On Borel probability measures and noncooperative game theory

In this article, the well-known minimax theorems of Wald, Ville and von Neumann are generalized under weaker topological conditions on the payoff function f and/or extended to the larger set of the Borel probability measures, instead of the set of mixed strategies.     

Location of terror response facilities: A game between state and terrorist

We study a leader follower game with two players: a terrorist and a state where the later one installs facilities that provide support in case of a terrorist attack. While the Terrorist attacks one of the metropolitan areas to maximize his utility, the State, which acts as a leader, installs the facilities such that the metropolitan area attacked is the one that minimizes her disutility (i.e., minimizes ‘loss’). We solve the problem efficiently for one facility and we formulate it as a mathematical programming problem for a general number of facilities. We demonstrate the problem via a case study of the 20 largest metropolitan areas in the United States.     

Parental care as a differential game: A dynamic extension of the Houston–Davies game

An interpretation of the conflict between male and female parents during the process of caring for their common offspring by means of Game Theory was given in Houston and Davies. [A.I. Houston, N.B. Davies, The evolution of cooperation and life history in the dunnock Prunella modularis, in: R.M. Sibly, R.H. Smith (Eds.), Behavioral Ecology, Blackwell Scientific Publications, 1985, pp. 471–487]. Mathematically, this model represents a static game with continuous strategy sets. Recently, this model was reconsidered in a dynamic discrete time framework which also included state dependencies [J.M. McNamara et al., A dynamic game-theoretic model of parental care, J. Theor. Biol. 205 (2000) 605–623]. In this article, we give an interpretation of the parental care conflict in continuous time by means of a differential game with state dependent strategies.     

Numerical solution of quasi-variational inequalities arising in stochastic game theory

We study the finite-difference approximation for the quasi-variational inequalities for a stochastic game involving discrete actions of the players and continuous and discrete payoff. We prove convergence of iterative schemes for the solution of the discretized quasi-variational inequalities, with estimates of the rate of convergence (via contraction mappings) in two particular cases. Further, we prove stability of the finite-difference schemes, and convergence of the solution of the discrete problems to the solution of the continuous problem as the discretization mesh goes to zero. We provide a direct interpretation of the discrete problems in terms of finite-state, continuous-time Markov processes.     

FMS scheduling based on timed Petri Net model and reactive graph search

This paper presents a new scheduling method for manufacturing system based on the Timed Petri Net model and a reactive fast graph search algorithm. The following two typical problems are addressed in this paper. (1) Minimization of the maximum completion time. (2) Minimization of the total tardiness. As for the problem (1), a new search algorithm which combines the RTA^∗ and a rule-based supervisor is proposed. As for problem (2), the original Petri Net model is converted to its reverse model and the algorithm developed for the problem (1) is applied, regarding the due date as the starting time in the reverse model. Some numerical experiments are carried out to demonstrate usefulness of our algorithm.     

博弈论视角的多属性逆向拍卖评标行为研究

技术属性和商务属性间强负相关性会诱导两组评标专家间的对立情绪和不合作行为,评标管理部门对评标专家的组织管理是评标公平性的重要因素. 以博弈论为工具分别建立了多属性逆向拍卖分组评标机制下技术专家和商务专家之间、管理部门与评标专家之间行为的理论模型和研究框架,分析了纯策略纳什均衡解存在的条件.然后,分析了影响技术与商务专家、 管理部门与评标专家之间策略选择的因素,揭示了评标参数对均衡的影响. 为便于研究博弈主体行为,基于Matlab GUI平台开发了分组多属性逆向拍卖评标和管理行为仿真系统. 数值仿真了评标环境的改变和决策参数的不同对均衡结果的影响.     

Modeling cooperation on a class of distribution problems

In this paper we study models of cooperation between the nodes of a network that represents a distribution problem. The distribution problem we propose arises when, over a graph, a group of nodes offers certain commodity, some other nodes require it and a third group of nodes neither need this material nor offer it but they are strategically relevant to the distribution plan. The delivery of one unit of material to a demand node generates a fixed profit, and the shipping of the material through the arcs has an associated cost. We show that in such a framework cooperation is beneficial for the different parties. We prove that the cooperative situation arising from this distribution problem is totally balanced by finding a set of stable allocations (in the core of an associated cooperative game). In order to overcome certain fairness problems of these solutions, we introduce two new solution concepts and study their properties.     

Methods for comparison of coalition influence on games in characteristic function form and their interrelationships

This paper extends two existent methods, called the blockability relation and the viability relation, for simple games to compare influence of coalitions, to those for games in characteristic function form, and shows that the newly defined relations satisfy transitivity and completeness. It is shown in this paper that for every game in characteristic function form the blockability relation and the viability relation have a complementary interrelationship.     

Agent‐based simulation of an N‐person game with parabolic payoff functions

We report computer simulation experiments based on our agent‐based simulation tool to model a new N‐person game based on John Conway's Game of Life. The individual agents may choose between two behavior options: cooperation or defection. The payoff (reward/penalty) functions are given as two parabolas: one for each option. After a certain number of iterations, the behavior of the agents stabilizes to either a constant value or oscillates around such a value. The simulation's goal is to investigate the effects of intermediate behavior on a society of agents. We have performed a systematic investigation of this game for all six possible cases of the mutual positions of parabolic payoff functions crossing each other at two points: x = 0.3 and 0.7 where x is the ratio of the cooperation choice to the total number of agents in the agent's neighborhood. The global ratios X(t) of the total number of cooperators in the entire array of agents as functions of time (iterations) and the solutions of the game X_final as functions of X₀ were observed for each case for Pavlovian, greedy, and conformist agents. The solutions have predictable tendencies only when the neighborhood is the entire array of greedy or conformist agents. In all other cases unexpected properties emerge. © 2009 Wiley Periodicals, Inc. Complexity, 2010     

Levy-type solution for free vibration analysis of orthotropic plates based on two variable refined plate theory

Closed-form solutions for free vibration analysis of orthotropic plates are obtained in this paper based on two variable refined plate theory. The theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Equations of motion are derived from the Hamilton’s principle. The closed-form solutions of rectangular plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions are obtained by applying the state space approach to the Levy-type solution. Comparison studies are performed to verify the validity of the present results. The effects of boundary condition, and variations of modulus ratio, aspect ratio, and thickness ratio on the natural frequency of orthotropic plates are investigated and discussed in detail.     

Edge-partitions of graphs of nonnegative characteristic and their game coloring numbers

Let G be a graph of nonnegative characteristic and let g(G) and Δ(G) be its girth and maximum degree, respectively. We show that G has an edge-partition into a forest and a subgraph H so that (1) Δ(H)?1 if g(G)?11; (2) Δ(H)?2 if g(G)?7; (3) Δ(H)?4 if either g(G)?5 or G does not contain 4-cycles and 5-cycles; (4) Δ(H)?6 if G does not contain 4-cycles. These results are applied to find the following upper bounds for the game coloring number col_g(G) of G: (1) col_g(G)?5 if g(G)?11; (2) col_g(G)?6 if g(G)?7; (3) col_g(G)?8 if either g(G)?5 or G contains no 4-cycles and 5-cycles; (4) col_g(G)?10 if G does not contain 4-cycles.     

Hopf cyclic cohomology and Hodge theory for proper actions on complex manifolds

We introduce two Hopf algebroids associated to a proper and holomorphic Lie group action on a complex manifold. We prove that the cyclic cohomology of each Hopf algebroid is equal to the Dolbeault cohomology of invariant differential forms. When the action is cocompact, we develop a generalized complex Hodge theory for the Dolbeault cohomology of invariant differential forms. We prove that every cyclic cohomology class of these two Hopf algebroids can be represented by a generalized harmonic form. This implies that the space of cyclic cohomology of each Hopf algebroid is finite dimensional. As an application of the techniques developed in this paper, we generalize the Serre duality and prove a Kodaira type vanishing theorem.     

The structure of stratified systems and the structure of mobility: A first approximation to a structural theory of vertical mobility

This essay summarizes an inquiry that explores relations between the structure of stratified systems and the processes of vertical mobility. The inquiry considers economic stratification (the distribution of wealth) and is directed to determining whether the structural properties of stratification systems are sufficient to generate basic patterns in vertical mobility observed in empirical research, especially, the rank‐distance effect. In particular, the question is whether these patterns can be generated even if movement is constrained by nothing more than the size of the population over which wealth is distributed and the total amount of wealth to be distributed. Our results show that the rank‐distance effect emerges even under these minimal assumptions and, further, that rates and distances of vertical mobility are closely related to changes in these boundary parameters of a stratified system. The basic theory developed to relate structure and mobility provides results that are highly consistent with many empirical observations. It also challenges existing claims concerning the nature of the mechanisms determining the relative status immobility of most people in large scale systems. The theory implies that the way in which system structure constrains opportunity for movement is, by itself, sufficient to produce this result and others commonly observed.     

Perturbation theory for games in normal form and stochastic games

In this paper, the effect on values and optimal strategies of perturbations of game parameters (payoff function, transition probability function, and discount factor) is studied for the class of zero-sum games in normal form and for the class of stationary, discounted, two-person, zero-sum stochastic games.A main result is that, under certain conditions, the value depends on these parameters in a pointwise Lipschitz continuous way and that the sets of -optimal strategies for both players are upper semicontinuous multifunctions of the game parameters.Extensions to general-sum games and nonstationary stochastic games are also indicated.     

Modeling the nonlinear deformation of composite laminates based on plasticity theory

The plasticity theory has been successfully used for describing the nonlinear deformation of laminated composite materials under a monotonically increasing loading. Generally, several tests are needed to determine the parameters of the plastic potential for a laminate. We explore an alternative approach and obtain the plastic potential by using theoretical considerations based on a laminate analysis. The model is shown to provide an accurate prediction for the response of a cross-ply glass/epoxy laminate under uniaxial tensile loading at different angles to the material orthotropy axes. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 3, pp. 309–318, May–June, 2007.     

Periodic solution for nonlinear vibration of a fluid-conveying carbon nanotube,based on the nonlocal continuum theory by energy balance method

A nonlinear model is developed for the vibration of a single-walled carbon nanotube (SWCNT) based on Eringen’s nonlocal elasticity theory. The nanotube is assumed to be embedded in a Pasternak-type foundation with simply supported boundary conditions. The nonlinear equation of motion is solved by the energy balance method (EBM) to obtain a sufficiently accurate flow-induced frequency. It is demonstrated that the nonlinearity of the model makes a reasonable change to the frequency at high flow velocity and for the large deformations. Furthermore, the deviation of the frequency from the linear frequency will be exaggerated with an increase in the nonlocal parameter and a decrease of the Pasternak parameters. Ultimately, the results show that the nonlinearity of the model can be effectively tuned by applying axial tension to the nanotube.     

On the algebraic solution of fuzzy linear systems based on interval theory

In this paper, fuzzy linear systems involving a crisp square matrix and a fuzzy right-hand side vector are considered. A new approach to solve such systems based on interval theory and the new concept “interval inclusion linear system” is proposed. Also, new necessary and sufficient conditions are derived for obtaining the unique algebraic solution. Numerical examples are given to illustrate the efficiency of the proposed method.     

The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands

By showing that there is an upper bound for the price of anarchyρ(Γ) for a non-atomic congestion game Γ with only separable cost maps and fixed demands, Roughgarden and Tardos show that the cost of forgoing centralized control is mild. This letter shows that there is an upper bound for ρ(Γ) in Γ for fixed demands with symmetric cost maps. It also shows that there is a weaker bound for ρ(Γ) in Γ with elastic demands.