Continuous-time integral dynamics for Aggregative Game equilibrium seeking

In this paper, we consider continuous-time semi-decentralized dynamics for the equilibrium computation in a class of aggregative games. Specifically, we propose a scheme where decentralized projected-gradient dynamics are driven by an integral control law. To prove global exponential convergence of the proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov function argument. We derive a sufficient condition for global convergence that we position within the recent literature on aggregative games, and in particular we show that it improves on established results

Supply Chain Network Competition in Time-Sensitive Markets

We develop a game theory model for supply chain network competition in time-sensitive markets in which consumers respond to the average delivery time associated with the various firms’ products. The firms’ behavior is captured, along with the supply chain network topologies, with the governing equilibrium concept being that of Nash equilibrium. We derive the variational inequality formulation of the equilibrium conditions and provide illustrative examples. We also identify special cases for distinct applications. An algorithm is proposed, and the framework further illustrated through a case study in which we explore varying sensitivities to the average time delivery with interesting results

A Splitting Equilibration Algorithm for the Computation of Large-Scale Constrained Matrix Problems; Theoretical Analysis and Applications

In this paper we introduce a general parallelizable computational method for solving a wide spectrum of constrained matrix problems. The constrained matrix problem is a core problem in numerous applications in economics. These include the estimation of input/output tables, trade tables, and social/national accounts, and the projection of migration flows over space and time. The constrained matrix problem, so named by Bacharach, is to compute the best possible estimate X of an unknown matrix, given some information to constrain the solution set, and requiring either that the matrix X be a minimum distance from a given matrix, or that X be a functional form of another matrix. In real-world applications, the matrix X is often very large (several hundred to several thousand rows and columns), with the resulting constrained matrix problem larger still (with the number of variables on the order of the square of the number of rows/columns; typically, in the hundreds of thousands to millions). In the classical setting, the row and column totals are known and fixed, and the individual entries nonnegative. However, in certain applications, the row and column totals need not be known a priori, but must be estimated, as well. Furthermore, additional objective and subjective inputs are often incorporated within the model to better represent the application at hand. It is the solution of this broad class of large-scale constrained matrix problems in a timely fashion that we address in this paper. The constrained matrix problem has become a standard modelling tool among researchers and practitioners in economics. Therefore, the need for a unifying, robust, and efficient computational procedure for solving constrained matrix problems is of importance. Here we introduce a.n algorithm, the splitting equilibration algorithm, for computing the entire class of constrained matrix problems. This algorithm is not only theoretically justiflid, hilt l'n fi,1 vl Pnitsf htnh thP lilnlprxing s-trlrtilre of thpCp !arop-Cspe mrnhlem nn the advantages offered by state-of-the-art computer architectures, while simultaneously enhancing the modelling flexibility. In particular, we utilize some recent results from variational inequality theory, to construct a splitting equilibration algorithm which splits the spectrum of constrained matrix problems into series of row/column equilibrium subproblems. Each such constructed subproblem, due to its special structure, can, in turn, be solved simultaneously via exact equilibration in closed form. Thus each subproblem can be allocated to a distinct processor. \We also present numerical results when the splitting equilibration algorithm is implemented in a serial, and then in a parallel environment. The algorithm is tested against another much-cited algorithm and applied to input/output tables, social accounting matrices, and migration tables. The computational results illustrate the efficacy of this approach

What is infidelity? Perceptions based on biological sex and personality

The study examines perceptions of infidelity, paying particular attention to how these perceptions differ based on biological sex and personality traits, specifically agency and communion and their unmitigated counterparts. The study utilizes a sample of 125 male and 233 female college students. In addition to the personality measures, participants completed a 19-item checklist that assessed their perceptions of specific items that could potentially be construed as infidelity. It was hypothesized that females would construe more items as infidelity than would males. It was also predicted that unmitigated communion and communion would be positively correlated with these perceptions and that unmitigated agency would be negatively correlated with these perceptions. No correlation was predicted between agency and infidelity. All hypotheses were supported. Implications and suggestions for future research are discussed

Parallel Computation of Large-Scale Dynamic Market Network Equilibria via Time Period Decomposition

In this paper we consider a dynamic market equilibrium problem over a finite time horizon in which a commodity is produced, consumed, traded, and inventoried over space and time. We first formulate the problem as a network equilibrium problem and derive the variational inequality formulation of the problem. We then propose a parallel decomposition algorithm which decomposes the large-scale problem into T + 1 subproblems, where T denotes the number of time periods. Each of these subproblems can then be solved simultaneously, that is, in parallel, on distinct processors. We provide computational results on linear separable problems and on nonlinear asymmetric problems when the algorithm is implemented in a serial and then in a parallel environment. The numerical results establish that the algorithm is linear in the number of time periods. This research demonstrates that this new formulation of dynamic market problems and decomposition procedure considerably expands the size of problems that are now feasible to solve

Parallel Computation of Large-Scale Nonlinear Network Problems in the Social and Economic Sciences

In this paper we focus on the parallel computation of large - scale equilibrium and optimization problems arising in the social and economic sciences. In particular, we consider problems which can be visualized and conceptualized as nonlinear network flow problems. The underlying network structure is then exploited in the development of parallel decomposition algorithms. We first consider market equilibrium problems, both dynamic and static, which are formulated as variational inequality problems, and for which we propose parallel decomposition algorithms by time period and by commodity, respectively. We then turn to the parallel computation of large-scale constrained matrix problems which are formulated as optimization problems and discuss the results of parallel decomposition by row/column

STGT program: Ada coding and architecture lessons learned

STGT (Second TDRSS Ground Terminal) is currently halfway through the System Integration Test phase (Level 4 Testing). To date, many software architecture and Ada language issues have been encountered and solved. This paper, which is the transcript of a presentation at the 3 Dec. meeting, attempts to define these lessons plus others learned regarding software project management and risk management issues, training, performance, reuse, and reliability. Observations are included regarding the use of particular Ada coding constructs, software architecture trade-offs during the prototyping, development and testing stages of the project, and dangers inherent in parallel or concurrent systems, software, hardware, and operations engineering

Supply Chain Network Sustainability Under Competition and Frequencies of Activities from Production to Distribution

In this paper, we develop a competitive supply chain network model with multiple firms, each of which produces a differentiated product by brand and weights the emissions that it generates through its supply chain network activities in an individual way. The supply chain network activities of production, transport and distribution, and storage have associated with them distinct capacities and the firms seek to determine their optimal product flows and frequencies of operation so that their utilities are maximized where the utilities consist of profits and weighted emissions. Multiple production, storage, and transport mode options are allowed. The governing equilibrium concept is that of Cournot-Nash equilibrium. We provide both path and link flow variational inequality formulations of the equilibrium conditions and then propose an algorithm, which, at each iteration, yields closed form expressions for the underlying variables.Numerical examples illustrate the generality of the model and the information provided to managerial decision-makers and policy-makers. This paper adds to the growing literature on sustainable supply chains through the development of a computable general competitive supply chain network game theory model, which brings a greater realism to the evaluation of profit and emission trade-offs through the incorporation of frequencies

Supply chain network capacity competition with outsourcing: a variational equilibrium framework

This paper develops a supply chain network game theory framework with multiple manufacturers/producers, with multiple manufacturing plants, who own distribution centers and distribute their products, which are distinguished by brands, to demand markets, while maximizing profits and competing noncooperatively. The manufacturers also may avail themselves of external distribution centers for storing their products and freight service provision. The manufacturers have capacities associated with their supply chain network links and the external distribution centers also have capacitated storage and distribution capacities for their links, which are shared among the manufacturers and competed for. We utilize a special case of the Generalized Nash Equilibrium problem, known as a variational equilibrium, in order to formulate and solve the problem. A case study on apple farmers in Massachusetts is provided with various scenarios, including a supply chain disruption, to illustrate the modeling and methodological framework as well as the potential benefits of outsourcing in this sector

Braess' paradox in a generalised traffic network

Copyright © 2014 John Wiley & Sons, Ltd. Braess' paradox illustrates situations when adding a new link to a transport network might lead to an equilibrium state in which travel times of users will increase. The classical network configuration introduced by Braess in 1968 to demonstrate the paradox is of fundamental significance because Valiant and Roughgarden showed in 2006 that 'the "global" behaviour of an equilibrium flow in a large random network is similar to that in Braess' original four-node example'. Braess' paradox has been studied mainly in the context of the classical problem introduced by Braess and his colleagues, assuming a certain type of symmetry in networks. Specifically, two pairs of links in those networks are assumed to have the same volume-delay functions. The occurrence of Braess' paradox for this specific case of network symmetry was investigated by Pas and Principio in 1997. Such a symmetry is not common in real-life networks because the parameters of volume-delay functions are associated with roads physical and functional characteristics, which typically differ from one link to another. This research provides an extension of previous studies on Braess' paradox by considering arbitrary volume-delay functions, that is, symmetry properties are not assumed for any of the network's links and the occurrence of Braess' paradox is studied for a general configuration