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This paper demonstrates that the delay has a dual effects of being destabilizer and stabilizer. For this purpose, we use a traditional neoclassical growth model augmented with two continuously distributed time delays, time-to-build delay and time-to-depreciate delay. Applying the Routh-Hurwitz stability criterion, we first construct a condition under which a stationary state loses stability and bifurcates to a cyclic oscillations. It is then numerically demonstrated that the delay has the dual effects: the main role of the delay is to destabilize an otherwise stable economy and it is found that the delay can also stabilize the economy, depending on the combination of two delays. The dual effect is specific to a two delay dynamic model.

One of the most common way of analyzing the evolution of networks of interacting agents is based on simulation. The interactions among the agents can be modeled by N-person social dilemma games, and the evolution of the network can be characterized by repeated transitions. The nature of the transitions as well as the long-term behavior of the state of the network depend on the structures of the particular games under consideration. The purpose of this paper is to present the transitions that occur between N-person social dilemma games, the agent behavior causing these transitions, and the impacts of various parameters. Formerly, N-person social dilemma games such as Prisoners’ Dilemma, Chicken, Stag Hunt and Battle of the Sexes have been separately researched and analyzed. In this paper the specific behavior of Pavlovian agents are explored in a two dimensional cellular automaton environment using parameters that extend over all of these games. It is found that there are three significantly different types of agent behavior: bipartisan, partisan, and unison. Bipartisan agents stochastically decide to cooperate or defect based on a cooperating probability greater than zero and less than one, partisan agents either cooperate with certainty or defect with certainty, and unison agents cooperate 100% of the time. Each agent behavior can be associated with a set of social dilemma games and be represented as plateaus on a three dimensional graph. These plateaus themselves and the transitions between them are investigated in terms of where and why they occur. Lastly, this paper reviews the impact of initial cooperating probability, neighborhood size, learning factors, and grid size on these plateaus and transitions.

In determining the optimal allocation of spare parts and labor in a machine shop, in addition to the planned inspections, the random failures must be considered. The expected number of failures must be therefore assessed. At present, literature on the subject mostly discusses minimal repairs and failure replacement, giving only a little attention to partial repairs. These models ignored the time period to perform repairs, when the equipment is idle. This paper includes a mathematical model in which partial repairs are considered, when at each repair the effective age decreases by a given constant multiplier. Times needed to perform repairs are also taken into account. Two integral equations are derived to find the expected number of failures in any time interval during the useful life of the machine. The first is an approximation, and the second is the exact solution. Based on this information, the allocation of spare parts and qualified labor can be appropriately planned.

This paper describes the transformation of conditioned-based data (CBD) signatures into functional-failure signatures (FFS) that are particularly amenable to processing by prediction algorithms. CBD signatures comprise feature data (FD) that creates a signature that is highly correlated to degradation. Degradation proceeds from the onset of damage to a level of damage at which a component, and its assembly, no longer functions within operational specifications: functional failure occurs. A CBD-based feature signature correlates a change in value (dP) of a parameter of interest (P0) as degradation progresses. This paper presents a theory that each failure mode generates a characteristic degradation signature: g(dP, P0). Further, a feature signature can be transformed into a dimensionless ratio to create a fault-to-failure progression (FFP) signature that is a function of a characteristic degradation signature. Finally, an FFP can be solved in terms of a ratio of parameter change to a parameter to produce degradation progression signature (DPS). Absent noise, a DPS is a linear straight-line transfer curve that is easily transformed into a functional-failure signature (FFS) that is particularly amenable to processing to produce prognostic information in support of Prognosis for Health Monitoring/Management (PHM): (1) an FFS approaches an ideal straight-line transfer curve as noise is ameliorated and/or mitigated; (2) has negative values in the absence of degradation; (3) has positive values below 100 when there is degradation below a defined level of functional failure; and (4) has values at or above 100 when the level of degradation is at or above a level defined as functional failure. Even in the presence of noise and feedback effects, and even when the rate of degradation is nonlinear, a DPS is still a very linear transfer curve. The authors present seven different families of increasing signatures and decreasing signatures that can be represented by seven degradation-signature models that, coupled with models for defining a level of function failure, are used to transform CBD-based signature data into FFS data.

An equipment is considered which is subject to repairable failures on the time interval [0, t]. At the time of each failure, repair is performed which requires length of time $T$ to perform, and as the result of each repair, the virtual age of the equipment decreases by time period u. Minimal repair is obtained by $u=0$ and complete repair / replacement by setting $u=t$ (all age accrued up to the point of failure). A mathematical model was derived for the expected number of failures with partial repairs which require a certain time period to perform. The model derived is a two-dimensional integral equation. It was also shown that in the special cases of minimal repairs and failure replacements the general model could be reduced to the well-known special formulas. A computer method was also suggested for finding solutions and a simple approximating rule was introduced to approximate the solutions. A Weibull numerical example illustrated the theoretical developments.

The purpose of this study is to present an analysis of the applicability of an analytical solution to the $N-$person social dilemma game. Such solution has been earlier developed for Pavlovian agents in a cellular automaton environment with linear payoff functions and also been verified using agent based simulation. However no discussion has been offered for the applicability of this result in all Prisoners 'Dilemma game scenarios or in other $N-$person social dilemma games such as Chicken or Stag Hunt. In this paper it is shown that the analytical solution works in all social games where the linear payoff functions are such that each agent's cooperating probability fluctuates around the analytical solution without cooperating or defecting with certainty. The social game regions where this determination holds are explored by varying payoff function parameters. It is found by both simulation and a special method that the analytical solution applies best in Chicken when the payoff parameter $S$ is slightly negative and then the analytical solution slowly degrades as $S$ becomes more negative. It turns out that the analytical solution is only a good estimate for Prisoners' Dilemma games and again becomes worse as $S$ becomes more negative. A sensitivity analysis is performed to determine the impact of different initial cooperating probabilities, learning factors, and neighborhood size.

This paper shows the utility of a new interval cooperative game theory as an effective water diplomacy tool to resolve competing and conflicting needs of water users from different sectors including agriculture, domestic, industry and environment. Interval parameter programming is applied in combination with cooperative game theoretic concepts such as Shapley values and the Nucleolus to provide mutually beneficial solutions for water allocation problems under uncertainty. The allocation problem consists of two steps: water resources are initially allocated to water users based on the Nash bargaining model and the achieved nonlinear interval parameter model is solved by transforming it into a problem with a deterministic weighted objective function. Water amounts and net benefits are reallocated to achieve efficient water usage through net benefit transfers. The net benefit reallocation is done by the application of different cooperative game theoretical methods. Then, the optimization problem is solved by linear interval programming and by converting it into a problem with two deterministic objective functions. The suggested model is then applied to the Zarrinehrud sub-basin, within Urmia Lake basin in Northwestern Iran. Findings suggest that a reframing of the problem using cooperative strategies within the context of water diplomacy framework - creating flexibility in water allocation using mutual gains approach - provides better outcomes for all competing users of water.

A classical $n$-firm oligopoly is considered first with linear demand and cost functions which has a unique equilibrium. We then assume that the output levels of the firms are bounded in a sense that they are unwilling to make small changes, the output levels are bounded from above, and if the optimal output level is very small then the firms quit producing, which are realistic assumptions in real economies. In the first part of the paper, the best responses of the firms are determined and the existence of infinitely many equilibria is verified. The second part of the paper examines the global dynamics of the duopoly version of the game. In particular we study the stability of the system, the bifurcations which can occur and the basins of attraction of the existing attracting sets, as a function of the speed of adjustment parameter.

The foundational research on blockmodeling focused on theorizing and identifying social roles and positions across multiple networks ( White et al., 1976 ). Generalized blockmodeling provided a breakthrough in theory and research by permitting ideal block types that implement a wider class of role equivalence within a network ( Doreian et al., 2005 ). Notwithstanding these successes and related progress that we discuss, a direct approach for the blockmodeling of multiple relations remains an open problem in the generalized blockmodeling literature ( Doreian, 2006 ). With this in mind, we propose a simple and novel means of formulating and fitting generalized blockmodels for multiple relations. We make use of existing capabilities of the open-source network analysis software Pajek ( Batagelj and Mrvar, 2011 , Mrvar and Batagelj, 2013 ). In particular, by constructing an appropriate augmented adjacency matrix and carefully crafted constraints and penalties, Pajek's criterion function can be simultaneously minimized over multiple relations. This technique is first described in detail using a hypothetical friendship network, and then its value is reinforced through reanalysis of a classic, real world example.

In this paper, we formulate and analyse a long-term multi-objective dynamic model for controlling invasive species. This optimization framework is then applied to the case of buffelgrass control in the Arizona desert. The proposed model simultaneously optimizes three objectives corresponding to three different valued and threatened resources including saguaros (a native cactus species), buildings and vegetation. The model is used to decide the optimal allocation of labour to these resources to control the population of the species in a multi-period planning horizon. The computational method to solve this problem is based on multi-objective integer programming.

Whether it be one security expert covering more systems or reducing total man-hours, there has always been a push to do more with less. Intuitively, we realize different systems need different levels of security. To aid in this effort, we develop multiresolution attacker/defender games by combining two game theoretic approaches: resource assignment and optimal response. We use the resource assignment game to determine the level of detail necessary to build the game needed to respond optimally to attacks. To aid in the selection of a resource assignment game and an optimal response game, we present considerations and survey numerous works. Further resource savings are possible when the optimal response games share features. Even though effort sharing between systems ought to be addressed during the resource-allocation game, we present both a linear effort sharing model and a method for solving post hoc. An illustrative example demonstrates the potential savings from our technique.

Mathematical models for conflict resolution are very important in integrated water resources and environmental management. This study proposes a new methodology to resolve conflicts among different water users and water suppliers while considering environmental requirements and the system’s constraints. A two-level leader–follower model is applied to maximize the net benefit with the Iran Water Resources Management Company as the leader and agricultural, domestic, and industrial users as followers subject to the system’s constraints. As a comparison, the Nash bargaining solution is also used to find a solution when simultaneous moves are assumed by the participants. The suggested method is then applied to the real case of the Zarrinehrud River basin that is one of the areas facing water shortages in Iran. For the actual optimization, Genetic Algorithm is used in order to avoid local optimum. As the contribution of this study, the results show that benefits for the leader in the leader–follower model increased in comparison with the Nash bargaining solutions.

The recent developments of advanced intrusion detection systems in the cyber security field provide opportunities to proactively protect the computer network systems and minimize the impacts of attackers on network operations. This paper is intended to assist the network defender find its best actions to defend against multistage attacks. The possible sequences of interactions between the attackers and the network defender are modeled as a two-player non-zero-sum non-cooperative dynamic multistage game with incomplete information. The players are assumed to be rational. They take turns in making decisions by considering previous and possible future interactions with the opponent and use Bayesian analysis after each interaction to update their knowledge about the opponents. We propose a Dynamic game tree-based Fictitious Play DFP approach to describe the repeated interactive decisions of the players. Each player finds its best moves at its decision nodes of the game tree by using multi-objective analysis. All possibilities are considered with their uncertain future interactions, which are based on learning of the opponent's decision process including risk attitude and objectives. Instead of searching the entire game tree, appropriate future time horizons are dynamically determined for both players. In the DFP approach, the defender keeps tracking the opponent's actions, predicts the probabilities of future possible attacks, and then chooses its best moves. Thus, a new defense algorithm, called Response by DFP RDFP, is developed. Numerical experiments show that this approach significantly reduces the damage caused by multistage attacks and it is also more efficient than other related algorithms. Copyright © 2013 John Wiley & Sons, Ltd.

In considering economic dynamics, it has been known that time delays are inherent in economic phenomena and could be crucial sources for oscillatory behavior. The main aim of this study is to shed light on what effects the delays can generate. To this end, different models of Cournot duopoly with different delays are built in a continuous time framework and their local and global dynamics are analytically and numerically examined. Three major findings are obtained. First, the stability switching conditions are analytically constructed. Second, it is numerically demonstrated that different lengths of the delays are sources for the birth of simple and complicated dynamics. Third, the delay for collecting information on the competitors' output alone does not affect stability.

The interactions between attackers and network administrator are modeled as a non-cooperative non-zero-sum dynamic game with incomplete information, which considers the uncertainty and the special properties of multi-stage attacks. The model is a Fictitious Play approach along a special game tree when the attacker is the leader and the administrator is the follower. Multi-objective optimization methodology is used to predict the attacker’s best actions at each decision node. The administrator also keeps tracking the attacker’s actions and updates his knowledge on the attacker’s behavior and objectives after each detected attack, and uses it to update the prediction of the attacker’s future actions. Instead of searching the entire game tree, appropriate time horizons are dynamically determined to reduce the size of the game tree, leading to a new, fast, adaptive learning algorithm. Numerical experiments show that our algorithm has a significant reduction in the damage of the network and it is also more efficient than other existing algorithms.

A common mistake in modeling systems is mixing elements of different levels in the same model. This paper explains levels, shows how levels can be obtained with decomposition techniques and gives many examples of levels in models, architectures and frameworks. Examples are given that show the confusion that results when levels are mixed. The paper shows that complex models are usually composed of many aspects. Each aspect has levels and the levels of one aspect are different from the levels of another aspect. The model must be constructed using elements of the same level for each aspect.

n -person Battle of Sexes (BOS) games are examined by a special simulation study. Two types of agents are considered and there are three possible ways of making the agents’ initial decisions. The simulation study confirms the theoretical results on the existence and number of equilibria. We also investigate the effect of the model parameters on the limiting states of the system.

Six water authorities share the Sefidrud watershed in the northwestern region of Iran and resolving the conflict among them is one of the major challenges of the water division of the government. In this paper a group decision support system will be developed for identifying the criteria and their weights, needed for ranking water resource projects in this watershed. This model will be based on extending the ordered weighted averaging (OWA) as an aggregation operator. The order weights of this operator will be determined first by using the minimal variability method. Second, a new measure will be developed to quantify consensus among the stakeholders. It guides the supervisor of the group decision making problem to negotiate with stakeholders effectively in the conflict resolution process. Using extended OWA, 13 water resources projects in the Sefidrud watershed will be ranked. A simulation study will also be reported, where the dependence of the optimal decision on the uncertainty level is examined. In addition, a new sensitivity analysis model will be introduced for the combined goodness measures of the projects with respect to the optimistic degree of the supervisor. A new composite measure of goodness will also be defined to obtain reliable solutions.

In the previous chapters, we were dealing with games with complete information, and in the case of dynamic games perfect information was also assumed. Complete information refers to games when every player knows the strategy sets and payoff functions of all players, that is, all players have complete information about the game. Perfect information refers to dynamic games when at each time period each player knows the previous strategy selections of all players and the previous chance moves if any. In short, complete information refers to the amount of information the players have about the game and perfect information refers to the amount of information the players have about the other players’ and their own previous moves (and about the possible chance moves). A game is under uncertainty if any of the above information is not available.

In this chapter repeated and dynamic games will be discussed in which the players know the strategy sets and payoff functions of all players, that is, the game has complete information. It is also assumed that at each time period each player knows the complete history of the game which consists of the past strategy selections and corresponding payoff values of all players. It means that the game also has perfect information.

A two-person conflict is analyzed, where a water company and a community are the players and water supply and health risk constitute the payoff functions. An aquifer's response to different pumping policies is estimated at points of interest by a computational neural network, which was trained using simulation data from MODFLOW, a large-scale complicated finite difference model. Using the weighting method, the Pareto frontier is first determined, and four particular resolution methodologies are applied. The numerical results are analyzed and compared.

This paper introduces a way of modelling bounded continuously distributed time lags in dynamic economic models. Past data are averaged only over a bounded interval thus avoiding the use of very old (“stale”) economic data and hence making dynamic economic models more realistic. Dynamic oligopolies are formulated and then examined under this new type of information lag. Stability analysis is presented and the possibility of the birth of limit cycles is examined. Some special cases are considered, the computational analysis of which illustrates the theoretical findings.

This paper presents a two-person bargaining model in which railway company and its passenger community are the players in the train-scheduling problem. The fuel consumption cost and the total passenger-time constitute the payoff functions. First, the Pareto frontier is determined using the ∊-constraint method and then conflict resolution is performed using five particular resolution methodologies, namely the non-symmetric Nash solution, the non-symmetric Kalai-Smorodinsky solution, the non-symmetric area monotonic solution, the non-symmetric equal loss solution, and a one-shot solution concept. A numerical example is presented to illustrate the methodology.

In a recent paper (Asker, 2007) [1] a dynamic Cournot oligopoly game is proposed and it is claimed that this model represents competition among firms that exploit a common access natural resource. According to the author’s claim, the feature that relates the model with renewable natural resource harvesting is given by the presence of a particular cost function where the total cost of each fisherman is proportional to the square of the own quantity of harvesting and inversely proportional to the total harvesting quantity. In contrast, the usual function used in the literature on the exploitation of natural resources (such as fisheries) is inversely proportional to the available resource stock, and not to the total harvesting. This, in some sense, assumes exactly the opposite (as the available resource is inversely proportional to the total harvesting). So, we believe that the paper (Asker, 2007) [1] contains an error which is probably due to a misunderstanding or a misreading and misinterpretation of the (well-established) literature on bioeconomic modelling, but nevertheless misleading to researchers interested in bioeconomic modelling. The aim of this short note is to explain the mistake and to summarize the correct derivation and interpretation of the cost function. Our goal is to avoid the propagation of a subtle (but nevertheless misleading) error.

Proactive maintenance improves the operational availability of a system and increases the owner's profit. To create more economic value along this direction, it is popular to outsource maintenance services to a service agent. However, due to various uncertainties in equipment failures and spare part logistics, making a service agreement between the owner and the service agent can be quite complex. In this paper, a game-theoretic cooperative model is presented to facilitate contract negotiation in such a joint decision-making process. In particular, the owner determines the time for preventive replacement and the service agent makes up a plan on ordering a spare part such that their overall profit is maximized. To sign a long-term contract, the two players need to share the overall profit in a fair manner based on Shapley values that satisfy certain axioms of fairness. Numerical examples are provided to illustrate the solution methodology and to highlight the managerial implications in reliability and maintenance management.

A novel numerical algorithm is developed for computation of diagonally matched impedance matrix of multiple coupled interconnecting lines in high-speed digital circuits. The algorithm is based on the properties of capacitance and inductance matrices of transmission lines and has unconditional monotonic convergence. The mathematical development is based on the theory of M matrices. The algorithm was applied to various metal lines with different dimensions, showing very good accuracy in comparison to other methods.

This paper introduces a new stochastic bargaining process with offer-dependent break-down probabilities for the case of discrete Pareto frontiers. Under realistic conditions the existence of the solution is proved and it is shown that the number of solutions is at most two. An example of two competing sets of jobs on a single machine illustrates the methodology.

Engineers often need to estimate component reliabilities from system failure data that are obtained either from in-house tests or field operations. The components that caused the system failures usually can be identified by checking the failed systems; however, in some cases, the exact cause of failure is very difficult or impossible to identify. For the latter case, the information on the system failures is not complete, and such data are usually called masked failure data. In this paper, we propose a method for estimating component reliabilities from masked system failure data. Solutions for systems with serial and parallel configurations are provided. The failure distribution of each component is obtained from the proposed method, and is then used to calculate the probability that a system failure is caused by the given component when the exact time or an interval time of the system failure is known. This probability is very useful since it can be used to decide which component should be analyzed first when a system failure occurs, depending on the failure time.

The alternating offer model is a non-cooperative bargaining scheme that is examined by assuming that the players do not have complete information on the feasible payoff set, and each player makes offers based on his/her estimation on the Pareto frontier. The existence and uniqueness of a stationary fictitious subgame perfect equilibrium is proved under the assumption that the estimates of the Pareto frontier used by the two players are sufficiently close to each other. Some limit properties are also investigated. The results of the paper can be applied to both deterministic and stochastic cases.

In computing parasitics of power interconnections to driving circuits in high speed electronics the two-dimensional integral of the measured voltage drops has to be computed, which makes the numerical results unreliable. In this paper we reduce the problem to the computation of a special single dimensional integral, which makes the method applicable in practical situations. A numerical example illustrates the methodology.

With the development of situational awareness in intrusion defense, a proactive response is a realistic and effective approach against the attackers. It is assumed that each player can update knowledge of the opponent and assess possible future scenarios of the dynamic game based on their previous interactions. Therefore, finding the best current move of the defender is modeled as a discrete-time stochastic control problem. An on-line, convergent, scenario based proactive defense (SPD) algorithm considering adaptive learning is developed based on differential dynamic programming (DDP) to solve the associated optimal control problem. Numerical experiment shows that the new algorithm can help the defender in finding the best dynamic strategies quickly and efficiently. Moreover, the SPD algorithm can provide optimal defensive efforts against possible future attacks within an appropriate time window, so the success of the attack in the possible future interactions can be assessed, improving situational awareness in computer network security.

Strategies of defending a computer network against random attacks are modeled by probabilistic methods. A single-stage model is introduced to find the optimal allocation of the resources of the administrator when the network has multiple possible targets. The location of the actual attack is random, the probability of which can be assessed by the administrator from previous interactions with the attacker and based on intelligence information. The expected value and the variance are combined to find the certain equivalent of the outcome, which depends on the allocation of the resources of the administrator between the vulnerabilities of the network. The mathematical model is a nonconvex programming problem, so application of standard optimization techniques cannot guarantee global optimum. By introducing new decision variables the problem can be transformed into a convex problem, the optimal solutions of which can be determined by a simple algorithm by solving a single-variable monotonic equation. This procedure makes the administrator able to find optimal resource allocations very fast and therefore can respond almost instantaneously.

Decision making in water resources and environmental management is usually based on the preferences of more than one DM. If the evaluation of the alternatives with respect to all DMs can be quantified, then the suitable MCDA formulation of the problem can be used as shown in the former chapters. However, in many cases the human preferences are difficult to be quantified. In most applications such opinions are quantified by using some subjective measures, say for example, the worst possibility is indicated by 0, the best by 10, and all values are characterized by a number on the scale [0, 10]. Even in the case of quantifiable criteria, the uncertainty in the objective functions makes any approach questionable. In most cases, many researchers therefore raise serious questions about the objectivity of these methods.

It has become more and more difficult to assess the consequences of water resources and environmental decisions in a single-dimensional way and to use only one criterion when judging their characteristics and making comparisons. However in practice the water and environmental managers always compare, rank, and then select decision alternatives with respect to only a specific criterion. A single criterion of choice can be fully satisfactory only in very simple and straightforward situations. For example, they may select the largest water transfer scheme from a lake, but they might worry whether the largest water transfer scheme is the least expensive, the most reliable, and the most suitable for the environment.

In this chapter, we introduce the most popular and most frequently used solution methods for continuous MCDA problems. The goal of these methods is to generate the set of technologically feasible and efficient alternatives and then choosing the most favorable ones.

In this chapter we will introduce the most popular and most frequently used solution methods for deterministic discrete MCDA problems. In deterministic models the evaluations of the alternatives, the criteria weights and all other parameters are assumed to be certain and known. Models with uncertainty will be discussed later in Chap. 7.

Decision analysis is the science and art of designing or choosing the best alternatives based on the goals and preferences of the decision maker (DM). Making a decision implies that there are alternative choices to be considered. In such cases, we do not want to identify only as many of these alternatives as possible but we want to choose the one that best fits our goals, desires, lifestyle, values, and so on (Harris 1997). In other words, decision analysis is the science of choice. For example, selecting the best technology for urban water supply, developing flood protection alternatives, or optimizing the operation of a reservoir are all the problems of choice.

Many researchers emphasize that a real challenge in modeling MCDA problems is how to incorporate the uncertainty of the input data. MCDA models for water and environmental management, similar to many areas, face uncertainties that generally arise from two sources: random or probabilistic uncertainty related to environmental, economic or technical data, and fuzzy uncertainty related to subjective judgments and the characteristics of the DM. By considering uncertainty, the decision analysis becomes more difficult, but by ignoring it we might miss reality. This chapter discusses and illustrates the main approaches for modeling these two types of uncertainty. The studies of Sahinidis (2004) and Stewart (2005) review the literature of the different types of the uncertain MCDA models and solution procedures.

In this chapter we will introduce the classical Cournot model, which is also known as the single-product quantity setting oligopoly model without product differentiation. In the first section of the chapter the Cournot model will be discussed as an N-firm static game and the best responses of the firms and the equilibria will be determined in a series of examples, many of which will be built upon in developing the ideas in subsequent chapters. Section 1.2 introduces the dynamic adjustment processes via which we shall assume that firms adjust output over time. We will in particular discuss expectation formation processes and adaptive adjustments and gradient adjustments. The final section will illustrate by simple examples the complexity of the dynamics that can arise in these models due to certain nonlinear features to be described below. The fundamental techniques for the global analysis of the dynamics of such models will be explained in Sect. 1.3.

The previous chapters have introduced and analyzed the classical Cournot model under a number of assumptions. In this chapter we discuss some important modifications and extensions. We first introduce market share attraction games where the dynamics are driven by a generalization of the gradient adjustment process introduced in Chaps. 1 and 1. We carry out both a local and global analysis of the stability of this game. In Sect. 4.2 we consider labor-managed oligopolies with best response dynamics. We give a detailed discussion of the local stability in the discrete time case and via an example show the type of global dynamical behavior that is possible in this model type. The section concludes with a brief discussion of the local stability of a continuous time version of the labor-managed oligopoly. In Sect. 4.3 we introduce intertemporal demand interaction effects, brought about for example by habit formation, into dynamic oligopolies with best response dynamics. We give a local and global stability analysis of the model in discrete time. For the continuous time version we study the local stability of the dynamics, including also the case when there are information lags. In Sect. 4.4 we analyze oligopolies with production adjustment costs. For the case of best reply dynamics in discrete time we give local stability conditions. In the final section we consider oligopolies where there is partial cooperation amongst the firms of the industry. We show various properties of the best response function, give local stability for best reply dynamics in continuous time, and analyze the global dynamics of a particular example under discrete time best response dynamics.

In Chap. 1 we introduced the classical Cournot model and after setting up the general framework we focused on a number of specific examples involving combinations of linear and hyperbolic price functions and linear and quadratic cost functions, also taking careful account of capacity constraints. These examples illustrated the variety of reaction functions that can occur and the various types of equilibria (possibly multiple) both in the interior of the domain of interest and on its boundaries. We then went on to introduce the various types of adjustment processes that underpin the dynamic processes, the study of the local and global dynamics of which has occupied much of the space in this book. In particular we considered discrete time and continuous time versions of partial adjustment towards the best response with naive expectations and adaptive expectations as well as the gradient adjustment process. We then introduced some of the basic tools for the analysis of global dynamics via some examples involving duopoly or symmetric and semi-symmetric oligopolies. We introduced the important concept of basins of attraction of different equilibria and the important tool of the critical curve and the concept of border collision bifurcations method. Already with the simple examples considered we see the types of complexity that can arise in oligopoly models under the type of dynamic adjustment processes we consider here.

Emergency Medical Service (EMS) systems can be modeled as spatially distributed queueing systems. Each location in the area has a preference ordering for the servers (usually based on proximity of calls to servers). When a call arrives, the dispatcher scans the preference list and assigns the most preferred idle vehicle to the call. If all vehicles are busy, the call is sent to a private ambulance system that operates in parallel to the EMS system. A major problem in designing and operating EMS systems is to estimate vehicle utilizations and busy probabilities for a given set of base locations. In earlier work, various systems of nonlinear equations have been proposed to estimate the vehicle utilization in EMS systems. In this paper we present a general model structure that encompasses much of the past work. We develop convergence conditions for the general model and show that a simple bisection method can be used to find solutions. The bisection method also leads to a test for the uniqueness of the solut...

A mathematical model and its implementation are presented to analyze the evolution of industrial clusters. The static model is a combination of basic ideas of oligopoly and oligopsony theory as well as fundamental economic results describing the effects of technology development. The dynamic model is based on gradient adjustment in which each decision variable is adjusted in proportion to the corresponding partial derivative of the profit function of the firm controlling this variable. The complexity of the model makes it analytically intractable, therefore computer simulation is used. A sensitivity analysis is performed to examine how the trajectories of the main characteristics of the firms depend on model parameters, and how the entire cluster develops in time.

Dynamic multiproduct oligopoly is discussed with discrete time scales under incomplete information on the inverse demand and/or cost functions. Mathematical models of these processes are formulated, and their global asymptotical stability is analysed. A general model is introduced first, and two particular models are derived from this general formulation. In the first model only the price functions are assumed to be unknown, and in the second the cost functions of the rivals are also assumed to be unknown to all participants. Our stability analysis is based on special adjustment processes.

A stochastic multiobjective dynamic programming model is described for the optimal utilization of mineral resources for satisfying the energy demand of the national economy. The model is based on a special block-structure, where each block is characterized by its input and output vectors and state variables. The whole system is considered as a superposition of the subsystems defined by the individual blocks. Input-output and state transition relations are defined for each block, and the overall objectives of the whole system are defined by investment cost, production cost, manpower demand and environmental effect.