Kristian Lindgren

Evolutionary dynamics of spatial games

Abstract A lattice model of coevolution of strategies for two-person 2 × 2 matrix games is introduced. The model allows evolution in an unbounded space of strategies. In particular we explore the region of parameter space corresponding to the Prisoners dilemma, and classify the types of dynamical and evolutionary behavior that appear. For certain restricted strategy spaces we explore the complete space of lattice games.

Socio-ecological Indicators for Sustainability.

A systematic framework of indicators for sustainability is presented. In our approach there is an emphasis on societal activities that affect nature and on the internal societal resource use, as opposed to environmental quality indicators. In this way the indicators may give a warning signal to an unsustainable use of resources early in the chain from causes in societal activities to environmental effects. The aim is that these socio-ecological indicators shall serve as a tool in planning and decision-making processes at various administrative levels in society. The formulation of the indicators is made with respect to four principles of sustainability, which lead to four complementary sets of indicators. The first deals with the societal use of lithospheric material. The second deals with emissions of compounds produced in society. The third set of indicators concerns societal manipulation of nature and the long-term productivity of ecosystems. Finally, the fourth set deals with the efficiency of the internal societal resource use, which includes indicators for a just distribution of resources.

Complexity of Two-Dimensional Patterns

In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy, with which we can measure the complexity of these sets of sequences, and thus the complexity of the systems which produce them. In this paper, we look at the first few levels of a hierarchy of complexity for two-or-more-dimensional patterns. We show that several definitions of “regular language” or “local rule” that are equivalent in d=1 lead to distinct classes in d≥2. We explore the closure properties and computational complexity of these classes, including undecidability and L, NL, and NP-completeness results. We apply these classes to cellular automata, in particular to their sets of fixed and periodic points, finite-time images, and limit sets. We show that it is undecidable whether a CA in d≥2 has a periodic point of a given period, and that certain “local lattice languages” are not finite-time images or limit sets of any CA. We also show that the entropy of a d-dimensional CAs finite-time image cannot decrease faster than t−d unless it maps every initial condition to a single homogeneous state.

Induced technological change in a limited foresight optimization model

The threat of global warming calls for a major transformation of the energy system the coming century. Modeling technological change is an important factor in energy systems modeling. Technological change may be treated as induced by climate policy or as exogenous. We investigate the importance of induced technological change (ITC) in GET-LFL, an iterative optimization model with limited foresight that includes learning-by-doing. Scenarios for stabilization of atmospheric CO2 concentrations at 400, 450, 500 and 550 ppm are studied. We find that the introduction of ITC reduces the total net present value of the abatement cost over this century by 3-9% compared to a case where technological learning is exogenous. Technology specific polices which force the introduction of fuel cell cars and solar PV in combination with ITC reduce the costs further by 4-7% and lead to significantly different technological solutions in different sectors, primarily in the transport sector.

Urban economy as a scale-free network

We present empirical evidence that land values are scale free and introduce a network model that reproduces the observations. The network approach to urban modeling is based on the assumption that the market dynamics that generates land values can be represented as a growing scale-free network. Our results suggest that the network properties of trade between specialized activities cause land values, and likely also other observables such as population, to be power-law distributed. In addition to being an attractive avenue for further analytical inquiry, the network representation is also applicable to empirical data and is thereby attractive for predictive modeling.

A spatial network explanation for a hierarchy of urban power laws

Power laws in socioeconomic systems are generally explained as being generated by multiplicative growth of aggregate objects. In this paper we formulate a model of geographic activity distribution with spatial correlations on the level of land lots where multiplicative growth is assumed to be dominant but not exclusive. The purpose is to retain the explanatory power of earlier models due to Simon, Gibrat and others while attaining some additional properties that are attractive for both empirical and modelling purposes. In this sense, the model presented here is a combination of the two factors that have been identified as central to urban evolution but rarely appear unified in the same model: transportation costs and multiplicative growth. The model is an elaboration of a previously reported complex network model of geographical land value evolution. We reproduce statistical properties of an empirical geographical distribution of land values on multiple hierarchical levels: land value per unit area, cluster areas, aggregated land value per cluster and cluster area/perimeter ratios. It is found that transportation effects are not strong enough to disturb the power law distribution of land values per unit area but strong enough to sort nodes to generate a new set of power laws on a higher level of aggregation. The main hypothesis is that all these relations can be understood as consequences of an underlying growing scale-free network of geographic economic interdependencies.

Cooperation driven by mutations in multi-person Prisoner's Dilemma

The n-person Prisoners Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be considered as isolated events. For this case, and assuming simple trigger strategies and many iterations per game, we analyse the rate of convergence to the evolutionarily stable populations. We find that for some values of the payoff parameters of the Prisoners Dilemma this rate is so low that the assumption, that mutations in the population are infrequent on that time-scale, is unreasonable. Furthermore, the problem is compounded as the group size is increased. In order to address this issue, we derive a deterministic approximation of the evolutionary dynamics with explicit, stochastic mutation processes, valid when the population size is large. We then analyse how the evolutionary dynamics depends on the following factors: mutation rate, group size, the value of the payoff parameters, and the structure of the initial population. In order to carry out the simulations for groups of more than just a few individuals, we derive an efficient way of calculating the fitness values. We find that when the mutation rate per individual and generation is very low, the dynamics is characterized by populations which are evolutionarily stable. As the mutation rate is increased, other fixed points with a higher degree of cooperation become stable. For some values of the payoff parameters, the system is characterized by (apparently) stable limit cycles dominated by cooperative behaviour. The parameter regions corresponding to high degree of cooperation grow in size with the mutation rate, and in number with the group size. For some parameter values, we find more than one stable fixed point, corresponding to different structures of the initial population.

Local information in one-dimensional cellular automata

A local information measure for a one-dimensional lattice system is introduced, and applied to describe the dynamics of one-dimensional cellular automata.

Low-CO2 Electricity and Hydrogen: A Help or Hindrance for Electric and Hydrogen Vehicles?

The title question was addressed using an energy model that accounts for projected global energy use in all sectors (transportation, heat, and power) of the global economy. Global CO(2) emissions were constrained to achieve stabilization at 400-550 ppm by 2100 at the lowest total system cost (equivalent to perfect CO(2) cap-and-trade regime). For future scenarios where vehicle technology costs were sufficiently competitive to advantage either hydrogen or electric vehicles, increased availability of low-cost, low-CO(2) electricity/hydrogen delayed (but did not prevent) the use of electric/hydrogen-powered vehicles in the model. This occurs when low-CO(2) electricity/hydrogen provides more cost-effective CO(2) mitigation opportunities in the heat and power energy sectors than in transportation. Connections between the sectors leading to this counterintuitive result need consideration in policy and technology planning.

Regular language inference using evolving neural networks

Regular language inference is studied using evolving recurrent neural networks that may change in size through mutations. The scaling of the learning time when information theoretic properties of the test problems are varied is also investigated.<<ETX>>