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.
In the context of multi-agent settings with no externalities, Arieli and Babichenko @cite_10 look at a model where the principal is trying to persuade individuals to adopt a product by sending signals. They characterize the optimal policy for supermodular, submodular, and supermajority utility functions of the principal. More recent work has been devoted to proving hardness or inefficacy results for finding the optimal information disclosure policy in such settings @cite_12 @cite_6 .
@cite_10 @cite_6 @cite_12
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We study the algorithmics of information structure design --- a.k.a. persuasion or signaling --- in a fundamental special case introduced by Arieli and Babichenko: multiple agents, binary actions, and no inter-agent externalities. Unlike prior work on this model, we allow many states of nature. We assume that the principal's objective is a monotone set function, and study the problem both in the public signal and private signal models, drawing a sharp contrast between the two in terms of both efficacy and computational complexity. When private signals are allowed, our results are largely positive and quite general. First, we use linear programming duality and the equivalence of separation and optimization to show polynomial-time equivalence between (exactly) optimal signaling and the problem of maximizing the objective function plus an additive function. This yields an efficient implementation of the optimal scheme when the objective is supermodular or anonymous. Second, we exhibit a (1-1 e)-approximation of the optimal private signaling scheme, modulo an additive loss of e, when the objective function is submodular. These two results simplify, unify, and generalize results of [Arieli and Babichenko, 2016] and [Babichenko and Barman, 2016], extending them from a binary state of nature to many states (modulo the additive loss in the latter result). Third, we consider the binary-state case with a submodular objective, and simplify and slightly strengthen the result of [Babichenko and Barman, 2016] to obtain a (1-1 e)-approximation via a scheme which (i) signals independently to each receiver and (ii) is "oblivious" in that it does not depend on the objective function so long as it is monotone submodular. When only a public signal is allowed, our results are negative. First, we show that it is NP-hard to approximate the optimal public scheme, within any constant factor, even when the objective is additive. Second, we show that the optimal private scheme can outperform the optimal public scheme, in terms of maximizing the sender's objective, by a polynomial factor. 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 Secretary Problem, one has to hire the best among n candidates. The candidates are interviewed, one at a time, at a random order, and one has to decide on the spot, whether to hire a candidate or continue interviewing. It is well known that the best candidate can be hired with a probability of 1 e (Dynkin, 1963). Recent works extend this problem to settings in which multiple candidates can be hired, subject to some constraint. Here, one wishes to hire a set of candidates maximizing a given set function. Almost all extensions considered in the literature assume the objective set function is either linear or submodular. Unfortunately, real world functions might not have either of these properties. Consider, for example, a scenario where one hires researchers for a project. Indeed, it can be that some researchers can substitute others for that matter. However, it can also be that some combinations of researchers result in synergy (see, e.g, , Science 2010, for a research about collective intelligence). The first phenomenon can be modeled by a submoudlar set function, while the latter cannot. In this work, we study the secretary problem with an arbitrary non-negative monotone function, subject to a general matroid constraint. It is not difficult to prove that, generally, only very poor results can be obtained for this class of objective functions. We tackle this hardness by combining the following: 1.Parametrizing our algorithms by the supermodular degree of the objective function (defined by Feige and Izsak, ITCS 2013), which, roughly speaking, measures the distance of a function from being submodular. 2.Suggesting an (arguably) natural model that permits approximation guarantees that are polynomial in the supermodular degree (as opposed to the standard model which allows only exponential guarantees). In many settings, a decision-maker wishes to learn a rule, or policy, that maps from observable characteristics of an individual to an action. Examples include selecting offers, prices, advertisements, or emails to send to consumers, as well as the problem of determining which medication to prescribe to a patient. While there is a growing body of literature devoted to this problem, most existing results are focused on the case where data comes from a randomized experiment, and further, there are only two possible actions, such as giving a drug to a patient or not. In this paper, we study the offline multi-action policy learning problem with observational data and where the policy may need to respect budget constraints or belong to a restricted policy class such as decision trees. We build on the theory of efficient semi-parametric inference in order to propose and implement a policy learning algorithm that achieves asymptotically minimax-optimal regret. To the best of our knowledge, this is the first result of this type in the multi-action setup, and it provides a substantial performance improvement over the existing learning algorithms. We then consider additional computational challenges that arise in implementing our method for the case where the policy is restricted to take the form of a decision tree. We propose two different approaches, one using a mixed integer program formulation and the other using a tree-search based algorithm.