Approximation of Optimal Control Surfaces for the Bass Model with Stochastic Dynamics

The Bass diffusion equation is a well-known and established modeling approach for describing new product adoption in a competitive market. This model also describes diffusion phenomena in various contexts: infectious disease spread modeling and estimation, rumor spread on social networks, prediction of renewable energy technology markets, among others. Most of these models, however, consider a deterministic trajectory of the associated state variable (e.g., market-share). In reality, the diffusion process is subject to noise, and a stochastic component must be added to the state dynamics. The stochastic Bass model has also been studied in many areas, such as energy markets and marketing. Exploring the stochastic version of the Bass diffusion model, we propose in this work an approximation of (stochastic) optimal control surfaces for a continuous-time problem arising from a $2\times2$ skew symmetric evolutionary game, providing the stochastic counter-part of the Fourier-based optimal control approximation already existent in the literature

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

An Evolutionary Economic Analysis of Energy Transitions

Evolutionary economics offers clear insights into the mechanisms that underlie innovations, structural change and transitions. It is therefore of great value for the framing of policies aimed at fostering a transition to a sustainable development. This paper offers an overview of the main insights of evolutionary economics and derives core concepts, namely ‘diversity’, ‘innovation’, ‘selection environment’, ‘bounded rationality’, ‘path dependence and lock-in’, and ‘coevolution’. These concepts are subsequently used to formulate guidelines for the role of the government and the design of public policies, such as the learning from historical technological pathways and the creation of an extended level playing field. In addition, the developments of certain energy technologies are examined in detail within the adopted evolutionary economics framework. Three particular technologies received attention, namely fuel cells, nuclear fusion, and photovoltaic cells.

Complex Systems: A Survey

A complex system is a system composed of many interacting parts, often called agents, which displays collective behavior that does not follow trivially from the behaviors of the individual parts. Examples include condensed matter systems, ecosystems, stock markets and economies, biological evolution, and indeed the whole of human society. Substantial progress has been made in the quantitative understanding of complex systems, particularly since the 1980s, using a combination of basic theory, much of it derived from physics, and computer simulation. The subject is a broad one, drawing on techniques and ideas from a wide range of areas. Here I give a survey of the main themes and methods of complex systems science and an annotated bibliography of resources, ranging from classic papers to recent books and reviews.Comment: 10 page