Chaos and Control of Game Model Based on Heterogeneous Expectations in Electric Power Triopoly

A dynamic repeated game model has been established based on heterogeneous expectations in electric power triopoly. Theoretical analysis and numerical simulation show the complexity of this model; suppose that the producers make decisions with naive expectation and bounded rationality. The straight-line stabilization chaos control method was successfully applied to the dynamic repeated game model. The results have important practical value for the producers in the electric power oligopoly

Complex Dynamics in Nonlinear Triopoly Market with Different Expectations

A dynamic triopoly game characterized by firms with different expectations is modeled by three-dimensional nonlinear difference equations, where the market has quadratic inverse demand function and the firm possesses cubic total cost function. The local stability of Nash equilibrium is studied. Numerical simulations are presented to show that the triopoly game model behaves chaotically with the variation of the parameters. We obtain the fractal dimension of the strange attractor, bifurcation diagrams, and Lyapunov exponents of the system

Network Capital and Social Trust: Pre-Conditions for ‘Good’ Diversity?

This paper unpicks the assumption that because social networks underpin social capital, they directly create it – more of one inevitably making more of the other. If it were that simple, the sheer quantity of networks criss-crossing a defined urban space would be a proxy measure for the local stock of social capital. Of course the interrelationships are more complex. Two kinds of complication stand out. The first is specific: networks have both quantitative and qualitative dimensions, but the two elements have no necessary bearing on each other. The shape and extent of a network says nothing about the content of the links between its nodes. Certainly the line we draw between any two of them indicates contact and potential connection, but what kind of contact, how often, how trusting, in what circumstances, to what end…? Reliable answers to these questions need more than surface maps or bird’s eye accounts of who goes where, who speaks to whom. The second complication is a general, not to say universal, difficulty. We are stuck with the fact that sociological concepts - networks, social capital and trust included - are ‘only’ abstractions. They are ways of thinking about the apparent chaos of people behaving all over the place – here, to make it worse, in multi-cultural urban environments - but none of them is visible to be measured, weighed or quantified. This does not make the concepts ‘untrue’, and it should not stop them being useful. My hope is that we can find a nuanced perspective which will at least make the complications intelligible. At best, a multi-layered model will account for diversity in the nature of trust; and for variations in the way social capital is hoarded or distributed within and across ethnic boundaries. It would be contribution enough if we were able to specify the conditions which cause social capital, as Puttnam formulates it, to be exclusionary or inclusionary in its effect.Network capital, Social trust, ‘Good’ diversity

Local and Global Interactions in an Evolutionary Resource Game

Conditions for the emergence of cooperation in a spatial common-pool resource game are studied. This combines in a unique way local and global interactions. A fixed number of harvesters are located on a spatial grid. Harvesters choose among three strategies: defection, cooperation, and enforcement. Individual payoffs are affected by both global factors, namely, aggregate harvest and resource stock level, and local factors, such as the imposition of sanctions on neighbors by enforcers. The evolution of strategies in the population is driven by social learning through imitation. Numerous types of equilibria exist in these settings. An important new finding is that clusters of cooperators and enforcers can survive among large groups of defectors. We discuss how the results contrast with the non-spatial, but otherwise similar, game of Sethi and Somanathan (1996).Common property, Cooperation, Evolutionary game theory, Global interactions, Local interactions, Social norms

Control Strategies for Multi-Controller Multi-Objective Systems

This dissertation\u27s focus is control systems controlled by multiple controllers, each having its own objective function. The control of such systems is important in many practical applications such as economic systems, the smart grid, military systems, robotic systems, and others. To reap the benefits of feedback, we consider and discuss the advantages of implementing both the Nash and the Leader-Follower Stackelberg controls in a closed-loop form. However, closed-loop controls require continuous measurements of the system\u27s state vector, which may be expensive or even impossible in many cases. As an alternative, we consider a sampled closed-loop implementation. Such an implementation requires only the state vector measurements at pre-specified instants of time and hence is much more practical and cost-effective compared to the continuous closed-loop implementation. The necessary conditions for existence of such controls are derived for the general linear-quadratic system, and the solutions developed for the Nash and Stackelberg controls in detail for the scalar case. To illustrate the results, an example of a control system with two controllers and state measurements available at integer multiples of 10% of the total control interval is presented. While both Nash and Stackelberg are important approaches to develop the controls, we then considered the advantages of the Leader-Follower Stackelberg strategy. This strategy is appropriate for control systems controlled by two independent controllers whose roles and objectives in terms of the system\u27s performance and implementation of the controls are generally different. In such systems, one controller has an advantage over the other in that it has the capability of designing and implementing its control first, before the other controller. With such a control hierarchy, this controller is designated as the leader while the other is the follower. To take advantage of its primary role, the leader\u27s control is designed by anticipating and considering the follower\u27s control. The follower becomes the sole controller in the system after the leader\u27s control has been implemented. In this study, we describe such systems and derive in detail the controls of both the leader and follower. In systems where the roles of leader and follower are negotiated, it is important to consider each controller\u27s leadership property. This property considers the question for each controller as to whether it is preferable to be a leader and let the other controller be a follower or be a follower and let the other controller be the leader. In this dissertation, we try to answer this question by considering two models, one static and the other dynamic, and illustrating the results with an example in each case. The final chapter of the dissertation considers an application in microeconomics. We consider a dynamic duopoly problem, and we derive the necessary conditions for the Stackelberg solution with one firm as a leader controlling the price in the marke