Existence of equilibrium in a differential game of spatial competition with advertising

We investigate a differential duopoly game with horizontal product differentiation and advertising efforts aimed at increasing market demand, to show that the standard approach to spatial competition fails to produce a pure-strategy price equilibrium in a dynamic game framework. This holds independently of the shape of the transportation cost function. Then, we introduce an endogenous cost associated with the choice of location and characterise the feedback equilibrium, identifying the necessary and sufficient condition for the existence of the pure-strategy (stationary) price equilibrium. The same condition is singled out for the static game where consumer population is constant. Finally, we show that the static game cannot be viewed as a special case of the dynamic one.     

The intrinsic comparative dynamics of locally differentiable feedback Nash equilibria of autonomous and exponentially discounted infinite horizon differential games

The comparative dynamics of locally differentiable feedback Nash equilibria are derived for the ubiquitous class of autonomous and exponentially discounted infinite horizon differential games. The resulting refutable implications are intrinsic to the said class of differential games, and thus form their basic, empirically testable, properties. Their relationship with extant results in the optimal control theory and the static game theory is discussed. Separability conditions are identified on the instantaneous payoff and transition functions under which the intrinsic comparative dynamics collapse, in form, to those in optimal control problems. Applications of the results to capital accumulation and sticky-price games are provided.     

Buying cooperation in an asymmetric environmental differential game

We consider a two-player asymmetric differential game of pollution control. One player is non-vulnerable to pollution, or unwilling to consider damages when choosing her production policy in a non-cooperative game. We characterize the feedback-Nash equilibrium and the cooperative solution. We establish conditions under which the vulnerable player can buy the cooperation of the non-vulnerable player to control her emissions. We further use the Nash bargaining solution to allocate the total cooperative dividend between the two players and propose a time-consistent decomposition overtime of the total payoff.     

The geometry of finite equilibrium datasets

We investigate the geometry of finite datasets defined by equilibrium prices, income distributions, and total resources. We show that the equilibrium condition imposes no restrictions if total resources are collinear, a property that is robust to small perturbations. We also show that the set of equilibrium datasets is pathconnected when the equilibrium condition does impose restrictions on datasets, as for example when total resources are widely noncollinear.     

Existence of an equilibrium for infinite horizon economies with and without complete information

This work proves the existence of an equilibrium for an infinite horizon economy where trade takes place sequentially over time. There exist two types of agents: the first correctly anticipates all future contingent endogenous variables with complete information as in Radner [Radner, R. (1972). Existence of equilibrium of plans, prices and price expectations in a sequence of markets. Econometrica, 289–303] and the second has exogenous expectations about the future environment as in Grandmont [Grandmont, J. M. (1977). Temporary general equilibrium theory. Econometrica, 535–572] and information based on the current and past aggregate variables including those which are private knowledge. Agents with exogenous expectations may have inconsistent optimal plans but have predictive beliefs in the context of Blackwell and Dubbins [Blackwell, D., Dubins, L. (1962). Merging of opinions with increasing information. The Annals of Mathematical Statistics, 882–886] with probability transition rules based on all observed variables. We provide examples of this framework applied to models of differential information and environments exhibiting results of market selection and convergence of an equilibrium. The existence result can be used to conclude that, by adding the continuity assumption on the probability transition rules, we obtain the existence of an equilibrium for some models of differential information and incomplete markets.     

A differential game in a duopoly with instantaneous incentives

In this paper, we study a differential game in which two competing firms exploit a public renewable resource that is relevant from a landscape point of view. We consider a policy maker that provides an instantaneous incentive to the firms in order to prevent the resource exhaustion during the whole extraction period, which coincides with the harvesting license period. We compute an open-loop Nash equilibrium of the differential game, showing that it coincides with a linear feedback Nash equilibrium. Finally, we compute the value of the incentive that leads to the maximization of social welfare considering the incentive both as a pure transfer and as a cost.     

Approximate equilibrium in pure strategies for a two-stage game of asset creation

The paper studies a two-stage economy where consumers choose first the asset structure and then use it in a standard general equilibrium framework to transfer wealth across time and states of nature. The financial structure is chosen by maximizing indirect utility functions, using continuous random selections from the second-stage equilibrium correspondence. We depart from Bisin (J Econ Theory 82:19–45, 1998) where an endogenous beliefs approach was used and the asset creation was left to financial intermediaries. Moreover, our approach allows us to go beyond a mixed strategies result as we obtain an approximate equilibrium in pure strategies for the economy with incomplete information about future endowments.     

Achieving a new equilibrium? The stability of cooperative employer–union relationships

The current popularity of ‘partnership’ in workplace industrial relations raises the question of the durability of such arrangements. This article investigates the stability of cooperative employer–union relationships by means of case studies. It analyses perceptions of the experience of negotiation and consultation. Continuing net benefits are reported both by managers and by union representatives in workplaces where cooperative relationships are robust. The benefits come primarily from the informal consultative processes and levels of trust that are engendered. Nonetheless, parties to the relationship, however robust they were, faced substantial challenges to their efforts to diffuse and sustain cooperative working. It is concluded that cooperative relationships are likely to be stable where employers wish to maintain an independent employee voice, especially where workplace union density remains relatively high.     

Continuous time vs. backward induction a new approach to modelling reputation in the finite time horizon context

This paper suggests a new approach to modeling credible reputation in the finite time horizon context, using continuous time and interactions which arrive via a Poisson process. Behavior in the present model does not depend on small ad hoc irrationalities as the end of the horizon nears, and the model preserves the intuitive result that as the end of the horizon nears, the level of reputation declines towards zero. While the current paper considers the predatory pricing case, the approach should also apply whenever reputation and/or cooperation are important.     

Dynamic voluntary provision of public goods with uncertainty: a stochastic differential game model

Fershtman and Nitzan (Eur. Econ. Rev. 35:1057–1067, 1991) presented a continuous dynamic public good game and solved the model for feedback Nash equilibria. Wirl (Eur. J. Polit. Econ. 12:555–560, 1996) extended the model and considered nonlinear strategies. Both models do not include uncertainty and hence neglect an important factor in the theory of public goods. We extend the framework of Nitzan and Fershtman and include a diffusion term. We consider two cases. In the first case, the volatility of the diffusion term is dependent on the current level of the public good. This set-up will in principle lead to the same type of feedback strategies computed under certainty. In the second case, the volatility is dependent on the current rate of public good provision by the agents. The results are qualitatively different. We provide a detailed discussion as well as numerical examples. In particular, we show that in both cases uncertainty signifies the free rider effect.     

On the dominance of capitalists leadership in a ‘Feedback-Stackelberg’ solution of a differential game model of capitalism

This paper deals with a modified version of the Lancaster model of capitalism, where it is assumed that there is a cost jointly borne by the two groups of players (workers versus capitalists) and associated with the bargaining of a larger share of consumption for the workers. It is shown that a Feedback- Stackelberg solution, with the capitalists acting as leaders and announcing their investment policy at the beginning of each period, is a solution dominating the Feedback-Nash solution. The paper is also intended to be a tutorial on the Feedback-Stackelberg solution, a concept not so often used by economic modelers.     

The Nash social welfare function for a measure space of individuals

In this paper we consider the Nash social welfare function for a society which is given as an arbitrary finite measure space. We show that the Nash social welfare function for the society is derived from certain rationality criteria.     

Optimal control and differential game models of military expenditure in less developed countries

This paper presents optimal control and differential game models of military expenditure in less developed countries. We emphasise the strategic interconnections between aggressive neighbours and explicitly stress the optimal resource allocation problem between civilian and military expenditure. A major innovation of the analysis is to analyse the asymmetric reaction functions of the two agents and the formalisation of the stylised fact that most LDC arms races have taken place between participants of ‘unequal’ size.     

The epsilon core of a large replica game

Sufficient conditions are given for large replica games without side payments to have non-empty approximate cores for all sufficiently large replications. No ‘balancedness’ assumptions are required. The conditions are superadditivity, a boundedness condition, and convexity of the payoff sets.     

改进的郭涛算法解一类有限元离散常微分方程

文章提出了改进的郭涛算法,并运用该算法解区域分裂、有限元离散之后的非线性常微分方程两点边值问题。数值结果表明该算法能很好地收敛到准确解,精度较高。     

On local relative stability of large sistems with small parameters. The example of a classical model of competition

The main purpose of this paper is to show how to deal with large relative variable systems, where the presence of small parameters makes the norm of some column (or row) blocks tend to zero with them. This will be achieved by using a specific example, namely a model of Classical competition withn goods. In this model capitals move from low-reward to high-reward employments, whilst in the determination of prices the full-cost principle plays the main role and excess-demand only a minor one. We shall also prove that in this model, transformed in relative variable form, if the positive parameter expressing the role of excess-demand in the formation of prices is sufficiently small, the equilibrium vector is asymptotically stable.     

The solution of the infinite horizon tracking problem for discrete time systems possessing an exogenous component

In this paper we derive an algorithm that yields, for a discrete-time system, a control minimizing a quadratic cost functional. The system considered is linear and possesses an exogenous component. The cost functional is a quadratic tracking equation over an infinite time horizon with positive semi-definite weighting matrices such that a weighted sum of these matrices is positive definite. The infinite planning horizon Minimum Variance cost criterion and the Linear Quadratic regulator are special cases. For stabilizable systems we give a characterization of the asymptotically admissible reference trajectories.     

Causal discourse in a game of incomplete information

Notions of cause and effect are fundamental to economic explanation. Although concepts such as price effects are intuitive, rigorous foundations justifying causal discourse in the wide range of economic settings remain lacking. We illustrate this deficiency using an N$N$-bidder private-value auction, posing causal questions that cannot be addressed within existing frameworks. We extend the frameworks of Pearl (2000) and White and Chalak (2009) to introduce topological settable systems (TSS), a causal framework capable of delivering the missing answers. Particularly, TSS accommodate choices belonging to general function spaces. Our analysis suggests how TSS enable causal discourse in various areas of economics.