We investigate the conventional wisdom that competition among interested parties attempting to influence a decision maker by providing verifiable information brings out all the relevant information. We find that, if the decision maker is strategically sophisticated and well informed about the relevant variables and about the preferences of the interested party or parties, competition may be unnecessary; while if the decision maker is unsophisticated or not well informed, competition is not generally sufficient. However, if the interested parties' interests are sufficiently opposed, or if the decision maker is seeking to advance the parties' decision maker's need for prior knowledge about the relevant variables and for strategic sophistication. In other settings, only the combination of competition among information providers and a sophisticated skepticism is sufficient to allow defective decision making.

Relying on the Information of Interested Parties

In this paper, I construct an equilibrium for markets with frictions, which is competitive in the sense that all agents are price takers and maximize utility subject to a set of market parameters. I show that the equilibrium allocation is socially optimal. I also show how the competitive search equilibrium can be achieved if employers with vacancies can advertise publicly the wages they pay.

Competitive Search Equilibrium

We examine a market in which long-lived firms face a short-term incentive to exert low effort, but could earn higher profits if it were possible to commit to high effort. There are two types of firms, "inept" firms who can only exert low effort, and "competent" firms who have a choice between high and low effort. There is occasional exit, and competent and inept potential entrants compete for the right to inherit the departing firm's reputation. Consumers receive noisy signals of effort choice, and so competent firms choose high effort in an attempt to distinguish themselves from inept firms. A competent firm is most likely to enter the market by purchasing an average reputation, in the hopes of building it into a good reputation, than either a very low reputation or a very high reputation. Inept firms, in contrast, find it more profitable to either buy high reputations and deplete them or buy low reputations.

Who wants a good reputation

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Recursive Methods In Economic Dynamics

The first price auction is the auction procedure awarding the item to the highest bidder at the price equal to his bid. Much attention has been devoted to the two bidder case or to the symmetric case where the bidders' valuations are identically and independently distributed. We consider the general case where the valuations' distributions may be different. Furthermore, we allow an arbitrary number of bidders as well as mixed strategies. We show that every Bayesian equilibrium is an " essentially " pure equilibrium formed by bid functions whose inverses are solutions of a system of differential equations with boundary conditions. We then prove the existence of a Bayesian equilibrium. We prove the uniqueness of the equilibrium when the valuation distributions have a mass point at the lower extremity of the support. When every bidder's valuation distribution is one of two atomless distributions, we give assumptions under which the equilibrium is unique. The n-tuples of distributions that result from symmetric settings after some bidders have colluded satisfy these assumptions. We establish inequalities between equilibrium strategies when relations of stochastic dominance exist between valuation distributions.

First Price Auctions in the Asymmetric N Bidder Case

We consider a class of multi-sender persuasion games that accommodate both sequential and simultaneous moves. If information can be arbitrarily correlated and new senders are added at the beginning of the game, then information cannot be lost. In contrast, we provide examples where the addition of a sender results in a loss of information when (i) senders move sequentially and a new sender is added after the pre-existing players; (ii) senders move simultaneously, and signals are not arbitrarily correlated; (iii) senders move simultaneously and mixed strategies are allowed. We also reinterpret the model with coordinated signals as one where senders moves sequentially and observe the history of experimental designs as well as the outcomes.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID2557043_code1535204.pdf?abstractid=2505277&mirid=4

On Bayesian Persuasion with Multiple Senders

A profit-maximizing monopolist seller has a fixed number of identical goods to sell before a deadline. Over time, buyers privately enter the market, and they strategically time their purchases. In the unique Markov perfect equilibrium, the seller sporadically holds fire sales to lower the stock of goods. This increases future buyers' willingness to pay, but it also lowers the willingness to pay of buyers who arrive early in the game. On the path of play, only one unit is offered in each fire sale, so buyers may be rationed. Interestingly, at the limit where the probability of a buyer being rationed vanishes, the seller gets rid of all but one unit of the good during a "big" initial fire sale.

Revenue Management Without Commitment: Dynamic Pricing and Periodic Flash Sales

https://www.sv.uio.no/esop/english/research/news-and-events/events/guest-lectures-seminars/esop-seminar/dokumenter/on-bayesian-persuasion-with-multiple-senders.pdf

On Bayesian persuasion with multiple senders

We propose a theory of reputation to explain how investors rationally respond to mutual fund star ratings. A fund's performance is determined by its information advantage, which can be acquired but decays stochastically. Investors form beliefs about whether the fund is informed based on its past performance. We refer to such beliefs as fund reputation, which determines fund flows. As performance changes continuously, equilibrium fund reputation may take discrete values only and thus can be labeled with stars. Star upgrades thus imply reputation jumps, leading to discrete increases in flows and expected performance, although stars do not provide new information.

Star Ratings and the Incentives of Mutual Funds

A seller has a fixed number of goods to sell by a deadline. At each time, he posts a regular price and decides whether to hold a flash sale. Over time, buyers privately enter the market and strategically time their purchases. If a buyer does not purchase when she arrives, she can pay an attention cost to recheck the regular price afterwards, or she can wait for future flash sales where she may obtain a good at a discounted price. In the unique Markov perfect equilibrium, the seller sporadically holds flash sales to lower the stock of goods. A flash sale increases the willingness to pay of future buyers, but decreases the willingness to pay of buyers who arrive early in the game. When it is very likely that a buyer will obtain a good in a flash sale, the seller holds a “big” initial flash sale for all but one unit of the good.

Fei Li

Papers

On Bayesian Persuasion with Multiple Senders

Revenue Management Without Commitment: Dynamic Pricing and Periodic Flash Sales

On Bayesian persuasion with multiple senders

Star Ratings and the Incentives of Mutual Funds

Revenue Management without Commitment: Dynamic Pricing and Periodic Flash Sales