I study sequential contests where the efforts of earlier players may be disclosed to later players by nature or by design. The model has many applications, including rent seeking, R&D, oligopoly, public goods provision, and tragedy of the commons. I show that information about other players' efforts increases the total effort. Thus, the total effort is maximized with full transparency and minimized with no transparency. I also show that in addition to the first-mover advantage, there is an earlier-mover advantage. Finally, I derive the limits for large contests and discuss the limit to perfectly competitive outcomes under different disclosure rules.
Externalities in Knowledge Production: Evidence from a Randomized Field Experiment
. Are there positive or negative externalities in knowledge production? We analyze whether current contributions to knowledge production increase or decrease the future growth of knowledge. To assess this, we use a randomized field experiment that added content to some pages in Wikipedia while leaving similar pages unchanged.
We compare subsequent content growth over the next four years between the treatment and control groups. Our estimates allow us to rule out effects on four-year growth of content length larger than twelve percent. We can also rule out effects on four-year growth of content quality larger than four points, which is less than one-fifth of the size of the treatment itself.
The treatment increased editing activity in the first two years, but most of these edits only modified the text added by the treatment.
Our results have implications for information seeding and incentivizing contributions. They imply that additional content may inspire future contributions in the short- and medium-term but do not generate large externalities in the long term.
We document a causal impact of online user-generated information on real-world economic outcomes. In particular, we conduct a randomized field experiment to test whether additional content on Wikipedia pages about cities affects tourists' choices of overnight visits. Our treatment of adding information to Wikipedia increases overnight stays in treated cities compared to non-treated cities. The impact is largely driven by improvements to shorter and relatively incomplete pages on Wikipedia. Our findings highlight the value of content in digital public goods for informing individual choices.
The standard model of sequential capacity choices is the Stackelberg quantity leadership model with linear demand. I show that under the standard assumptions, leaders' actions are informative about market conditions and independent of leaders' beliefs about the arrivals of followers. However, this Stackelberg independence property relies on all standard assumptions being satisfied. It fails to hold whenever the demand function is non-linear, marginal cost is not constant, goods are differentiated, firms are non-identical, or there are any externalities. I show that small deviations from the linear demand assumption may make the leaders' choices completely uninformative.
Before purchase, a buyer of an experience good learns about the product's fit using various information sources, including some of which the seller may be unaware of. The buyer, however, can conclusively learn the fit only after purchasing and trying out the product. We show that the seller can use a simple mechanism to best take advantage of the buyer's post-purchase learning to maximize his guaranteed-profit. We show that this mechanism combines a generous refund, which performs well when the buyer is relatively informed, with non-refundable random discounts, which work well when the buyer is relatively uninformed.
Risk-neutral sellers can extract high profits from risk-loving buyers by selling them lotteries. To limit risk-taking, gambling is heavily regulated in most countries. I show that protecting risk-loving buyers is essentially impossible.
Even if buyers are risk-loving only asymptotically, the seller can construct a non-random winner-pays auction that ensures unbounded profits. Buyers are asymptotically risk-loving, for example, when their preferences satisfy Savage's axioms or they have cumulative prospect theory preferences. The profits are unbounded even if the seller cannot use any mechanism that resembles a lottery. Asymptotically risk-loving preferences are both sufficient and necessary for unbounded profits.
We consider optimal pricing policies for airlines when passengers are uncertain at the time of ticketing of their eventual willingness to pay for air travel. Auctions at the time of departure efficiently allocate space and a profit maximizing airline can capitalize on these gains by overbooking flights and repurchasing excess tickets from those passengers whose realized value is low. Nevertheless profit maximization entails distortions away from the efficient allocation. Under standard regularity conditions we show that the optimal mechanism can be implemented by a modified double auction. In order to encourage early booking, passengers who purchase late are disadvantaged. In order to capture the information rents of passengers with high expected values, ticket repurchases at the time of departure are at a subsidized price, sometimes leading to unused capacity.
I study a repeated mechanism design problem where a revenue-maximizing monopolist sells a fixed number of service slots to randomly arriving buyers with private values and increasing exit rates. In addition to characterizing the fully optimal mechanism, I study the optimal mechanisms in two restricted classes. First, the pure calendar mechanism, where the seller allocates future service dates instead of general promises. The unique optimal pure calendar mechanism is characterized in terms of the opportunity costs of allocating additional service slots. Second, I analyze the waiting list mechanism, where promises of delayed service can depend on future arrivals, but the seller cannot discriminate among buyers who are offered the same position in the waiting list. Both the waiting list and the fully optimal mechanism are implemented by non-standard auctions with a scoring rule where the distance between buyers' bids affects the allocation. A novel property of these auctions is that for buyers it is better to win by a close margin and it is worse to lose by a close margin. Finally, I model partial commitment power as a penalty that the seller has to pay when forfeiting a promise. All the results are given for general partial commitment and therefore include full commitment and no commitment as special cases.
This paper studies penny auctions, a novel auction format in which every bid increases the price by a small amount, but placing a bid is costly. Outcomes of real-life penny auctions are often surprising. Even when selling cash, the seller may obtain revenue that is much higher or lower than its nominal value, and losers in an auction sometimes pay much more than the winner. This paper characterizes all symmetric Markov-perfect equilibria of penny auctions and studies penny auctions' properties. The results show that a high variance of outcomes is a natural property of the penny auction format and high revenues are inconsistent with rational risk-neutral participants.
We study a buyer-seller problem of a novel good for which the seller does not yet know the production cost. A contract can be agreed upon at either the ex-ante stage, before learning the cost, or at the ex-post stage, when both parties will incur a costly delay, but the seller knows the production cost. We show that the optimal ex-ante contract for a profit-maximizing seller is a fixed price contract with an ``at-will'' clause: the seller can choose to cancel the contract upon discovering her production cost. However, sometimes the seller can do better by offering a guaranteed-delivery price at the ex-ante stage and a second price at the ex-post stage if the buyer rejects the first offer. Such a ``limited commitment'' mechanism can raise profits, allowing the seller to make the allocation partially dependent on the cost while not requiring it to be embedded in the contract terms. Analogous results hold in a model where the buyer does not know her valuation ex-ante and offers a procurement contract to a seller.
We study partial commitment in leader-follower games. A collection of subsets covering the leader's action space determines her commitment opportunities. We characterize the outcomes resulting from all possible commitment structures of this kind. If the commitment structure is an interval partition, then the leader's payoff is bounded by the payoffs she obtains under the full and no-commitment benchmarks. We apply our results to study new design problems.
Influencer marketing is a large and growing but mostly unregulated industry.
The majority of influencers are not paid based on their marketing campaigns' success. Instead, their prices are based on engagement (number of likes and comments). This gives incentives for fraudulent behavior---for inflating engagement. We study influencer cartels, where groups of influencers collude to increase engagement to improve their market outcomes. Our theoretical model shows that such cartels mitigate the free-rider problem and may increase or decrease welfare, depending on the quality of induced engagement. We use a novel dataset of Instagram influencer cartels and confirm that the cartels increase engagement as intended. Importantly, we show that engagement from non-specific cartels is of lower quality, whereas engagement from topic-specific cartels may be as good as natural engagement. Therefore topic-specific cartels may sometimes be welfare-improving, whereas typical non-specific cartels hurt everyone.
Most products are produced and sold by supply chain networks, where an interconnected network of producers and intermediaries set prices to maximize their profits. I show that there exists a unique equilibrium in a price-setting game on a network. The key distortion reducing both total profits and social welfare is multiple-marginalization, which is magnified by strategic interactions. Individual profits are proportional to influentiality, a new measure of network centrality defined by the equilibrium characterization. The results emphasize the importance of the network structure when considering policy questions such as mergers or trade tariffs.
I study optimal disclosure policies in sequential contests. A contest designer chooses at which periods to publicly disclose the efforts of previous contestants. I provide results for a wide range of possible objectives for the contest designer. While different objectives involve different trade-offs, I show that under many circumstances the optimal contest is one of the three basic contest structures widely studied in the literature: simultaneous, first-mover, or sequential contest.