We study the use of Bayesian persuasion (i.e., strategic use of information disclosure signaling) in endogenous team formation. This is an important consideration in settings such as crowdsourcing competitions, open science challenges and group-based assignments, where a large number of agents organize themselves into small teams which then compete against each other. A central tension here is between the strategic interests of agents who want to have the highest-performing team, and that of the principal who wants teams to be balanced. Moreover, although the principal cannot choose the teams or modify rewards, she often has additional knowledge of agents' abilities, and can leverage this information asymmetry to provide signals that influence team formation. Our work uncovers the critical role of self-awareness (i.e., knowledge of one's own abilities) for the design of such mechanisms. For settings with two-member teams and binary-valued agents partitioned into a constant number of prior classes, we provide signaling mechanisms which are asymptotically optimal when agents are agnostic of their own abilities. On the other hand, when agents are self-aware, then we show that there is no signaling mechanism that can do better than not releasing information, while satisfying agent participation constraints.
The basic idea originates from the seminal work of Kamenica and Gentzkow @cite_14 , which considers a principal who commits to a signaling policy which maps the true state of the world to a signal sent to a single agent, and derives conditions on the principal's utility function under which she strictly benefits from persuasion. Going beyond, @cite_15 consider a dynamic setting in which agents arrive sequentially and choose an action with an unknown (but deterministic) reward. The goal of the principal is to find the optimal disclosure (or recommendation) policy of a planner who wants to maximize social welfare, whereas agents simply seek to maximize their own expected reward. The authors show that the optimal policy is a threshold policy which explores as much as possible, and then always recommends the best action, and obtain a similar near-optimal threshold policy with stochastic rewards; recent papers greatly generalize this line of work @cite_2 @cite_7 .
@cite_15 @cite_14 @cite_7 @cite_2
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We study a novel mechanism design model in which agents each arrive sequentially and choose one action from a set of actions with unknown rewards. The information revealed by the principal affects the incentives of the agents to explore and generate new information. We characterize the optimal disclosure policy of a planner whose goal is to maximize social welfare. One interpretation of our result is the implementation of what is known as the "wisdom of the crowd." This topic has become increasingly relevant with the rapid spread of the Internet over the past decade. In the on-line Explore and Exploit literature, central to Machine Learning, a central planner is faced with a set of alternatives, each yielding some unknown reward. The planner's goal is to learn the optimal alternative as soon as possible, via experimentation. A typical assumption in this model is that the planner has full control over the experiment design and implementation. When experiments are implemented by a society of self-motivated agents the planner can only recommend experimentation but has no power to enforce it. (JPE, 2014) introduce the first study of explore and exploit schemes that account for agents' incentives. In their model it is implicitly assumed that agents do not see nor communicate with each other. Their main result is a characterization of an optimal explore and exploit scheme. In this work we extend (JPE, 2014) by adding a layer of a social network according to which agents can observe each other. It turns out that when observability is factored in the scheme proposed by (JPE, 2014) is no longer incentive compatible. In our main result we provide a tight bound on how many other agents can each agent observe and still have an incentive-compatible algorithm and asymptotically optimal outcome. More technically, for a setting with N agents where the number of nodes with degree greater than N^alpha is bounded by N^beta and 2*alpha+beta < 1 we construct incentive-compatible asymptotically optimal mechanism. The bound 2*alpha+beta < 1 is shown to be tight. Individual decision-makers consume information revealed by the previous decision makers, and produce information that may help in future decision makers. This phenomenon is common in a wide range of scenarios in the Internet economy, as well as elsewhere, such as medical decisions. Each decision maker when required to select an action, would individually prefer to exploit, select the highest expected reward action conditional on her information. At the same time, each decision maker would prefer previous decision makers to explore, producing information about the rewards of various actions. A social planner, by means of carefully designed information disclosure, can incentivize the agents to balance the exploration and exploitation, and maximize social welfare. We formulate this problem as a multi-arm bandit problem (and various generalizations thereof) under incentive-compatibility constraints induced by agents' Bayesian priors. We design an incentive-compatible bandit algorithm for the social planner with asymptotically optimal regret. Further, we provide a black-box reduction from an arbitrary multi-arm bandit algorithm to an incentive-compatible one, with only a constant multiplicative increase in regret. This reduction works for very general bandit settings, even ones that incorporate contexts and arbitrary partial feedback.