal matching does not have a cost less than Θ( n). Our results shed light on the important role of (small) excess supply in spatial matching markets.

We present a polynomial-time algorithm that determines, given some choice rule, whether there exists an obviously strategy-proof mechanism for that choice rule.

### Algorithmic Mechanism Design with Investment, (with Mohammad Akbarpour, Scott Kominers, and Paul Milgrom) [revise & resubmit at Econometrica]

We study the investment incentives created by truthful mechanisms that allocate resources using approximation algorithms. Some approximation algorithms guarantee nearly 100% of the optimal welfare, but have only a zero guarantee when one bidder can invest before participating. An algorithm’s worst-case allocative and investment guarantees coincide if and only if that algorithm’s *confirming negative externalities *are sufficiently small. We introduce new fast approximation algorithms for the knapsack problem that have no confirming negative externalities, with guarantees close to 100% both with and without investments.

## Publications

### Discovering Auctions: Contributions of Paul Milgrom and Robert Wilson, The Scandinavian Journal of Economics 2021 (with Alex Teytelboym, Scott Kominers, Mohammad Akbarpour, and Piotr Dworczak)

This is the customary article that reviews the contributions of the most recent Nobel laureates in economics.

Consider an extensive-form mechanism, run by an auctioneer who communicates sequentially and privately with bidders. Suppose the auctioneer can deviate from the rules provided that no single bidder detects the deviation. A mechanism is *credible* if it is incentive-compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first-price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy-proof mechanism.

Akbarpour, Mohammad and Shengwu Li, Credible Auctions, *Econometrica*, Vol. 88, No. 2 (March, 2020), 425–467

Preprint (includes online appendices)

### Thickness and Information in Dynamic Matching Markets, Journal of Political Economy 2020, lead article (with Mohammad Akbarpour and Shayan Oveis-Gharan)

We introduce a simple model of dynamic matching in networked markets, where agents arrive and depart stochastically, and the composition of the trade network depends endogenously on the matching algorithm. Varying the timing properties of matching algorithms can substantially affect their performance, and this depends crucially on the information structure. More precisely, if the planner can identify agents who are about to depart, then waiting to thicken the market substantially reduces the fraction of unmatched agents. If the planner cannot identify such agents, then matching agents greedily is close-to-optimal. We specify conditions under which local algorithms that choose the right time to match agents, but do not exploit the global network structure, are close-to-optimal. Finally, we consider a setting where agents have private information about their departure times, and design a continuous-time dynamic mechanism to elicit this information.

Here are short videos that exposit the paper:

An agent makes consumption choices in multiple periods. Choice objects vary in type and quality; objects of the same type are inter-temporal substitutes. The current choice set is informative about the distribution over future choice sets. Thus, the presence of unchosen alternatives may rationally alter the agent's choice. Under some simple assumptions, the optimal policy exhibits context-dependent choice behavior, such as the decoy effect and choice overload.

### Belief Updating and the Demand for Information, Games and Economic Behavior 2018 (with Sandro Ambuehl)

How do individuals value noisy information that guides economic decisions? In our laboratory experiment, we find that individuals underreact to increasing the informativeness of a signal, thus undervalue high-quality information, and that they disproportionately prefer information that may yield certainty. Both biases appear to be mainly due to non-standard belief updating. We find that individuals differ consistently in their *responsiveness to information* – the extent that their beliefs move upon observing signals. Individual parameters of responsiveness to information have explanatory power in two distinct choice environments and are unrelated to proxies for mathematical aptitude.

A strategy is obviously dominant if, for any deviation, at any information set where both strategies first diverge, the best outcome under the deviation is no better than the worst outcome under the dominant strategy. A mechanism is obviously strategy-proof (OSP) if it has an equilibrium in obviously dominant strategies. This has a behavioral interpretation: a strategy is obviously dominant if and only if a cognitively limited agent can recognize it as weakly dominant. It also has a classical interpretation: a choice rule is OSP-implementable if and only if it can be carried out by a social planner under a particular regime of partial commitment.

I propose a new solution concept, obvious ex post (OXP) equilibrium. This is a formal standard of cognitive simplicity for mechanisms, in settings with interdependent values. Under some standard assumptions, the ascending auction has an efficient OXP equilibrium. I discuss a decision theoretic foundation for OXP mechanisms.

This paper examines the relationship between ethics and market design. It argues that market design should not rely wholly on preference utilitarianism in order to make ethical judgements. It exposits an alternative normative framework—informed neutrality between reasonable ethical positions.