Information transmission in monopolistic credence goods markets

We study a general credence goods model with N problem types and N treatments. Communication between the expert seller and the client is modeled as cheap talk. We find that the expert's equilibrium payoffs admit a geometric characterization, described by the quasiconcave envelope of his belief-based profits function under discriminatory pricing. We establish the existence of client-worst equilibria, apply the geometric characterization to previous research on credence goods, and provide a necessary and sufficient condition for when communication benefits the expert. For the binary case, we solve for all equilibria and characterize client's possible welfare among all equilibria.Comment: 34 page

The optimality of (stochastic) veto delegation

We analyze the optimal delegation problem between a principal and an agent, assuming that the latter has state-independent preferences. Among all incentive-compatible direct mechanisms, the veto mechanisms -- in which the principal commits to mixing between the status quo option and another state-dependent option -- yield the highest expected payoffs for the principal. In the optimal veto mechanism, the principal uses veto (i.e., choosing the status quo option) only when the state is above some threshold, and both the veto probability and the state-dependent option increase as the state gets more extreme. Our model captures the aspect of many real-world scenarios that the agent only cares about the principal's final decision, and the result provides grounds for the veto delegation pervasive in various organizations.Comment: 47 pages including Appendi

Convolution theorems associated with quaternion linear canonical transform and applications

Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are consistent once in complex or real space. Various types of convolution formulas are discussed. Consequently, the QLCT of the convolution of two quaternionic functions can be implemented by the product of their QLCTs, or the summation of the products of their QLCTs. As applications, correlation operators and theorems of the QLCT are derived. The proposed convolution formulas are used to solve Fredholm integral equations with special kernels. Some systems of second-order partial differential equations, which can be transformed into the second-order quaternion partial differential equations, can be solved by the convolution formulas as well. As a final point, we demonstrate that the convolution theorem facilitates the design of multiplicative filters

Fixed-time control of delayed neural networks with impulsive perturbations

This paper is concerned with the fixed-time stability of delayed neural networks with impulsive perturbations. By means of inequality analysis technique and Lyapunov function method, some novel fixed-time stability criteria for the addressed neural networks are derived in terms of linear matrix inequalities (LMIs). The settling time can be estimated without depending on any initial conditions but only on the designed controllers. In addition, two different controllers are designed for the impulsive delayed neural networks. Moreover, each controller involves three parts, in which each part has different role in the stabilization of the addressed neural networks. Finally, two numerical examples are provided to illustrate the effectiveness of the theoretical analysis

Research on Multi-Dimensional Dynamic Clustering Method of Big Data Alliance Users

In order to improve the clustering accuracy of big data alliance users, this paper studies users\u27 dynamic clustering based on their multi-dimensional attributes. First of all, the user profile of big data alliance is constructed from five dimensions of user basic attribute, domain attribute, preference attribute, social attribute and value attribute. And the K-means algorithm is used to cluster user profiles to complete the initial clustering. Then, based on the group user profile, combined with the user\u27s recent dynamic behavior data, the FCM algorithm is used to achieve secondary clustering. Finally, the proposed user clustering method is tested by recommending data resources to the clustered user groups. The experimental results show that the user clustering method proposed in this paper has higher accuracy and lower error rate