Rationality-Robust Information Design: Bayesian Persuasion under Quantal Response

Classic mechanism/information design imposes the assumption that agents are fully rational, meaning each of them always selects the action that maximizes her expected utility. Yet many empirical evidence suggests that human decisions may deviate from this full rationality assumption. In this work, we attempt to relax the full rationality assumption with bounded rationality. Specifically, we formulate the bounded rationality of an agent by adopting the quantal response model (McKelvey and Palfrey, 1995). We develop a theory of rationality-robust information design in the canonical setting of Bayesian persuasion (Kamenica and Gentzkow, 2011) with binary receiver action. We first identify conditions under which the optimal signaling scheme structure for a fully rational receiver remains optimal or approximately optimal for a boundedly rational receiver. In practice, it might be costly for the designer to estimate the degree of the receiver's bounded rationality level. Motivated by this practical consideration, we then study the existence and construction of robust signaling schemes when there is uncertainty about the receiver's bounded rationality level

Flow Structures of Gaseous Jets Injected into Water for Underwater Propulsion

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90659/1/AIAA-2011-185-740.pd

Competitive Information Disclosure with Multiple Receivers

This paper analyzes a model of competition in Bayesian persuasion in which two symmetric senders vie for the patronage of multiple receivers by disclosing information about the qualities (i.e., binary state -- high or low) of their respective proposals. Each sender is allowed to commit to a signaling policy where he sends a private (possibly correlated) signal to every receiver. The sender's utility is a monotone set function of receivers who make a patron to this sender. We characterize the equilibrium structure and show that the equilibrium is not unique (even for simple utility functions). We then focus on the price of stability (PoS) in the game of two senders -- the ratio between the best of senders' welfare (i.e., the sum of two senders' utilities) in one of its equilibria and that of an optimal outcome. When senders' utility function is anonymous submodular or anonymous supermodular, we analyze the relation between PoS with the ex ante qualities $\lambda$ (i.e., the probability of high quality) and submodularity or supermodularity of utility functions. In particular, in both families of utility function, we show that $\text{PoS} = 1$ when the ex ante quality $\lambda$ is weakly smaller than $1/2$, that is, there exists equilibrium that can achieve welfare in the optimal outcome. On the other side, we also prove that $\text{PoS} > 1$ when the ex ante quality $\lambda$ is larger than $1/2$, that is, there exists no equilibrium that can achieve the welfare in the optimal outcome. We also derive the upper bound of $\text{PoS}$ as a function of $\lambda$ and the properties of the value function. Our analysis indicates that the upper bound becomes worse as the ex ante quality $\lambda$ increases or the utility function becomes more supermodular (resp.\ submodular)

Performative Prediction with Bandit Feedback: Learning through Reparameterization

Performative prediction, as introduced by Perdomo et al. (2020), is a framework for studying social prediction in which the data distribution itself changes in response to the deployment of a model. Existing work on optimizing accuracy in this setting hinges on two assumptions that are easily violated in practice: that the performative risk is convex over the deployed model, and that the mapping from the model to the data distribution is known to the model designer in advance. In this paper, we initiate the study of tractable performative prediction problems that do not require these assumptions. To tackle this more challenging setting, we develop a two-level zeroth-order optimization algorithm, where one level aims to compute the distribution map, and the other level reparameterizes the performative prediction objective as a function of the induced data distribution. Under mild conditions, this reparameterization allows us to transform the non-convex objective into a convex one and achieve provable regret guarantees. In particular, we provide a regret bound that is sublinear in the total number of performative samples taken and only polynomial in the dimension of the model parameter

Formation of amyloid fibrils from β-amylase

AbstractFibril formation has been considered a significant feature of amyloid proteins. However, it has been proposed that fibril formation is a common property of many proteins under appropriate conditions. We studied the fibril formation of β-amylase, a non-amyloid protein rich in α-helical structure, because the secondary structure of β-amylase is similar to that of prions. With the conditions for the fibril formation of prions, β-amylase proteins were converted into amyloid fibrils. The features of β-amylase proteins and fibrils are compared to prion proteins and fibrils. Furthermore, the cause of neurotoxicity in amyloid diseases is discussed.Structured summary of protein interactionsBeta-Amylase and Beta-Amylase bind by fluorescence technology (View Interaction: 1, 2) MoPrP and MoPrP bind by circular dichroism (View interaction) MoPrP and MoPrP bind by transmission electron microscopy (View interaction) Beta-Amylase and Beta-Amylase bind by circular dichroism (View interaction) MoPrP and MoPrP bind by fluorescence technology (View Interaction: 1, 2) Beta-Amylase and Beta-Amylase bind by transmission electron microscopy (View interaction