Ferenc Szidarovszky

University of Pecs | PTE · Department of Applied Mathematics

Klasszikus oligopol játékot vizsgálunk olyan feltétel mellett, hogy a játékosok a termeléssel környezetszennyező anyagokat is létrehoznak és kibocsátanak. Figyelembe vesszük a termék egységárán és a termelési költségeken kívül a szennyező anyag egy része közömbösítésének költségeit és a megmaradó rész kibocsátásáért járó büntetés mértékét. Alkalmas...

This paper investigates the optimal environmental policy for non-point source pollution in a Cournot duopoly competition with product differentiation. Under linear price and cost functions, the optimal environmental policy is determined. In the case of non-point source pollutants, the standard policies cannot be applied since the government has lim...

This chapter proposes a dynamic game of two regional monopolies in the same industry. It contains two special features: spillovers and time delays. Other than the usual profit maximization through a linear price function in its region, one regional monopoly experiences a cost-increasing spillover associated with the presence of the other regional m...

The repeated failures of any equipment or systems are modeled as a renewal process. The management needs an assessment of the number of future failures to allocate the resources needed for fast repairs. Based on the idea of expectation by conditioning, special Volterra-type integral equations are derived for general types of repairs, considering th...

Egy speciális lineáris rendszerosztályt vizsgálunk, ahol az egyes részrendszerek kimenet-bemenet relációkkal vannak összekötve, amelyek egy olyan irányított gráfot generálnak, amely körmentes. Azaz, a részerendszereket összekötő relációk mindig előre haladnak. Rendszerek irányíthatóságának vizsgálatához feltétlenül szükséges az összes olyan állapot...

An n-person cooperative oligopoly is considered without product differentiation. It is assumed that the firms know the unit price function but have no access to the cost functions of the competitors. From market data, they have information about the industry output. The firms want to find the output levels that guarantee maximum industry profit. Fi...

This study analyzes a two-market cobweb model involving production delays for agricultural products and information delays concerning cross-market prices. Our cobweb model has two markets because interdependency between agricultural markets is observed. It has multiple delays because each commodity good has a different length of production delay ba...

The asymptotical properties of a special dynamic two-person game are examined under best-response dynamics in both discrete and continuos time scales. The direction of strategy changes by the players depend on the best responses to the strategies of the competitors and on their own strategies. Conditions are given first for the local asymptotical s...

In this paper, we introduce the delayed-advanced Kaldorian business cycle model and consider how time-delay and time-advance affect economic fluctuations. Given the asymptotic stability of the original Kaldor model, we first show that an approximated Kaldor model by a Taylor series expansion can accurately describe the dynamics of the delayed Kaldo...

This study considers whether the ambient charge tax policy can effectively control non-point source pollution in a duopoly market. Price and production cost functions are linear, and goods are differentiated. The optimal decisions are determined in a two-stage process. At the second stage, the duopolistic firms determine their outputs, taking the a...

A special oligopoly model is considered when the firms compete on the factor market, and the used factor volumes determine their outputs. In the N firm case conditions are given for the existence of the Nash equilibrium, and in the cooperative case, sufficient conditions are derived for the existence and uniqueness of the joint profit maximizer. In...

This paper studies the dynamic characteristics of a nonlinear monopoly model involving two boundedly rational monopolists with different information and knowledge on the market demand. The ℓ-monopolist knows only the actual values of output and the profit in the immediate past two periods, whereas the k-monopolist knows the marginal revenue but lac...

An n-firm oligopoly is introduced in which, in addition to production levels, the pollution emissions are also included. A regulator cannot monitor individual emission volumes of firms, so uniform incentives are introduced to firms to reduce pollution concentrations. The regulator cannot observe the exact concentrations, so the incentives are also...

Two types of boundedly rational monopolists are studied when the marginal revenue is not necessarily negative sloping. A limited monopolist (ℓ-monopolist) knows only the price and output values in two previous periods. A knowledgeable monopolist (k-monopolist) knows the analytic expression of the marginal profit function and forms sales expectation...

Given a duopoly of firms that produce differentiated outputs maximizing profits and emitting pollution, this paper introduces an emission charge as an environmental policy and analyses its static and dynamic effects on emission reductions. Among other results, it is shown that the emission charge effectively controls the aggregate emission level. A...

Repeated asymmetric contest games are examined under conditions which guarantee the existence and uniqueness of pure Nash equilibrium (Hirai and Szidarovszky 2013). Conditions are derived for the local asymptotical stability of the equilibrium under continuous and discrete dynamics with gradient adjustments. In both cases, a crucial assumption is t...

Two types of boundedly rational monopolists are considered, when they are unable to determine the profit maximizing output levels. In the first case, the monopolist knows the price function and in the second case it can access only past output and price values. In applying gradient dynamics, the marginal profit is either known or approximated by fi...

This paper reexamines the Lotka-Volterra competition model with two delays. The steady state is shown to be locally asymptotically stable without delay. If the two delays are identical, then the model becomes a one-delay system. The critical value of the delay is determined when stability might be lost. If the delays are different, then the stabili...

This study demonstrates the possibility of cyclic capital accumulation in the case in which there are delays in capital implementation and estimation of capital depreciation. For this purpose, a two-sector growth model with Cobb–Douglas production function is built. It is shown that the stability of the balanced growth may change as lengths of dela...

This paper constructs an n-firm Cournot oligopoly in which the price function is hyperbolic. It provides a game-theoretic approach to characterize the ambient charge’s impact on NPS pollution’s total and individual emission levels. The main findings are as follows: (1) the positivity of individual Cournot output depends on the marginal production c...

A three-delay duopoly is considered where the firms have identical implementation delays with different information delays. The equilibrium is locally asymptotically stable without delays however this stability is lost with increasing values of the delays. The stability properties of the equilibrium depend on the common implementation delay of the...

This paper investigates the asymptotical behavior of the equilibrium of linear classical duopolies by reconsidering the two-delay model with two different positive delays. In a two-dimensional analysis, the stability switching curves were first analytically determined. Numerical studies verified and illustrated the theoretical results. In the sensi...

A regulator can observe the total concentration of non-point source (NPS) pollution, however, cannot monitor individual emissions with low cost and high enough accuracy. This information asymmetry makes adequate standard instruments of environmental policy impossible. This paper constructs a simple Cournot competitive model and considers how much t...

In cases of nonpoint pollution sources, the regulator can observe the total emission but unable to distinguish between the firms. The regulator then selects an environmental standard. If the total emission level is higher than the standard, then the firms are uniformly punished, and if lower, then uniformly awarded. This environmental regulation is...

This paper analyses the effectiveness of the ambient charges for controlling emissions of non-point source pollutions. To this end, we construct a two-stage Bertrand duopoly game, in which optimal abatement technologies are chosen first and then the optimal prices as well as the optimal productions are determined. It is shown that the ambient charg...

This study is devoted to consider the dynamic properties of a Lotka–Volterra competition model with two discrete delays. First, it reviews stability conditions of the no-delay model as a benchmark. Second, it examines the delay model and analytically establishes the stability switching curve on which stability is switched to instability and vice ve...

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...

A growth model with a special production function augmented with physical capital and human capital is modified and used to explain the birth of cyclical dynamics. Crucial feature of the model is the assumption that there are a gestation delay and a maturation delay in constructing physical capital and human capital, respectively. Dynamics is descr...

Dynamic asymmetric contest games are examined under the assumption that the assessed value of the prize by each agent depends on the total effort of all agents, and each agent has only delayed information about the efforts of the competitors. Assuming gradient dynamics with continuous time scales, first the resulting one-delay model is investigated...

This paper presents a static and a dynamic model of an environmental policy of the ambient tax related to nonpoint source pollution that has many different sources. We apply the model to controllability by the ambient tax rate, showing that increasing the rate reduces the total level of the pollution. We also consider dynamic characteristics in the...

“Delay” has been considered as one of destabilizing factors in economic dynamics for a long time. Dynamic macroeconomics is concerned with explaining growth and fluctuations. This paper shows how various dynamics involving cyclic fluctuations can emerge in the standard neoclassical growth model when two distinct delays, a delay in production and a...

This study demonstrates the conditions under which an increase in the ambient charge positively or negatively affects the total level of non-point source pollutions. For this purpose, an n-firm Bertrand framework is used in which goods are differentiated and the corresponding price functions are linear. It is shown first that the effect is definite...

This study constructs a heterogeneous agents model of a financial market in a continuous-time framework. There are two types of agents, fundamentalists and chartists. The former follows the traditional efficiency market theory and has a linear demand function, whereas the latter experiences delays in the formation of price trends and possesses a S-...

We investigate love dynamics of two individuals in a delay love affair model in which both are assumed to be cautious, the most natural romantic style. The local stability analysis proves first that the steady state is fairly stable when there are no delays and second that solving the characteristic equation generates a set of positive delays for w...

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 und...

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 fram...

An extended n -firm oligopoly with product differentiation is considered. It is assumed that the government selects an emission standard for the industry and based on the output and technology of each firm it selects a maximum allowed amount of emission for each firm. If the actual amount is higher than the allowed maximum, then the firm has to pay...

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 of...

A machine shop is considered with machines having different virtual ages and failure distributions. Performing maintenance on any one of the machines decreases its virtual age by a given factor resulting in lower probability of the occurrence of later non-repairable failures. Due to limited maintenance budget the optimal choice of machines to be ma...

In the previous chapters, we always assumed that the firms had complete knowledge about the types and the parameters of all functions involved in the mathematical models. In reality, however, this is not always the case. The firms are able to assess their actual costs by accurate bookkeeping, and then, the function forms of price function can be ob...

In the previous chapters on duopolies and oligopolies, it was assumed that the firms made their decisions independently of each other without any consideration about the competitors. In industries, however, the situation is much more complicated because there are several ways of forming joint ventures, having partial equity interests or being invol...

Consider two firms which produce identical or related products or offer identical or related services to a homogeneous market. Their objective is to have as much profit as possible.

This is the first book to comprehensively examine the asymptotic behavior of dynamic monopolies, duopolies, and oligopolies where firms face information and implementation delays. It considers discrete and continuous timescales, continuously distributed delays, as well as single and multiple delays. It also discusses models with linear and hyperbol...

Monopoly models describe an economic situation where a single firm produces a homogeneous product or offers a service to a homogeneous market. Its objective is to maximize profit.

Oligopoly models describe the behavior of n firms who produce related goods or offer related services to a homogeneous market. They are generalizations of duopoly models with arbitrary number of firms.

This paper investigates the effect caused by an increase in ambient charges on firm-specific and total pollutions in a Cournot oligopoly market. Formalising profit-maximising behaviour in the n-firm framework with product differentiation, we show the static result that ambient charge can reduce industrial pollution. We then demonstrate three dynami...

Dynamics of Goodwin’s accelerator business cycle model is reconsidered. The model is characterized by a nonlinear accelerator and an investment time delay. The role of the nonlinearity for the birth of persistent oscillations is fully discussed in the existing literature. On the other hand, not much of the role of the delay has yet been revealed. T...

Warranty prediction is a very important task in reliability engineering. It needs to estimate the expected number of failures in any given time period during the length of the warranty contract. Several commercial software packages have been already implemented and used in the industry, including Minitab and Weibull++. The time to failure is usuall...

Single-product oligopolies without product differentiation are examined with linear production, production adjustment, flexible workforce and investment costs. The price function is assumed to be hyperbolic which makes the non-linearity of the model much stronger than in the case of linear price function examined earlier in the literature. The best...

This paper considers a continuous-time heterogeneous agent model of a financial market with one risky asset, two types of agents (i.e., the fundamentalists and the chartists), and three time delays. The chartist's demand is determined through a nonlinear function of the difference between the current price and a weighted moving average of the delay...

The intersection of the price function with the vertical axis is called the maximum price and the slope of the price function is called the marginal price. It is assumed that a monopoly has full information about the marginal price and its own cost function but is uncertain about the maximum price. Based on repeated price observations an adaptive l...

A modified version of single-product discrete Cournot oligopolies is introduced, where the additional costs of decreasing or increasing the output level from the previous time period as well as increasing the output level from the already built up capacity limit are included. In this way the costs of laying off or hiring new workers and making inve...

This chapter studies the dynamics of the Kaldor–Kalecki model of national income and capital stock. The investment function is assumed to have not only a Kaldorian characteristics, namely, a S-shaped form but also a Kaleckian characteristics, that is, a gestation delay between “investment decision” and “investment implementation.” We divide the ana...

In this chapter some special classes of matrix games will be discussed.

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 payo...

The equilibrium problem of N-person games has strong relation to other important mathematical problem areas such as optimization and fixed point problems. In this chapter we will discuss this issue.

In the previous chapters we considered two types of cooperation of the players. In the first case, they form a grand coalition , obtain the largest possible overall payoff which is then divided among the players based on certain concepts of fairness. In the second case the players negotiate to reach a fair settlement. In many cases a third way of c...

In the previous chapter, conditions were given for the existence of equilibria in N-person games. The Nikaido-Isoda theorem was based on the Kakutani fixed point theorem, which guarantees the existence of at least one fixed point without providing computational method for finding the fixed points. In this chapter, a general method will be introduce...

In an optimization problem , we have a single decision maker, his feasible decision alternative set, and an objective function depending on the selected alternative. In game theoretical models, we have several decision makers who are called the players , each of them has a feasible alternative set, which is called the player’s strategy set, and eac...

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...

In the cases of noncooperative games the players cannot or do not want to make binding agreements, so they select strategies independently of each other, and receive the corresponding payoffs. The Nash equilibrium does not need agreement between the players, since at an equilibrium situation the interest of each player is to keep the equilibrium st...

Within economic literature random outcomes can be characterized by their certainty equivalents. In this article, a general approach for their extension is first outlined and then special cases are shown. The two most simple of these cases result in the classical formula of certainty equivalent, and by increasing the degree of the approximating Tayl...

An IS-LM model is developed for the dynamics of income, interest rate and money stock with delay in tax revenue. The main aim is to show that the delay matters in macro dynamics. Two different delays, fixed time delays and continuously distributed time delays, are considered explicitly and described by delay-differential equations and integro-diffe...

In this paper, we study game-theoretic models for lease contracts, by which the owner (lessor) rents a piece of equipment to a user (lessee). The lessee decides on the optimal lease period and usage rate, and the lessor is responsible for developing a maintenance policy for the equipment. Two non-cooperative game-theoretic models and a cooperative...

A modified Cournot oligopoly is introduced and examined in which the firms can treat their wastes up to a certain amount, and if the amount of waste is even higher then an outside facility is used with a given fixed cost and higher unit cost. The resulting payoff functions become discontinuous. The best response functions of firms are nonincreasing...

Models are introduced and examined for the optimum scheduling of preventive replacements. The “replace first” and “replace last” models are known from the literature if the long term expected cost per unit time is minimized. We will first introduce the one cycle counterparts of these models when the expected costs per unit time in a single cycle is...

Management of surface and ground water resources in drought-stricken regions with increasing water consumption poses a major challenge to water resource managers and decision makers. The situation is even graver in areas naturally classified as semiarid regions. Conjunctive management of ground and surface water is an appropriate strategy in such r...

In Chaps. 2 and 3 we have already introduced simple examples of games modeling situations in competition, social issues, tax evasion, waste management, advertisement, homeland security, elections, military, economics, location for a business, market sharing, duel, espionage, and auctions among others. In this chapter some additional applications of...

Let N denote the number of players . It is usually assumed that the set of all feasible strategies of each player has at least two elements. If \(S_k\) is the strategy set of player k, then its payoff function \(\phi _k\) is defined on the set of all simultaneous strategies , which is denoted by \(S=S_1 \times S_2 \times \dots \times S_N\), and \(\...

There are decision problems where the consequences of the choices of the different alternatives cannot be quantified. This is the case, for example, in considering environmental issues like esthetics. In such cases no numerical payoff functions are given, only the rankings of the alternatives are possible. Then social choice concepts provide soluti...

In the previous chapter, we assumed that the players were able to collect their payoff values to a common basket, and this common payoff was distributed among the players. There are, however, many cases when this is impossible. First, if the payoffs of the different players are not transferable, second, if the players are unable to agree on the mec...

In examining the existence conditions for equilibria in N-person games either the Banach or the Kakutani fixed point theorem was used. The Banach fixed point theorem guaranteed the existence of the unique equilibrium, and an iteration algorithm was also suggested to compute the equilibrium. However, the existence theorems based on the Kakutani fixe...

In Chap. 2 we have seen examples of discrete static games which had no equilibrium (Example 2. 7), unique equilibrium (Example 2. 1), and multiple equilibria (Example 2. 6). We faced similar situation with continuous games in Chap. 3 (Examples 3. 1–3. 3). In this chapter, we will give sufficient conditions for the existence of equilibria in continu...

A new model and solution methods are introduced to find the optimal time of preventive replacement of a working object. Most models consider only the replacement costs and the distribution of the time to failure. Very few models take the random termination time of ongoing projects into account, when project interruption results in additional cost....

This book reflects the state of the art in nonlinear economic dynamics, providing a broad overview of dynamic economic models at different levels. The wide variety of approaches ranges from theoretical and simulation analysis to methodological study. In particular, it examines the local and global asymptotical behavior of both macro- and micro- lev...

In the recent literature the introduction of modified cost functions has added reality into the classical oligopoly analysis. Furthermore, the market evolution requires much more flexibility to firms, and in several countries contingent workforce plays an important role in the production choices by the firms. Therefore, an analysis of dynamic adjus...

We call the intercept of the price function with the vertical axis the maximum price and the slope of the price function the marginal price. In this paper it is assumed that a monopolistic firm has full information about the marginal price and its own cost function but is uncertain on the maximum price. However, by repeated interaction with the ma...

We construct a Cournot duopoly model in a continuous-time framework and consider its dynamic behavior when the firms are heterogeneous in determining their output decision: one firm has an information delay in the competitor's output as well as an implementation delay in its own output while the other firm does not have any delays. Two main results...

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...

We study the effects of production delays on the local as well as global dynamics of nonlinear cobweb models in a continuous-time framework. After reviewing a single delay model, we proceed to two models with two delays. When the two delays are used to form an expected price or feedback for price adjustment, we have a winding stability switching c...

This paper shows how cyclic dynamics of national income can emerge in the multiplier–accelerator model with continuous time scale when delays in investment and consumption are present. An S-shaped functional form of investment and a linear consumption function are adopted to illustrate the phenomenon and to compute the stability-switching curves on...

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 pr...

We study the effects of two delays on the local as well as on global stability of nonlinear Cournot duopoly dynamics. The two major findings are an analytical construction of the stability switching curve on which stability is lost and the numerical confirmation of the birth of aperiodic global dynamics when the stationary state is locally unstable...

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)....

This book integrates the fundamentals, methodology, and major application fields of noncooperative and cooperative games including conflict resolution. The topics addressed in the book are discrete and continuous games including games represented by finite trees; matrix and bimatrix games as well as oligopolies; cooperative solution concepts; games...

The majority of system failures do not occur without any warning signs. This is especially true for failures caused by degradation. By examining the failure-critical indexes during scheduled inspections, actions can be taken to address degraded components and prevent big losses due to failures. In this paper, we assume that an imminent failure can...

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 includ...

This paper aims to show that delay matters in continuous- and discrete-time framework. It constructs a simple dynamic model of a boundedly rational monopoly. First the existence of the unique equilibrium state is proved under general price and cost function forms. Conditions are derived for its local asymptotical stability with both continuous and...

Oligopolies with product differentiation are examined with both quantity-adjusting and price-adjusting firms. Conditions are given for the positivity of the equilibrium outputs as well as for that of the equilibrium prices. The stability of the positive equilibria is then investigated; the positivity and stability conditions are also compared. The...

In this paper we study an oligopoly market where profit-maximizing firms and socially concerned firms compete in quantities. Confronting remarks by Milton Friedman and Gary Becker, we are using an evolutionary setting to investigate the endogenous choice of the proper objective of business firms and the influence of product differentiation on the l...

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...