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. This paper studies a generalized class of restless multi-armed bandits with hidden states and allow cumulative feedback, as opposed to the conventional instantaneous feedback. We call them lazy restless bandits (LRBs) as the events of decision making are sparser than the events of state transition. Hence, feedback after each decision event is the cumulative effect of the following state transition events. The states of arms are hidden from the decision maker and rewards for actions are state dependent. The decision maker needs to choose one arm in each decision interval, such that the long-term cumulative reward is maximized. As the states are hidden, the decision maker maintains and updates its belief about them. It is shown that LRBs admit an optimal policy which has threshold structure in belief space. The Whittle-index policy for solving the LRB problem is analyzed; indexability of LRBs is shown. Further, the closed-form index expressions are provided for two sets of special cases; for more general cases, an algorithm for index computation is provided. An extensive simulation study is presented; Whittle-index, modified Whittle-index, and myopic policies are compared. The Lagrangian relaxation of the problem provides an upper bound on the optimal value function; it is used to assess the degree of sub-optimality various policies. We consider settings in which we wish to incentivize myopic agents (such as Airbnb landlords, who may emphasize short-term profits and property safety) to treat arriving clients fairly, in order to prevent overall discrimination against individuals or groups. We model such settings in both classical and contextual bandit models in which the myopic agents maximize rewards according to current empirical averages, but are also amenable to exogenous payments that may cause them to alter their choices. Our notion of fairness asks that more qualified individuals are never (probabilistically) preferred over less qualified ones []. We investigate whether it is possible to design inexpensive subsidy or payment schemes for a principal to motivate myopic agents to play fairly in all or almost all rounds. When the principal has full information about the state of the myopic agents, we show it is possible to induce fair play on every round with a subsidy scheme of total cost @math (for the classic setting with @math arms, @math , and for the @math -dimensional linear contextual setting @math ). If the principal has much more limited information (as might often be the case for an external regulator or watchdog), and only observes the number of rounds in which members from each of the @math groups were selected, but not the empirical estimates maintained by the myopic agent, the design of such a scheme becomes more complex. We show both positive and negative results in the classic and linear bandit settings by upper and lower bounding the cost of fair subsidy schemes. This paper considers agency in the setting of embodied or active inference. In brief, we associate a sense of agency with prior beliefs about action and ask what sorts of beliefs underlie optimal behaviour. In particular, we consider prior beliefs that action minimises the Kullback-Leibler divergence between desired states and attainable states in the future. This allows one to formulate bounded rationality as approximate Bayesian inference that optimises a free energy bound on model evidence. We show that constructs like expected utility, exploration bonuses, softmax choice rules and optimism bias emerge as natural consequences of this formulation. Previous accounts of active inference have focused on predictive coding and Bayesian filtering schemes for minimising free energy. Here, we consider variational Bayes as an alternative scheme that provides formal constraints on the computational anatomy of inference and action – constraints that are remarkably consistent with neuroanatomy. Furthermore, this scheme contextualises optimal decision theory and economic (utilitarian) formulations as pure inference problems. For example, expected utility theory emerges as a special case of free energy minimisation, where the sensitivity or inverse temperature (of softmax functions and quantal response equilibria) has a unique and Bayes-optimal solution – that minimises free energy. This sensitivity corresponds to the precision of beliefs about behaviour, such that attainable goals are afforded a higher precision or confidence. In turn, this means that optimal behaviour entails a representation of confidence about outcomes that are under an agent's control.