Hao Li

Professor

He goes to University of C. To get his economics PhD. Coffee for tea, Starbucks for SOE. He’s as lost as he can be.

I’ve made up a complete plan. Wanna be a sequentially rational man. Trembling hand, perfect Bayesian. I am doing the very best I can.

You’ve got private information. Gotta use direct revelation. Cheap talking, discrimination. All together now with no deviation.

Please click on paper titles for abstracts and full text downloads.

MAKING DECISIONS IN COMMITTEES

We consider a committee problem in which efficient information aggregation is hindered by differences in preferences. Sufficiently large delays could foster information aggregation but would require commitment. In a dynamic delay mechanism with limited commitment, successive rounds of decision-making are punctuated by delays that are uniformly bounded from above. Any optimal sequence of delays is finite, inducing in equilibrium both a "deadline play," in which a period of no activity before the deadline is followed by full concession at the end to reach the efficient decision, and "stop-and-start" in the beginning, in which the maximum concession feasible alternates with no concession. Stop-and-start is achieved by binding and slackening the bound on delay in turn.

[go to paper]

We study a model of collective decision making in which agents vote on the decision repeatedly until they agree, with the agents receiving no exogenous new information between two voting rounds but incurring a delay cost. Although preference conflict between the agents makes information aggregation impossible in a single round of voting, in the equilibrium of the repeated voting game agents are increasingly more willing to vote their private information after each disagreement. Information is efficiently aggregated within a finite number of rounds. As delay becomes less costly, agents are less willing to vote their private information, and efficient information aggregation takes longer. Even as the delay cost converges to zero, agents are strictly better off in the repeated voting game than in any single round game for moderate degrees of initial conflict.

[go to paper]

We provide a welfare analysis of the deadline effect in a repeated negotiation game in which costly delay can produce information that improves the quality of the decision. We characterize equilibrium strategies and the evolution of beliefs in continuous time, and study how the length of the negotiation horizon affects players' behavior and welfare. The optimal deadline is positive if and only if the ex ante probability that the players disagree on the preferred decision is neither too high nor too low. When it is positive, the optimal deadline is given by the shortest time that would allow efficient information aggregation in equilibrium, which is increasing in the ex ante probability of disagreement and is finitely long.

[go to paper]

This article reviews recent developments in the theory of committee decision-making. A committee consists of self-interested members that make a public decision by aggregating imperfect information dispersed among them according to a pre-specified decision rule. We focus on costly information acquisition, strategic information aggregation, and rules and processes that enhance the quality of the committee decision. Seeming ineffciencies of the committee decision-making process such as over-cautiousness, voting, and delay emerge as partial remedies to these incentive problems.

[go to paper]

A model of delegation and expertise is presented, with self-interested and privately-informed decisionmakers and experts. Conflict of interests exists both between the decisionmakers and the experts, and between experts within a team. A balanced team of experts with extreme and opposite biases is shown to be acceptable to decisionmakers with a wide range of preferences, but the value of expertise from such a team is low. We also find that a decisionmaker wants to appoint experts who are less partisan than himself, in order to facilitate the pooling of information and thereby increase the quality of decisions by the expert team. Selective delegation, either by controlling the decisionmaking process or by conditioning the delegation decision on his own information, is another effective way for the decisionmaker to safeguard own interests while making use of expert information.

Committees improve decisions by pooling independent information of members, but promote manipulation, obfuscation, and exaggeration of private evidence when members have conflicting preferences. We study how self-interest mediates these conflicting forces. When members' preferences differ, no person ever submits a report that allows perfect inference of his private information. Instead, equilibrium strategies are many-to-one mappings that transform continuous data into ordered ranks: voting procedures are the equilibrium methods of achieving a consensus in committees. Voting necessarily coarsens the transmission of information among members, but is necessary to control conflicts of interest. The degree of coarseness of the equilibrium voting procedure is determined by the extent of conflicting preferences. Though self-interests necessarily reduce the efficient use of information in committees, real information sharing occurs nonetheless. Committees make better decisions for each member than would any individual on the basis of own information. Committees are viable, though imperfect ways of making decisions when information is dispersed among members.

A free-rider problem arises in a group when a public decision between two alternatives must be made based on privately collected evidence, leading to insufficient effort in gathering evidence and ex ante welfare loss for the group. To alleviate the free-rider problem, the group can commit to a "conservative'' rule whereby the decision is made against the alternative favored by the group's preference or prior when evidence supports the alternative but is not preponderant. For example, if a recruitment committee is biased toward making an offer to a job candidate, either because the committee is more concerned with wrongful rejection than with wrongful hiring or because it has high prior that the candidate is qualified, then a conservative rule with a hiring standard higher than what is ex post optimal given the evidence can induce committee members to examine the candidate's record more carefully and improve the quality of the hiring decision. This result that a conservative decision rule induces greater individual effort in collecting evidence explains why sometimes groups appear overly cautious toward favored alternatives. It is further extended to heterogeneous groups and private evidence.


AGGREGATING INFORMATION

Recounting introduces multiple pivotal events in two-candidate elections. In addition to determining which candidate is elected, an individual's vote is pivotal when the vote margin is just at the levels that would trigger a recount. In large elections, the motive to avoid recount cost can become the dominant consideration for rational voters, inducing them to vote sincerely according to their private signals. In environments where elections without recount fail to aggregate information efficiently, a suitably modified election rule with small recount cost can produce asymptotically efficient outcomes with a vanishing small probability of actually invoking a recount.

[go to paper]

In a financial market where all investors have valuable private information, full rationality requires that investors have unlimited ability of figuring out the equilibrium model. Instead, I assume that due to lack of knowledge or experience, some investors do not know the equilibrium model and use only their private information in forming their demand. By investigating the investment behavior of these "boundedly rational'' investors contrasting it with that of the rational ones, I find that in a market where the two kinds of investors coexist, it is the boundedly rational investors who contribute to price stability. The welfare implication is that, although each investor benefits from conditioning his asset demand on the information carried by the equilibrium price, it can happen that all investors lose by doing so because the equilibrium price becomes too volatile.

[go to paper]


SIGNALING

A political candidate chooses both the target and the informativeness of his campaign to signal his type, which consists of private information about himself and about his rival. A more informative positive (negative) campaign generates a more accurate public signal about his (the rival's) qualifications, but is more costly. In the unique least cost separating equilibrium of a two-type model, the high type separates by choosing the kind of campaign in which he has a comparative advantage over the low type. The comparative advantage in positive (negative) campaigns is stronger if the high type has favorable (unfavorable) information about his own qualifications and unfavorable (favorable) information about his rival. Additional ex post public information about the candidate (his rival) strengthens (weakens) the comparative advantage in positive (negative) campaigns. Allowing both positive and negative campaigns does not help the high type to separate if the campaign cost is concave in the informativeness, while allowing information campaigns by both candidates does.

[go to paper]

This paper considers a model of a rating agency with multiple clients. Each client has a separate market (end-user of the rating); the only connection among them is that the underlying qualities of the clients are correlated. In the benchmark case of individual rating, the market for each client does not know the ratings for other clients. In centralized rating, the agency rates all clients together and shares the rating information among all markets. In decentralized rating, the ratings are again shared among all markets, but each client is rated by a self-interested rater of the agency with no access to the quality information of other clients. Both centralized rating and decentralized rating weakly dominate individual rating for the agency. When the underlying qualities are weakly correlated, centralized rating can dominate decentralized rating, but the reverse holds when the qualities are strongly correlated.

[go to paper]

When employers cannot tell whether a school truly has many good students or just gives easy grades, schools have an incentive to inflate grades to help mediocre students, despite concerns about preserving the value of good grades for good students. We construct a signaling model where grades are inflated in equilibrium. The inability to commit to an honest grading policy reduces the informativeness of grades and hurts schools. Grade inflation by one school makes it easier for another school to fool the market with inflated grades. Easy grades are strategic complements, providing a channel to make grade exaggeration contagious.

PRICING

We consider a price discrimination problem in which a seller has a single object for sale to a potential buyer. At the time of contracting, the buyer's private type is his incomplete private information about his value, and the seller can disclose additional private information to the buyer. We study the question of whether discriminatory information disclosure can be profitable to the seller under the assumption that, for the same disclosure policy, the amount of additional private information that the buyer can learn depends on his private type. We establish sufficient conditions under which it is profit-maximizing for the seller to grant each private type of the buyer full access to all additional private information under her control. In general, however, discriminatory disclosure can be optimal, because it reduces the information rent accrued to private types of the buyer without much impact on the trade surplus.

[go to paper]

Two sellers with ex-ante identical products, whose qualities can be either high or low, first choose a binary information structure, modeled as the probability that the signal reveals the state. After the buyer independently draws one private signal from each information structure, the sellers then each choose a price in the second stage. We identify two equilibria in information structures, a symmetric equilibrium with two perfectly informative structures, and an asymmetric equilibrium with one perfectly informative structure and one completely uninformative structure. The symmetric equilibrium is efficient while the asymmetric equilibrium is not, but the latter generates a greater revenue to the sellers because price competition is less fierce due to a greater quality difference when they compete.

[go to paper]

We present a model of price discrimination where a monopolist faces consumers with unitary demands who learn their valuations over time. Consumers are privately informed at the time of contracting about valuation distribution, but they privately learn their actual valuations after contracting. The monopolist sequentially screens consumers with a menu of contracts: they first choose a contract and then choose the level of consumption according to the terms specified in the contract. A deterministic sequential mechanism is a menu of refund contracts, each consisting of an advance payment and a refund amount in case of no consumption, but general sequential mechanisms may also involve randomization. We characterize the optimal sequential mechanism both when some consumers are more eager than others in the sense of first-order stochastic dominance, and when some face greater valuation uncertainty than others in the sense of mean-preserving-spread. We show that it can be optimal to subsidize consumers with smaller valuation uncertainty through low refund in order to reduce the rent to those with greater uncertainty, who purchase more ``flexible'' contracts with greater refund. The size of distortion depends on how informative consumers' initial private knowledge is about their valuations from the monopolist's point of view, but not on the size of valuation uncertainty if it affects all consumers.

We present a model of timing of seasonal sales where stores choose several designs at the beginning of the season without knowing which one, if any, will be fashionable. Fashionable designs have a chance to fetch high prices in fashion markets while non-fashionable ones must be sold in a discount market. In the beginning of the season, stores charge high prices in the hope of capturing their fashion market. As the end of the season approaches with goods still on the shelves, stores adjust downward their expectations that they are carrying a fashionable design, and may have sales to capture the discount market. Having a greater number of designs induces a store to put one of them on sales earlier to test the market. Moreover, price competition in the discount market induces stores to start sales earlier because of a greater perceived first-mover advantage in capturing the discount market. More competition, perhaps due to decreases in the cost of product innovation, makes sales occur even earlier. These results are consistent with the observation that the trend toward earlier sales since mid-1970's coincides with increasing product varieties in fashion good markets and increasing store competition.


DESIGNING CONTRACTS

This paper studies a principal-agent problem where the only commitment for the uninformed principal is to restrict the set of decisions she makes following a report by the informed agent. Compared to no commitment, the principal improves the quality of communication from the agent. An ex ante optimal equilibrium for the principal corresponds to a finite partition of the state space, and each retained decision is suboptimal for the principal, biased toward the agent's preference. Generally an optimal equilibrium does not maximize the number of decisions the principal can credibly retain.

[go to paper]

In a dynamic model of sports competition, we show that when spectators care only about the level of effort exerted by contestants, rewarding schemes that depend linearly on the final score difference provide more efficient incentives for efforts than schemes based only on who wins and loses. This result is puzzling because rank order schemes are the dominant forms of reward in sports competitions. The puzzle can be explained if one takes into account the fact that spectators also care about the suspense in the game. We define spectators' demand for suspense as greater utility derived from contestants' efforts when the game is closer. As the demand for suspense increases, so does the advantage of rank order schemes relative to linear score difference schemes. When the demand for suspense is sufficiently high, the optimal rank order scheme dominates all linear score difference schemes, and with plausible additional restrictions, it dominates a broad class of incentive schemes that reward contestants on the basis of the final score difference.

[go to paper]


SORTING

Though individuals prefer to join groups with high quality peers, there are advantages to being high up in the pecking order within a group if higher ranked members of a group have greater access to the group's resources. When two organizations try to attract members from a fixed population of heterogeneous agents, how resources are distributed among the members according to their rank affects how agents choose between the organizations. Competition between the two organizations has implications for both the equilibrium sorting of agents and the way resources are distributed within each organization. To compete more intensely for the more talented agents, both organizations are selective and give no resources to their low ranks. In both organizations, higher ranks are rewarded with more resources, with a greater rate of increase in the organization that has a lower average quality in equilibrium.

[go to paper]

Though individuals prefer to join groups with high quality peers, there are also advantages from being high up in the pecking order within the group. We show that sorting of agents in this environment results in an overlapping interval structure in the type space. Segregation and mixing coexist in a stable equilibrium. A greater degree of egalitarianism within organizations leads to greater segregation across organizations. Policies that are effective for lower-quality organizations to attract talent may be counterproductive for higher-quality organizations to retain talent. The degree and the pattern of segregation are shown to depend also on whether higher types are less concerned with relative ranking within the organization, on relative size of organizations, and on the extent of idiosyncratic preferences for other organizational attributes.

[go to paper]

We consider a two-sided, finite-horizon model of search and matching with heterogeneous types and complementarity between types. The quality of the pool of potential matches deteriorates as agents who have found mutually agreeable matches exit the market. With automatic participation of all agents in each round, the market performs a sorting function in that attractive types of agents have multiple chances to meet and match with their peers. However, the sorting function of the market is lost if agents incur an arbitrarily small cost in order to participate in each round. The market unravels as almost all agents rush to participate in the first round and match and exit with anyone they meet.


MATCHING WITH PRIVATION INFORMATION

We study how matchmakers use prices to sort heterogeneous participants into competing matching markets, and how equilibrium outcomes compare with monopoly in terms of prices, matching market structure and sorting efficiency under the assumption of complementarity in the match value function. The role of prices to facilitate sorting is compromised by the need to survive price competition. We show that price competition leads to a high quality market that is insufficiently exclusive. As a result, the duopolistic outcome can be less efficient in sorting than the monopoly outcome in terms of total match value in spite of servicing more participants.

[go to paper]

This paper considers the problem of a monopoly matchmaker that uses a schedule of entrance fees to sort different types of agents on the two sides of a matching market into different markets, where agents randomly form pairwise matches. We make the standard assumption that the match value function exhibits complementarities, so that matching types at equal percentiles maximizes total match value. We provide necessary and sufficient conditions for the revenue-maximizing market structure to be efficient. These conditions require complementarities in the match value function to be sufficiently strong along the efficient matching path.


MATCHING WITH INCOMPLETE INFORMATION

In labor markets for entry-level professionals and in other related markets, job applicants' concern for availability of positions and employers' concern for availability of qualified applicants can drive some participants on the two sides to sign early job contracts. The rush to early contracting can be self-fulfilling, as both its effect on expectations about demand-supply balance in the subsequent spot market and the effect on it from changes in the demand-supply balance can be non-monotone. Matching markets with more risk-averse participants, a greater uncertainty regarding relative supply of positions, or a more polarized distribution of applicant qualities can be more vulnerable to self-fulfilling early contracting rushes. Employers can have a collective interest in preventing early offers to a few promising applicants from starting the rushes.

In an assignment market with uncertainty regarding productive ability of participants, early contracting can occur before the uncertainty is resolved as participants balance the trade-off between insurance provided by early bilateral contracts and the gains from more efficient sorting by remaining in the market. We apply competitive equilibrium analysis to determine the patterns of early contracting, the terms of early contracts, and the distribution of benefits of early contracting. Early contracts can be signed between more promising agents (who are more likely to have higher abilities) because the gains from insurance outweigh the loss of inefficient sorting, while less promising agents wait because the loss outweighs the gains. We establish conditions under which other patterns of early contracting are possible. We show that more promising agents on one side of the market (job applicants) can be driven to sign early contracts with the less promising agents of the other side (firms), because applicants are more risk-averse than firms, have greater uncertainty regarding their qualities, or face a tighter market. Early contracting in this case unambiguously hurts the more promising firms which choose to wait.

We use a two-period matching model with initial uncertainty about productivities of participants to analyze incentives for early contracting or unraveling. Unraveling provides insurance in the absence of complete markets, but causes inefficient assignments. Unraveling is more likely, the smaller the applicant pool, the smaller the proportion of more promising applicants, and the greater the heterogeneity in the pool. Banning early contracts hurts firms and benefits less promising applicants; the effects on more promising applicants depend on how the gains from early contracts are shared. Ex post buyouts eliminate inefficient assignments, and more promising applicants always unravel.


PROCESSING INFORMATION

This paper analyzes organizational structures that minimize information processing costs for a specific organizational task. Organizations consist of agents of limited ability connected in a network. These agents collect and process information, and make decisions. Organizations implement strategies---mappings from environmental circumstances to decisions. The strategies are exogenously given from a class of "pie"' problems to be defined in this paper. The notion of efficiency is lexicographic: the primary criterion is minimizing the number of agents, and the secondary criterion is minimizing the number of connections between the agents. In this modeling framework, efficient organizations are not hierarchical for a large number of problems. Hierarchies often fail to exploit fully the information processing capabilities of the agents because in a hierarchy, subordinates have a single superior.

This paper examines implications of complexity cost in implementing repeated game strategies through networks with finitely many classifiers. A network consists of individual classifiers that summarize history of repeated play according to a weighted sum of empirical frequency of the outcomes of the stage game, and a decision unit that chooses an action in each period based on the summaries of the classifiers. Each player maximizes his long run average payoff, while minimizing the complexity cost of implementing his strategy through a network, measured by its number of classifiers. We examine locally stable equilibria where the selected networks are robust against small perturbations. In any locally stable equilibrium, no player uses a network with more than a single classifier. Moreover, the set of locally stable equilibrium payoff vectors lies on two line segments in the payoff space of the stage game.

Winter 2016

ECON420 Optimization and Economic Theory Sections

An introduction to static and dynamic optimization methods with economic applications.