Epidemic prevalence information on social networks can mediate emergent collective outcomes in voluntary vaccine schemes.

The effectiveness of a mass vaccination program can engender its own undoing if individuals choose to not get vaccinated believing that they are already protected by herd immunity. This would appear to be the optimal decision for an individual, based on a strategic appraisal of her costs and benefits, even though she would be vulnerable during subsequent outbreaks if the majority of the population argues in this manner. We investigate how voluntary vaccination can nevertheless emerge in a social network of rational agents, who make informed decisions whether to be vaccinated, integrated with a model of epidemic dynamics. The information available to each agent includes the prevalence of the disease in their local network neighborhood and/or globally in the population, as well as the fraction of their neighbors that are protected against the disease. Crucially, the payoffs governing the decision of agents vary with disease prevalence, resulting in the vaccine uptake behavior changing in response to contagion spreading. The collective behavior of the agents responding to local prevalence can lead to a significant reduction in the final epidemic size, particularly for less contagious diseases having low basic reproduction number [Formula: see text]. Near the epidemic threshold ([Formula: see text]) the use of local prevalence information can result in divergent responses in the final vaccine coverage. Our results suggest that heterogeneity in the risk perception resulting from the spatio-temporal evolution of an epidemic differentially affects agents' payoffs, which is a critical determinant of the success of voluntary vaccination schemes.

When big data fails: Adaptive agents using coarse-grained information have competitive advantage.

The recent trend for acquiring big data assumes that possessing quantitatively more and qualitatively finer data necessarily provides an advantage that may be critical in competitive situations. Using a model complex adaptive system where agents compete for a limited resource using information coarse grained to different levels, we show that agents having access to more and better data perform worse than others in certain situations. The relation between information asymmetry and individual payoffs is seen to be complex, depending on the composition of the population of competing agents.

Co-action provides rational basis for the evolutionary success of Pavlovian strategies.

Strategies incorporating direct reciprocity, e.g., Tit-for-Tat and Pavlov, have been shown to be successful for playing the Iterated Prisoners Dilemma (IPD), a paradigmatic problem for studying the evolution of cooperation among non-kin individuals. However it is an open question whether such reciprocal strategies can emerge as the rational outcome of repeated interactions between selfish agents. Here we show that adopting a co-action perspective, which takes into account the symmetry between agents - a relevant consideration in biological and social contexts - naturally leads to such a strategy. For a 2-player IPD, we show that the co-action solution corresponds to the Pavlov strategy, thereby providing a rational basis for it. For an IPD involving many players, an instance of the Public Goods game where cooperation is generally considered to be harder to achieve, we show that the cooperators always outnumber defectors in the co-action equilibrium. This can be seen as a generalization of Pavlov to contests involving many players. In general, repeated interactions allow rational agents to become aware of the inherent symmetry of their situation, enabling them to achieve robust cooperation through co-action strategies - which, in the case of IPD, is a reciprocal Pavlovian one.

Symmetry warrants rational cooperation by co-action in Social Dilemmas.

Is it rational for selfish individuals to cooperate? The conventional answer based on analysis of games such as the Prisoners Dilemma (PD) is that it is not, even though mutual cooperation results in a better outcome for all. This incompatibility between individual rationality and collective benefit lies at the heart of questions about the evolution of cooperation, as illustrated by PD and similar games. Here, we argue that this apparent incompatibility is due to an inconsistency in the standard Nash framework for analyzing non-cooperative games and propose a new paradigm, that of the co-action equilibrium. As in the Nash solution, agents know that others are just as rational as them and taking this into account lead them to realize that others will independently adopt the same strategy, in contrast to the idea of unilateral deviation central to Nash equilibrium thinking. Co-action equilibrium results in better collective outcomes for games representing social dilemmas, with relatively "nicer" strategies being chosen by rational selfish individuals. In particular, the dilemma of PD gets resolved within this framework, suggesting that cooperation can evolve in nature as the rational outcome even for selfish agents, without having to take recourse to additional mechanisms for promoting it.

Continuum percolation of overlapping disks with a distribution of radii having a power-law tail.

We study the continuum percolation problem of overlapping disks with a distribution of radii having a power-law tail; the probability that a given disk has a radius between R and R+dR is proportional to R(-(a+1)), where a>2. We show that in the low-density nonpercolating phase, the two-point function shows a power-law decay with distance, even at arbitrarily low densities of the disks, unlike the exponential decay in the usual percolation problem. As in the problem of fluids with long-range interaction, we argue that in our problem, the critical exponents take their short-range values for a>3-η(sr) whereas they depend on a for a<3-η(sr) where η(sr) is the anomalous dimension for the usual percolation problem. The mean-field regime obtained in the fluid problem corresponds to the fully covered regime, a≤2, in the percolation problem. We propose an approximate renormalization scheme to determine the correlation length exponent ν and the percolation threshold. We carry out Monte Carlo simulations and determine the exponent ν as a function of a. The determined values of ν show that it is independent of the parameter a for a>3-η(sr) and is equal to that for the lattice percolation problem, whereas ν varies with a for 2