The Price of Anarchy (PoA) is a well-established game-theoretic concept to shed light on coordination issues arising in open distributed systems. Leaving agents to selfishly optimize comes with the risk of ending up in sub-optimal states (in terms of performance and or costs), compared to a centralized system design. However, the PoA relies on strong assumptions about agents' rationality (e.g., resources and information) and interactions, whereas in many distributed systems agents interact locally with bounded resources. They do so repeatedly over time (in contrast to "one-shot games"), and their strategies may evolve. Using a more realistic evolutionary game model, this paper introduces a realized evolutionary Price of Anarchy (ePoA). The ePoA allows an exploration of equilibrium selection in dynamic distributed systems with multiple equilibria, based on local interactions of simple memoryless agents. Considering a fundamental game related to virus propagation on networks, we present analytical bounds on the ePoA in basic network topologies and for different strategy update dynamics. In particular, deriving stationary distributions of the stochastic evolutionary process, we find that the Nash equilibria are not always the most abundant states, and that different processes can feature significant off-equilibrium behavior, leading to a significantly higher ePoA compared to the PoA studied traditionally in the literature.
More specifically, we revisited 's virus inoculation game @cite_32 in this paper. Traditional virus propagation models studied virus infection in terms of birth and death rates of viruses @cite_2 @cite_16 as well as through local interactions on networks @cite_6 @cite_3 @cite_43 (e.g., the Internet @cite_11 @cite_1 ). An interesting study is due to Montanari and Saberi @cite_15 who compare game-theoretic and epidemic models, investigating differences between the viral behavior of the spread of viruses, new technologies, and new political or social beliefs.
@cite_1 @cite_32 @cite_3 @cite_6 @cite_43 @cite_2 @cite_15 @cite_16 @cite_11
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The strong analogy between biological viruses and their computational counterparts has motivated the authors to adapt the techniques of mathematical epidemiology to the study of computer virus propagation. In order to allow for the most general patterns of program sharing, a standard epidemiological model is extended by placing it on a directed graph and a combination of analysis and simulation is used to study its behavior. The conditions under which epidemics are likely to occur are determined, and, in cases where they do, the dynamics of the expected number of infected individuals are examined as a function of time. It is concluded that an imperfect defense against computer viruses can still be highly effective in preventing their widespread proliferation, provided that the infection rate does not exceed a well-defined critical epidemic threshold. > Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number @math , the contact number @math , and the replacement number @math are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for @math are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of @math and @math are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed. The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible infective removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are nonuniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks. To understand the current extent of the computer virus problem and predict its future course, the authors have conducted a statistical analysis of computer virus incidents in a large, stable sample population of PCs and developed new epidemiological models of computer virus spread. Only a small fraction of all known viruses have appeared in real incidents, partly because many viruses are below the theoretical epidemic threshold. The observed sub-exponential rate of viral spread can be explained by models of localized software exchange. A surprisingly small fraction of machines in well-protected business environments are infected. This may be explained by a model in which, once a machine is found to be infected, neighboring machines are checked for viruses. This kill signal idea could be implemented in networks to greatly reduce the threat of viral spread. A similar principle has been incorporated into a cost-effective anti-virus policy for organizations which works quite well in practice. >