Online Information Acquisition: Hiring Multiple Agents
Federico Cacciamani, Matteo Castiglioni, Nicola Gatti
TL;DR
This paper studies the design of mechanisms for a principal hiring multiple agents to gather costly information, addressing coordination, effort correlation, and online learning challenges, and providing algorithms with provable guarantees.
Contribution
It introduces a polynomial-time algorithm for optimal incentive-compatible mechanisms in multi-agent information acquisition and develops a no-regret online learning algorithm for repeated interactions.
Findings
Optimal mechanisms must correlate agents' efforts, creating externalities.
The polynomial-time algorithm efficiently finds incentive-compatible mechanisms.
The online algorithm achieves T^{2/3} regret, matching single-agent bounds.
Abstract
We investigate the mechanism design problem faced by a principal who hires \emph{multiple} agents to gather and report costly information. Then, the principal exploits the information to make an informed decision. We model this problem as a game, where the principal announces a mechanism consisting in action recommendations and a payment function, a.k.a. scoring rule. Then, each agent chooses an effort level and receives partial information about an underlying state of nature based on the effort. Finally, the agents report the information (possibly non-truthfully), the principal takes a decision based on this information, and the agents are paid according to the scoring rule. While previous work focuses on single-agent problems, we consider multi-agents settings. This poses the challenge of coordinating the agents' efforts and aggregating correlated information. Indeed, we show that…
Peer Reviews
Decision·ICLR 2024 poster
-The problem seems well-motivated and the model captures a wide set of applications. -I think the paper has interesting results such as characterization of optimality and suboptimality of uncorrelated mechanisms in section 4. -I did not check the proofs carefully. But the technical details in the paper seem interesting.
A-The presentation of the paper can be improved. There seem to be some missing text, see the following: 1-what is the auxiliary variables z_i in eq (2c) equal to? Further, Theorem 3.1 has a collection of values C_1, C_n, have they been specified? 2-3rd line in section 2, why are some c’s (for the cost function) capitalized and others are not 3-in the cumulative regret formula on page 6, why is T’_c not included is it because it is assumed to be empty, I
1. Algorithmic Design and Optimization in Multi-Agent Settings: This paper works on designing an efficient algorithm for the multi-agent information acquisition problem, addressing both the optimization and online learning dimensions of interactions between a principal and unknown agents. The proposed algorithm, which navigates through a quadratic optimization problem via linear relaxation, culminates in a polynomial-time solution to the original problem. 2. Addressing Uncertainty in Online Le
1. This paper would benefit significantly from the inclusion of empirical demonstrations to substantiate the theoretical assertions made therein. 2. In terms of sample size efficiency, the paper presents an opportunity for enhancement through the integration of more sample-efficient online learning algorithms, such as Upper Confidence Bound (UCB) or Thompson Sampling. These methodologies hold potential for yielding a more favorable regret profile. 3. The articulation throughout the paper nece
For originality, the authors formulation of the information elicitation problem under the multi-agent setting. I appreciate the discussions of the computation issue and the separation between the correlated/uncorrelated scoring mechanism. Overall, the paper is well written, but a little bit redundant in terms of the notations. The paper achieves state-of-art learning guarantee for the multiple-agent setting. The algorithm design and the analysis look sound to me.
1. The authors should make it clear if agents can communicate with each other their signals/actions or not, as this can cause a huge difference. I understood that the agents cannot communicate with each other by forms of the deviation functions. Please correct me if I'm wrong. 2. There are some typos that could cause confusions, e.g., it should be $\sum_{s'\in\mathcal{S}:s_i'=s_i\mathbb{P}(s' \| b, \theta)}$ at the bottom of Page 2. 3. The authors may need to justify Assumption 1, perhaps by pr
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Taxonomy
TopicsAuction Theory and Applications · Game Theory and Applications · Experimental Behavioral Economics Studies