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on Contract Theory and Applications |
| By: | Xiaoyun Qiu; Liren Shan |
| Abstract: | How should one jointly design tests and the arrangement of agencies to administer these tests (testing procedure)? To answer this question, we analyze a model where a principal must use multiple tests to screen an agent with a multi-dimensional type, knowing that the agent can change his type at a cost. We identify a new tradeoff between setting difficult tests and using a difficult testing procedure. We compare two settings: (1) the agent only misrepresents his type (manipulation) and (2) the agent improves his actual type (investment). Examples include interviews, regulations, and data classification. We show that in the manipulation setting, stringent tests combined with an easy procedure, i.e., offering tests sequentially in a fixed order, is optimal. In contrast, in the investment setting, non-stringent tests with a difficult procedure, i.e., offering tests simultaneously, is optimal; however, under mild conditions offering them sequentially in a random order may be as good. Our results suggest that whether the agent manipulates or invests in his type determines which arrangement of agencies is optimal. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.12264 |
| By: | Zexin Ye |
| Abstract: | When the current demand shock is observable, with a high discount factor, Q-learning agents predominantly learn to implement symmetric rigid pricing, i.e., they charge constant prices across demand states. Under this pricing pattern, supra-competitive profits can still be obtained and are sustained through collusive strategies that effectively punish deviations. This shows that Q-learning agents can successfully overcome the stronger incentives to deviate during the positive demand shocks, and consequently algorithmic collusion persists under observed demand shocks. In contrast, with a medium discount factor, Q-learning agents learn that maintaining high prices during the positive demand shocks is not incentive compatible and instead proactively charge lower prices to decrease the temptation for deviating, while maintaining relatively high prices during the negative demand shocks. As a result, the countercyclical pricing pattern becomes predominant, aligning with the theoretical prediction of Rotemberg and Saloner (1986). These findings highlight how Q-learning algorithms can both adapt pricing strategies and develop tacit collusion in response to complex market conditions. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.15084 |
| By: | Rachitesh Kumar; Omar Mouchtaki |
| Abstract: | First-price auctions are one of the most popular mechanisms for selling goods and services, with applications ranging from display advertising to timber sales. Unlike their close cousin, the second-price auction, first-price auctions do not admit a dominant strategy. Instead, each buyer must design a bidding strategy that maps values to bids -- a task that is often challenging due to the lack of prior knowledge about competing bids. To address this challenge, we conduct a principled analysis of prior-independent bidding strategies for first-price auctions using worst-case regret as the performance measure. First, we develop a technique to evaluate the worst-case regret for (almost) any given value distribution and bidding strategy, reducing the complex task of ascertaining the worst-case competing-bid distribution to a simple line search. Next, building on our evaluation technique, we minimize worst-case regret and characterize a minimax-optimal bidding strategy for every value distribution. We achieve it by explicitly constructing a bidding strategy as a solution to an ordinary differential equation, and by proving its optimality for the intricate infinite-dimensional minimax problem underlying worst-case regret minimization. Our construction provides a systematic and computationally-tractable procedure for deriving minimax-optimal bidding strategies. When the value distribution is continuous, it yields a deterministic strategy that maps each value to a single bid. We also show that our minimax strategy significantly outperforms the uniform-bid-shading strategies advanced by prior work. Our result allows us to precisely quantify, through minimax regret, the performance loss due to a lack of knowledge about competing bids. We leverage this to analyze the impact of the value distribution on the performance loss, and find that it decreases as the buyer's values become more dispersed. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.09907 |
| By: | Kento Hashimoto; Keita Kuwahara; Reo Nonaka |
| Abstract: | Finding the optimal (revenue-maximizing) mechanism to sell multiple items has been a prominent and notoriously difficult open problem. Existing work has mainly focused on deriving analytical results tailored to a particular class of problems (for example, Giannakopoulos (2015) and Yang (2023)). The present paper explores the possibility of a generally applicable methodology of the Automated Mechanism Design (AMD). We first employ the deep learning algorithm developed by D\"utting et al. (2023) to numerically solve small-sized problems, and the results are then generalized by educated guesswork and finally rigorously verified through duality. By focusing on a single buyer who can consume one item, our approach leads to two key contributions: establishing a much simpler way to verify the optimality of a wide range of problems and discovering a completely new result about the optimality of grand bundling. First, we show that selling each item at an identical price (or equivalently, selling the grand bundle of all items) is optimal for any number of items when the value distributions belong to a class that includes the uniform distribution as a special case. Different items are allowed to have different distributions. Second, for each number of items, we established necessary and sufficient conditions that $c$ must satisfy for grand bundling to be optimal when the value distribution is uniform over an interval $[c, c + 1]$. This latter model does not satisfy the previously known sufficient conditions for the optimality of grand bundling Haghpanah and Hartline (2021). Our results are in contrast to the only known results for $n$ items (for any $n$), Giannakopoulos (2015) and Daskalakis et al. (2017), which consider a single buyer with additive preferences, where the values of items are narrowly restricted to i.i.d. according to a uniform or exponential distribution. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.10086 |