We study the equipment sharing problem where a group of food & beverage companies share the same equipment of a contractor and wish to have their processing tasks coordinated such that the total cost is minimized. The raw materials to be processed are perishable, which incur a decay cost as time goes. One key issue of this equipment sharing problem is how to allocate the total cost among the participants. We apply cooperative game theory to tackle this issue and formulate the problem as an equipment sharing game. First, we study the 1-equipment sharing game in which all participants share one equipment. We show that the 1-equipment sharing game is quasi-concave when the fixed operation cost is larger than a certain value. We then discuss the special case where the processing time for all participants is equal. For this case, we further investigate the properties of the 1-equipment sharing game and the multi-equipment sharing game. We identify the conditions under which the Shapely value and the τ-value can be easily calculated for the 1-equipment and multi-equipment sharing games.

In this paper, we provide a new theoretical framework of pyramid Markov processes to solve some open and fundamental problems of blockchain selfish mining under a rigorous mathematical setting. We first describe a more general model of blockchain selfish mining with both a two-block leading competitive criterion and a new economic incentive mechanism. Then we establish a pyramid Markov process and show that it is irreducible and positive recurrent, and its stationary probability vector is matrix-geometric with an explicitly representable rate matrix. Also, we use the stationary probability vector to study the influence of orphan blocks on the waste of computing resource. Next, we set up a pyramid Markov reward process to investigate the long-run average mining profits of the honest and dishonest mining pools, respectively. As a by-product, we build one-dimensional Markov reward processes and provide some new interesting interpretation on the Markov chain and the revenue analysis reported in the seminal work by Eyal and Sirer (2014). Note that the pyramid Markov (reward) processes can open up a new avenue in the study of blockchain selfish mining. Thus we hope that the methodology and results developed in this paper shed light on the blockchain selfish mining such that a series of promising research can be developed potentially.

Scientists may shift research interests and span multiple research areas in their careers, reflecting the research diversification of scientists. Quantifying the scientists’ research diversity can help to understand the research patterns of scientists. In this paper, we study the research diversification of scientists in Physics based on the Physics and Astronomy Classification Scheme (PACS) which can well reflect the research topics of physics papers. For each scientist, we first build a PACS codes co-occurrence network and reveal the research diversity by analyzing the connectivity and community structure of this network. Then we use diversity indicators to measure the research diversification of scientists and analyze the distribution of each indicator. Finally, we investigate the relationship between scientists’ diversity indicators and their scientific impact using multiple regression analysis. The results show that the numbers of connected components of most PACS codes co-occurrence networks are less than 5, and some networks have significant community structures. The diversity indicators show the heterogeneity of the research diversity of physicists. We also find that some diversity indicators are weakly correlated with scientific impact indicators. Based on our findings, we suggest that physicists should focus on their main research fields and span multiple research fields over their entire careers which could promote their scientific impact.

This paper explores the coordination problem of a socially responsible supply chain, in which the supplier contributes corporate social responsibility by donating a specific amount of money to a cause marketing and the retailer cares for consumer surplus in addition to its own profit. We consider two donation formats: absolute amount donation and percentage of profit donation. For each donation format, the optimal solutions for the centralized and decentralized decisions are derived, and the effects of system parameters on the optimal decisions and other outcome variables are investigated. Moreover, a two-part tariff contract and a quantity discount plus cost sharing contract are proposed to coordinate the socially responsible supply chain. This study may provide theoretical support and operational procedures for supply chain managers to integrate corporate social responsibility into business routines.

Herd behavior in financial markets often leads to unjustified macroscopic phenomena. However, despite existing studies on modeling herd behavior, how it varies across individual agents and over time remains unclear. We show that herd behavior in mutual fund companies can be understood from the functional networks representing interactions inferred from investment similarities. Specifically, in this paper, the spatial characteristics of herd behavior stand for the topology relationships of observations in networks. We analyze the collective dynamics of mutual fund investment from 2003 to 2019 in China using the language of network science and show that herding behavior accompanies this industry’s development but dwindles after the 2015 Chinese market crash. By integrating community detection analysis, we found an increased degree of coherence in the collective herding behavior of the system, even though the localization of herding behavior decreases for clusters of mutual fund companies when the systemic risk builds up. Further analysis showed that herding behavior impacts the payoff of individual fund companies differently across years. The spatial-temporal changes of herding behavior between mutual funds presented in this paper shed light on the debate of individual versus systemic risk and, thus, could interest regulators and investors.