Proximal point algorithm for a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings

We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.

Equilibrium Arrivals to Preemptive Queueing System with Fixed and Random Population Size

A single-server queueing system with preemptive access is considered.Each customer has one attempt to enter the system at its working interval[0,T].As soon as the customer request enters the system,the server immediately starts the service.But when the next request arrives in the system,the previous one leaves the system even he has not finished his service yet.We study a non-cooperative game in which the customers wish to maximize their probability of obtaining service within a certain period of time.We characterize the Nash equilibrium and the price of anarchy,which is defined as the ratio between the optimal and equilibrium social utility.Two models are considered.In the first model the number of players is fixed,while in the second it is random and obeys the Poisson distribution.We demonstrate that there exists a unique symmetric equilibrium for both models.Finally,we calculate the price of anarchy for both models and show that the price of anarchy is not monotone with respect to the number of customers.

Competitive Resource Allocation Among Urban Congestion Areas in a Modern Big City

The continuing growth of modern big cities leads to their spatial expansion and the emergence of new road connections and urban areas.Areas where large transportation flows of pedestrians,passengers,and drivers come together create demand points,which attract business companies that strive to allocate their resources in the most sought-after places.However,the law of supply and demand restrains companies from allocating all their resources solely in the most popular congestion areas since the more valuable an urban area,the higher the cost to be paid for a resource unit allocation there.As a result,companies act in a non-cooperative manner and try to minimize their own overall costs when allocating resources across available commercial areas in a big city.Non-cooperative behavior of companies leads to the problem of Nash equilibrium search in the game of competing entrepreneurs.In this paper,we study the corresponding resource allocation game under affine cost functions and obtain Nash equilibrium strategies in explicit form.These findings allow us to develop a simple procedure for computing Nash equilibria in the game of companies allocating their resources among urban congestion areas.The computational study demonstrates the dependence of the average price for resource allocation on the number of players and their resource volumes.The outcome of the paper contributes to flow theory and seems to be fresh and useful for managers.

Preface: The Special Issue on Dynamic and Networking Games

Numerous game theory-based techniques to characterize agent behavior haveemerged in response to the swift advancements in technology,communications,indus-trial organization,economic integration,and international trade.There is a huge varietyof mathematical techniques used in game theory.The application of dynamic and net-working game techniques is the main topic of this special issue.Studying strategicinteractions between many decision-makers with dynamic and varied connections isthe focus of research in the game theory discipline of dynamic and networking games.This field of study examines how agents or people make choices in dynamic circum-stances and how those choices impact their overall outcomes and payoffs.