Latest Advances in Mathematical Economics

Dear Colleagues,

The purpose of this Special Issue is to publish the work of mathematicians interested in studying a number of mathematical methods to represent theories and analyze problems in economics. Some of the potential topics of papers could be well-understood problems from a novel computer-aided perspective, whereas others could present new and challenging mathematical problems.

The potential topics including, but not limited to, the following will be considered for publication: 

• Revisiting the research of classical economic problems, replication studies of established papers, and/or classical models; 
• Solutions for differential and integral calculus, difference and differential equations, matrix algebra, and mathematical programming in new, innovative computational environments;
• ICT tools for teaching mathematical economics courses and evaluating students’ theoretical and practical knowledge;
• The recent results in graph theory for problems that represent and explain economic behavior, income, and wealth distribution;
• Games theory;
• Computational and algorithmic methods in economics;
• The formation and analysis of input–output structures with matrix algebra formulations;
• Topological issues answering open questions regarding the well-posedness of problems, and theorems on the existence of a solution, i.e., of a time-dependent equilibrium, and/or the uniqueness of a solution, i.e., of a stationary equilibrium.

Dr. Kyriaki Tsilika
Prof. Dr. Stelios Kotsios
Dr. Loukas Zachilas
Guest Editors

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• stability
• convergence issues
• analytical solutions
• coefficient matrices
• computational and algorithmic methods

Title: Multi-user water allocation under deep uncertainty and model misspecification concerns
Authors: I. Mourtos; G Papayiannis; P. Xepapadeas; A. Xepapadeas; A. Yannacopoulos.
Affiliation: Department of Statistics Athens University Economics and Business
Abstract: We study a water allocation problem over time from two sources, surface water and underground water to three users, industrial, residential, and agricultural when the users or a water regulator are uncertainty averse and have misspecifications concerns regarding water dynamics from each source. Deep uncertainty in water dynamics is associated with uncertain weather conditions, which cannot be captured by a unique probability distribution, and which are further intensified by climate change. We formulate the problem in the context of multi agent resource allocation problem in which allocation to users can be implemented by sequential serial dictatorship or simultaneous cooperative or non-cooperative approaches. Deep uncertainty and model misspecification is modeled by considering a benchmark model for water dynamics which is surrounded by other possible models whose distance from the benchmark is measured by Kullback-Leibler entropy. Alternative models are contained in an entropy ball with center the benchmark model and radius the maximum distance between the benchmark and the alternative model that agents are willing to consider. Users cannot determine with existing data, which is the true model - benchmark or alternatives - within the ball, and this introduces ambiguity in the decision process. Assuming that agents are ambiguity averse we solve the problem in a maxmin expected utility framework by using robust control methods. We compare, serial dictatorship, cooperative and non-cooperative water path allocations as well as individual and global utility associated with each approach and provide policy recommendations

Title: A Microeconomic Model Evaluating the Dynamic Behaviour of A Two Stage Supply Chain with Autocorrelated Demand under a VMI Program
Authors: Ilias S. Kevork; Christos N. Tziourtzioumis
Affiliation: Department of Economics, University of Thessaly, Greece
Abstract: Collaborative mechanisms among supply chain members, when they are expressed by some form of information sharing, are important to the effective performance of supply chains. In this paper, we develop a microeconomic model for a two stage supply chain which relates demand forecasting and inventory performance. Particularly, assuming that (a) demand at the retailer (downstream member) is modelled by an ARMA (1,1) process, (b) the lead time is fixed in both members and (c) an order- up-to (OUT) level inventory policy is adopted by the two members of the chain, the benefits of two information sharing scenarios are investigated. The first, known as No Information Sharing (NIS) scenario, considers that the supplier (upstream member) does not have access to any information concerning demand data and the demand model with its parameter values being used by the retailer. The second scenario requires that the supplier, not only has access to all information concerning the demand faced by the retailer, but also is responsible for managing the inventory of retailer through a “Vendor Managed Inventory (VMI)” program. In the aforementioned context, initially we derive mathematically, through stochastic analysis of time series, the values of key-criteria, such as the bullwhip ratio, the average on-hand inventory level, and holding and shortage cost, as functions of the duration of lead-time and the parameters of exogenous and endogenous demand models being used by the retailer and the supplier respectively. Finally, we specify the conditions under which the adoption of a VMI collaboration program is beneficial for both members of the supply chain.