Optimal Diversity in Investments with Recombinant Innovation

The notion of dynamic, endogenous diversity and its role in theories of investment and technological innovation is addressed. We develop a formal model of an innovation arising from the combination of two existing modules with the objective to optimize the net benefits of diversity. The model takes into account increasing returns to scale and the effect of different dimensions of diversity on the probability of emergence of a third option. We obtain analytical solutions describing the dynamic behaviour of the values of the options. Next diversity is optimized by trading off the benefits of recombinant innovation and returns to scale. We derive conditions for optimal diversity under different regimes of returns to scale. Threshold values of returns to scale and recombination probability define regions where either specialization or diversity is the best choice. In the time domain, when the investment time horizon is beyond a threshold value, a diversified investment becomes the best choice. This threshold will be larger the higher the returns to scale.

The arrival of the new

In this work we present a number of urn models in which, contrary to standard Pólya urns, the number of competing alternatives is not given from the outset but may increase with the arrival of innovations. We begin by describing a variant of Pólya urns, first introduced by Fred Hoppe, in which balls of previously non-existing colors are added with some (declining) probability. We then propose new variants in which the probability of the arrival of new colors is itself subject to adaptive change depending on the success of past innovations and discuss applications to evolutionary models of technologies and industries. We numerically simulate different specifications of these urns with adaptively changing mutation rate and show that they can account for complex patterns of evolution in which periods of exploration and innovation are followed by periods in which the dynamics of the system is driven by selection among a stable set of alternatives.</p

The complexity of transitions

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Competing recombinant technologies for environmental innovation

This article presents a model of sequential decisions about investments in environmentally dirty and clean technologies, which extends the path-dependence framework of Arthur (1989). This allows us to evaluate if and how an economy locked into a dirty technology can be unlocked and move towards the clean technology. The main extension involves the inclusion of the effect of recombinant innovation of the two technologies. A mechanism of endogenous competition is described involving a positive externality of increasing returns to investment which are counterbalanced by recombinant innovation. We determine conditions under which lock-in can be avoided or escaped. A second extension is symmetry breaking of the the system due to the introduction of an environmental policy that charges a price for polluting. A final extension adds a cost of environmental policy in the form of lower returns on investment implemented through a growth-depressing factor. We compare cumulative pollution under different scenarios, so that we can evaluate the combination of environmental regulation and recombinant innovation

Diffusion of ideas, social reinforcement and percolation

This paper analyzes how social structure and social reinforcement affect the diffusion of an idea in a population of human agents. A percolation approach is used to model the diffusion process. This framework assumes that information is local and embedded in a social network. We introduce social reinforcement in the model by softening the condition to adopt when the number of adopting neighbors increases. Our numerical analysis shows that social reinforcement severely affects the output of the process. Some ideas with an original value so low that it would never get diffused can be spread due to the strength of social reinforcement. This effect also interacts with the structure of the network, with a more sizeable impact on small worlds with a low rewiring probability. Also, social reinforcement completely changes the effect of clustering links, because sequential adoption of neighbors can make one agent adopt at later stages

Global competition dynamics of fossil fuels and renewable energy under climate policies and peak oil:A behavioural model

International audienc

Optimal Diversity in Investments with Recombinant Innovation

We address the notion of dynamic, endogenous diversity and its role in theories of investment and technological innovation. We develop a formal model of an innovation arising from the combination of two existing modules with the objective to optimize the net benefits of diversity. The model takes into account increasing returns to scale and the effect of different dimensions of diversity on the probability of emergence of a third option. We obtain analytical solutions describing the dynamic behaviour of the values of the options. Next we optimize diversity by trading off the benefits of diversity (due to recombinant innovation) and the benefits associated with returns to scale. We derive conditions for optimal diversity under different regimes of returns to scale. When the investment time horizon is beyond a threshold value, the best choice becomes diversity. This threshold will be larger the higher the returns to scale

Diffusion of ideas and complex propagations

Trabajo presentado a la DRUID Academy Conference, celebrada en Aalborg (Dinamarca) del 21 al 23 de enero de 2015.This paper analyzes how social structure and social reinforcement affect the diffusion of an idea in a population of human agents. A percolation approach is used to model the diffusion process. This framework assumes that information is local and embedded in a social network. We introduce social reinforcement in the model by softening the condition to adopt when the number of adopting neighbors increases. Our numerical analysis shows that social reinforcement severely affects the output of the process. Some ideas with an original value so low that it would not get diffused through percolation can be spread due to the strength of social reinforcement. This effect also interacts with the structure of the network, getting a more sizeable impact on small worlds with a low rewiring probability. Also, social reinforcement completely changes the effect of clustering links, because sequential adoption of neighbors can make one agent adopt at later stages.Peer Reviewe