Mathematical Social Sciences最新文献

This paper examines the conditions under which separating outcomes occur in informed persuasion, that is, in Bayesian persuasion settings in which the sender is privately informed about the payoff-relevant state prior to committing to an experiment. We consider a setting with finite payoff-relevant states and sender payoffs that are continuous and monotonic in the receiver’s posterior beliefs. The paper finds that if full disclosure of the payoff-relevant state reduces the sender’s expected payoff under any common prior (i.e., if the sender’s payoff function is outer concave), then single-crossing properties arise such that the high sender type can separate from the low type by choosing more informative experiments. This single-crossing condition leads to the selection of “least costly” separating equilibria by the D1 criterion, i.e., the sender’s choice of experiment signals his type. Further, separating equilibria are characterized by simple constrained maximization problems.

We consider rent-seeking contests where the impact function, which measures how much impact effort has, takes an exponential form. The resulting contest success function (CSF) is a difference-form CSF and the contest is a difference-form contest. Rent dissipation measures the rent lost due to rent-seeking. Cost functions in our difference-form contest are also exponential. We establish the equivalence between such difference-form contests and Tullock contests. We then solve finite-player symmetric difference-form contests in closed form. But if there are asymmetries, the contest cannot be solved. We, therefore, approximate an asymmetric difference-form contest with a large population contest, which can be solved. Rent dissipation in the large population contest is the ratio of the elasticity of the impact function to that of the cost function. Hence, this ratio also approximates rent dissipation in a finite-player contest.

We introduce the anonymity group, the neutrality group and the symmetry group of a social preference function. Inspired by an unsolved problem posed by Kelly in 1991, we investigate the problem of recognizing which permutation groups may arise as anonymity, neutrality and symmetry groups of a social preference function. A complete description is provided for neutrality groups. In the case of anonymity groups, we derive a sufficient condition, which largely captures the desired class of objects. Our approach also is of relevance for the notion of representability by Boolean functions and, therefore, the results of this paper also shed some light on this field of study.

We study the structure of probabilistic voting rules that are ordinal Bayesian incentive compatible (OBIC) with respect to independently distributed prior beliefs that can be considered generic (Majumdar and Sen (2004)). We first identify a class of priors, such that for each prior in that class there exists a probabilistic voting rule that puts a positive probability weight on “compromise” candidates. The class of priors include generic priors. Next, we consider a class of randomized voting rules that have a “finite range”. For this class of rules, we identify an appropriate generic condition on priors such that, any rule in this class is OBIC with respect to a prior satisfying the generic condition if and only if the rule is a random dictatorship.

We study a setting where a receiver must design a questionnaire to recover a sequence of symbols known to a strategic sender, whose utility may not be incentive compatible. We allow the receiver the possibility of selecting the alternatives presented in the questionnaire, and thereby linking decisions across the components of the sequence. We show that, despite the strategic sender and the noise in the channel, the receiver can recover exponentially many sequences, but also that exponentially many sequences are unrecoverable even by the best strategy. We define the growth rate of the number of recovered sequences as the information extraction capacity. A generalization of the Shannon capacity, it characterizes the optimal amount of communication resources required while communicating with a strategic sender. We derive bounds leading to an exact evaluation of the information extraction capacity in many cases. Our results form the building blocks of a novel, non-cooperative regime of communication involving a strategic sender.

Two acts are comonotonic if they co-vary in the same direction. The main purpose of this paper is to derive a new characterization of Cumulative Prospect Theory (CPT) through simple properties involving comonotonicity. The main novelty is a concept dubbed gain–loss hedging: mixing positive and negative acts creates hedging possibilities even when acts are comonotonic. This allows us to clarify in which sense CPT differs from Choquet expected utility. Our analysis is performed under the assumption that acts are real-valued functions. This entails a simple (piece-wise) constant marginal utility representation of CPT, which allows us to clearly separate the perception of uncertainty from the evaluation of outcomes.