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Ian Ball

Publications and source records attributed to Ian Ball.

17 recordsLinked to original sources
arXiv2026

Competitive Sequential Screening

We study competition between firms that contract with consumers before the consumers fully learn their product preferences. In a Hotelling duopoly, firms screen consumers by offering menus of option contracts. We characterize the unique equilibrium. Consumers select contracts from both firms. Each consumer is endogenously locked into the firm from which he chooses an option with a lower strike price. Lock-in yields inefficient consumption. Yet earlier contracting stiffens competition because less informed consumers are more homogeneous. Sufficiently early contracting raises consumer surplus relative to spot pricing -- reversing the ranking under monopoly. Exclusive contracting further increases consumer surplus by intensifying competition.

econ.TH↗
arXiv2025

Checking Cheap Talk

We consider a sender-receiver game in which the receiver's action is binary and the sender's preferences are state-independent. The state is multidimensional. The receiver can select one dimension of the state to check (i.e., observe) before choosing his action. We identify a class of influential equilibria in which the sender's message reveals which components of the state are highest, and the receiver selects one of these components to check. The sender can benefit from communication if and only if she prefers one of these equilibria to the no-communication outcome. Similar equilibria exist when the receiver can check multiple dimensions.

econ.TH↗
arXiv2024

On Regularity and Normalization in Sequential Screening

We comment on the regularity assumptions in the multi-agent sequential screening model of Eso and Szentes (2007). First, we observe that the regularity assumptions are not invariant to relabeling each agent's signal realizations. Second, we show that the regularity assumptions rule out valuation distributions with common bounded support. Third, we show that if each signal realization is labeled to equal the expected valuation, then the regularity assumptions imply that each agent's valuation is equal to his signal realization plus independent mean-zero noise.

econ.TH↗
arXiv2024

Robust Robustness

We propose a refinement of the maxmin approach to robustness. A mechanism's payoff guarantee over an ambiguity set is robust if the guarantee is approximately satisfied at priors near the ambiguity set (in the weak topology). We show that many maxmin-optimal mechanisms in the literature give payoff guarantees that are not robust. Such mechanisms are often tailored to degenerate worst-case priors, making them simple but fragile. Conversely, some commonly used ambiguity sets satisfy a structural property, termed richness, ensuring that every associated payoff guarantee is robust. We show how to slightly enlarge any ambiguity set to make it rich.

econ.TH↗
arXiv2024

Optimal Auction Design with Contingent Payments and Costly Verification

We study the design of an auction for an income-generating asset such as an intellectual property license. Each bidder has a signal about his future income from acquiring the asset. After the asset is allocated, the winner's income from the asset is realized privately. The principal can audit the winner, at a cost, and then charge a payment contingent on the winner's realized income. We solve for an auction that maximizes the principal's revenue, net of auditing costs. The winning bidder is charged linear royalties up to a cap, beyond which there is no auditing. A higher bidder pays more in cash upfront and faces a lower royalty cap.

econ.TH↗
arXiv2023

Benefiting from Bias: Delegating to Encourage Information Acquisition

A principal delegates decisions to a biased agent. Payoffs depend on a state that the principal cannot observe. Initially, the agent does not observe the state, but he can acquire information about it at a cost. We characterize the principal's optimal delegation set. This set features a cap on high decisions and a gap around the agent's ex ante favorite decision. It may even induce ex-post Pareto-dominated decisions. Under certain conditions on the cost of information acquisition, we show that the principal prefers delegating to an agent with a small bias than to an unbiased agent.

econ.TH↗
arXiv2023

Quota Mechanisms: Finite-Sample Optimality and Robustness

A quota mechanism, such as a mandatory grading curve, links together multiple decisions. We analyze the performance of quota mechanisms when the number of linked decisions is finite and the designer has imperfect knowledge of the type distribution. Using a new optimal transport approach, we derive an ex-post decision error guarantee for quota mechanisms. This guarantee cannot be improved by any mechanisms without transfers. We quantify the sensitivity of quota mechanisms to errors in the designer's estimate of the type distribution. Finally, we show that quotas are robust to a range of agents' beliefs about each other.

econ.TH↗
arXiv2023

Should the Timing of Inspections be Predictable?

A principal hires an agent to work on a long-term project that culminates in a breakthrough or a breakdown. At each time, the agent privately chooses to work or shirk. Working increases the arrival rate of breakthroughs and decreases the arrival rate of breakdowns. To motivate the agent to work, the principal conducts costly inspections. She fires the agent if shirking is detected. We characterize the principal's optimal inspection policy. Predictable inspections are optimal if work primarily generates breakthroughs. Random inspections are optimal if work primarily prevents breakdowns. Crucially, the agent's actions affect the survival rate of the project, which determines his risk attitude over the timing of planned inspections.

econ.TH↗
arXiv2023

Dynamic Information Provision: Rewarding the Past and Guiding the Future

I study the optimal provision of information in a long-term relationship between a sender and a receiver. The sender observes a persistent, evolving state and commits to send signals over time to the receiver, who sequentially chooses public actions that affect the welfare of both players. I solve for the sender's optimal policy in closed form: the sender reports the value of the state with a delay that shrinks over time and eventually vanishes. Even when the receiver knows the current state, the sender retains leverage by threatening to conceal the future evolution of the state.

econ.TH↗
arXiv2023

A Unified Theorem of the Alternative

This note presents a unified theorem of the alternative that explicitly allows for any combination of equality, componentwise inequality, weak dominance, strict dominance, and nonnegativity relations. The theorem nests 60 special cases, some of which have been stated as separate theorems.

econ.TH↗
arXiv2022

Content Filtering with Inattentive Information Consumers

We develop a model of content filtering as a game between the filter and the content consumer, where the latter incurs information costs for examining the content. Motivating examples include censoring misinformation, spam/phish filtering, and recommender systems. When the attacker is exogenous, we show that improving the filter's quality is weakly Pareto improving, but has no impact on equilibrium payoffs until the filter becomes sufficiently accurate. Further, if the filter does not internalize the information costs, its lack of commitment power may render it useless and lead to inefficient outcomes. When the attacker is also strategic, improvements to filter quality may sometimes decrease equilibrium payoffs.

econ.TH↗
arXiv2022

Comment on Jackson and Sonnenschein (2007) "Overcoming Incentive Constraints by Linking Decisions"

We correct a bound in the definition of approximate truthfulness used in the body of the paper of Jackson and Sonnenschein (2007). The proof of their main theorem uses a different permutation-based definition, implicitly claiming that the permutation-version implies the bound-based version. We show that this claim holds only if the bound is loosened. The new bound is still strong enough to guarantee that the fraction of lies vanishes as the number of problems grows, so the theorem is correct as stated once the bound is loosened.

econ.TH↗
arXiv2019

Scoring Strategic Agents

I introduce a model of predictive scoring. A receiver wants to predict a sender's quality. An intermediary observes multiple features of the sender and aggregates them into a score. Based on the score, the receiver makes a decision. The sender prefers "higher" decisions, and she can distort each feature at a privately known cost. I characterize the scoring rule that maximizes decision accuracy. This rule underweights some features to deter sender distortion, and overweights other features so that the score is correct on average. The receiver prefers this scoring rule to full disclosure because it mitigates his commitment problem.

econ.TH↗
arXiv2019

Probabilistic Verification in Mechanism Design

We introduce a model of probabilistic verification in mechanism design. The principal elicits a message from the agent and then selects a test to give the agent. The agent's true type determines the probability with which he can pass each test. We characterize whether each type has an associated test that best screens out all other types. If this condition holds, then the testing technology can be represented in a tractable reduced form. We use this reduced form to solve for profit-maximizing mechanisms with verification. As the verification technology varies, the solution continuously interpolates between the no-verification solution and full surplus extraction.

econ.TH↗