Social and individual learning in the Minority Game

We study the roles of social and individual learning on outcomes of the Minority Game model of a financial market. Social learning occurs via agents adopting the strategies of their neighbours within a social network, while individual learning results in agents changing their strategies without input from other agents. In particular, we show how social learning can undermine efficiency of the market due to negative frequency dependent selection and loss of strategy diversity. The latter of which can lock the population into a maximally inefficient state. We show how individual learning can rescue a population engaged in social learning from such inefficiencies

Truncation selection and diffusion on random graphs

Two-strategy evolutionary games on graphs have been extensively studied in the literature. A variety of graph structures, degrees of graph dynamics, and behaviours of replicators have been explored. These models have primarily been studied in the framework of facilitation of cooperation, and much excellent work has shed light on this field of study. However, there has been little attention to truncation selection as most models employ proportional selection (reminiscent of the replicator equation) or "imitate the best." Here we systematically explore truncation selection on random graphs, where replicators below a fitness threshold are culled and the reproduction probabilities are equal for all survivors. We employ two variations of this method: independent truncation, where the threshold is fixed; and dependent truncation, which is a generalization of "imitate the best." Further, we explore the effects of diffusion in our networks in the following orders of operation: diffusion-combat-offspring (DCO), and combat-diffusion-offspring (CDO). For independent truncation, we find three regimes determined by the fitness threshold: cooperation decreases as we raise the threshold; cooperation initially rises as we raise the threshold and there exists an optimal threshold for facilitating cooperation; and the entire population goes extinct. We find that dependent truncation affects games differently; lower levels reduce cooperation for the hawk-dove game and increase it for the stag hunt, and higher levels produce the opposite effects. DCO reduces cooperation in the static case. However, CDO has approximately as much or more cooperation than the static case

Strategic Interactions in Antiviral Drug Use During an Influenza Pandemic

Background: The evolution of antiviral drug resistance during influenza pandemics has created widespread concern. Use of antiviral drugs is a main contributor to the evolution of drug-resistant strains. Moreover, there are recent examples of influenza viruses acquiring drug resistance seemingly without incurring a fitness penalty that reduces their transmission rate. This creates the possibility of strategic (game theoretical) interaction between jurisdictions making decisions about use of antiviral drug stockpiles. Methods: We developed and analyzed a 2-player 2-strategy game theoretical model. Each ‘player’ (an authority in a health jurisdiction) can choose to treat with antiviral drugs at a low rate or a high rate. High treatment rates are more likely to cause emergence of a drug-resistant strain, and once a drug-resistant strain has evolved, it can spread between the two jurisdictions. We determine the Nash equilibria of the game. Results: We show that there is a coordination game between the jurisdictions, where both players choosing a low treatment rate, or both choosing a high treatment rate, are the only stable outcomes. The socially optimal outcome occurs if both players cooperate by choosing a low treatment rate, thereby avoiding generating drug-resistant mutants. However, such cooperation may fail to materialize if the jurisdictions are closely connected through travel; if the drug-resistant mutant is tolerated (not seen as undesirable); or if the antiviral drug has partial efficacy against transmission of the drug-resistant strain. Conclusions: Inter-jurisdictional cooperation could be essential during a severe influenza pandemic, but we know little about how jurisdictions will interact in a scenario where highly pathogenic, drug-resistant mutant strains are able to transmit as effectively as non-resistant strains. Therefore, strategic multi-population interactions during influenza pandemics should be further studied.Canadian Institutes of Health Researc

Emergence and spread of drug resistant influenza: A two-population game theoretical model

Background The potential for emergence of antiviral drug resistance during influenza pandemics has raised great concern for public health. Widespread use of antiviral drugs is a significant factor in producing resistant strains. Recent studies show that some influenza viruses may gain antiviral drug resistance without a fitness penalty. This creates the possibility of strategic interaction between populations considering antiviral drug use strategies. Methods To explain why, we develop and analyze a classical 2-player game theoretical model where each player chooses from a range of possible rates of antiviral drug use, and payoffs are derived as a function of final size of epidemic with the regular and mutant strain. Final sizes are derived from a stochastic compartmental epidemic model that captures transmission within each population and between populations, and the stochastic emergence of antiviral drug resistance. High treatment levels not only increase the spread of the resistant strain in the subject population but also affect the other population by increasing the density of the resistant strain infectious individuals due to travel between populations. Results We found two Nash equilibria where both populations treat at a high rate, or both treat at a low rate. Hence the game theoretical analysis predicts that populations will not choose different treatment strategies than other populations, under these assumptions. The populations may choose to cooperate by maintaining a low treatment rate that does not increase the incidence of mutant strain infections or cause case importations to the other population. Alternatively, if one population is treating at a high rate, this will generate a large number of mutant infections that spread to the other population, in turn incentivizing that population to also treat at a high rate. The prediction of two separate Nash equilibria is robust to the mutation rate and the effectiveness of the drug in preventing transmission, but it is sensitive to the volume of travel between the two populations. Conclusions Model-based evaluations of antiviral influenza drug use during a pandemic usually consider populations in isolation from one another, but our results show that strategic interactions could strongly influence a population's choice of antiviral drug use policy. Furthermore, the high treatment rate Nash equilibrium has the potential to become socially suboptimal (i.e. non-Pareto optimal) under model assumptions that might apply under other conditions. Because of the need for players to coordinate their actions, we conclude that communication and coordination between jurisdictions during influenza pandemics is a priority, especially for influenza strains that do not evolve a fitness penalty under antiviral drug resistance.Game theoryStochastic compartmental modelAntiviral drugsDrug resistanceH1N1Fitness penalt

Complete analysis of the B-cell response to a protein antigen, from in vivo germinal centre formation to 3-D modelling of affinity maturation

Somatic hypermutation of immunoglobulin variable region genes occurs within germinal centres (GCs) and is the process responsible for affinity maturation of antibodies during an immune response. Previous studies have focused almost exclusively on the immune response to haptens, which may be unrepresentative of epitopes on protein antigens. In this study, we have exploited a model system that uses transgenic B and CD4<sup>+</sup> T cells specific for hen egg lysozyme (HEL) and a chicken ovalbumin peptide, respectively, to investigate a tightly synchronized immune response to protein antigens of widely differing affinities, thus allowing us to track many facets of the development of an antibody response at the antigen-specific B cell level in an integrated system <i>in</i> <i>vivo</i>. Somatic hypermutation of immunoglobulin variable genes was analysed in clones of transgenic B cells proliferating in individual GCs in response to HEL or the cross-reactive low-affinity antigen, duck egg lysozyme (DEL). Molecular modelling of the antibody–antigen interface demonstrates that recurring mutations in the antigen-binding site, selected in GCs, enhance interactions of the antibody with DEL. The effects of these mutations on affinity maturation are demonstrated by a shift of transgenic serum antibodies towards higher affinity for DEL in DEL-cOVA immunized mice. The results show that B cells with high affinity antigen receptors can revise their specificity by somatic hypermutation and antigen selection in response to a low-affinity, cross-reactive antigen. These observations shed further light on the nature of the immune response to pathogens and autoimmunity and demonstrate the utility of this novel model for studies of the mechanisms of somatic hypermutation