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Register a new userFixation and escape times in stochastic game learning
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Evolutionary dynamics in finite populations is known to fixate eventually in the absence of mutation. We here show that a similar phenomenon can be found in stochastic game dynamical batch learning, and investigate fixation in learning processes in a simple 2x2 game, for two-player games with cyclic interaction, and in the context of the best-shot network game. The analogues of finite populations in evolution are here finite batches of observations between strategy updates. We study when and how such fixation can occur, and present results on the average time-to-fixation from numerical simulations. Simple cases are also amenable to analytical approaches and we provide estimates of the behaviour of so-called escape times as a function of the batch size. The differences and similarities with escape and fixation in evolutionary dynamics are discussed.
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Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding of the dynamics. In this paper, we study the transient dynamics of the well-mixed Moran process through constructing a landscape function. It is shown that the landscape playing a central theoretical device that integrates several lines of inquiries: the stable behavior of the replicator dynamics, the long-time fixation, and continuous diffusion approximation associated with asymptotically large population. Several issues relating to the transient dynamics are discussed: (i) multiple time scales phenomenon associated with intra- and inter-attractoral dynamics; (ii) discontinuous transition in stochastically stationary process akin to Maxwell construction in equilibrium statistical physics; and (iii) the dilemma diffusion approximation facing as a continuous approximation of the discrete evolutionary dynamics. It is found that rare events with exponentially small probabilities, corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that are made possible by strong nonlinear dynamics, plays an important role in understanding the origin of the complexity in evolutionary, nonlinear biological systems.
Facing the threats of infectious diseases, we take various actions to protect ourselves, but few studies considered an evolving system with competing strategies. In view of that, we propose an evolutionary epidemic model coupled with human behaviors, where individuals have three strategies: vaccination, self-protection and laissez faire, and could adjust their strategies according to their neighbors strategies and payoffs at the beginning of each new season of epidemic spreading. We found a counter-intuitive phenomenon analogous to the well-known emph{Braesss Paradox}, namely a better condition may lead to worse performance. Specifically speaking, increasing the successful rate of self-protection does not necessarily reduce the epidemic size or improve the system payoff. This phenomenon is insensitive to the network topologies, and can be well explained by a mean-field approximation. Our study demonstrates an important fact that a better condition for individuals may yield a worse outcome for the society.
The maintenance of cooperation in the presence of spatial restrictions has been studied extensively. It is well-established that the underlying graph topology can significantly influence the outcome of games on graphs. Maintenance of cooperation could be difficult, especially in the absence of spatial restrictions. The evolution of cooperation would naturally depend on payoffs. However, payoffs are generally considered to be invariant in a given game. A natural yet unexplored question is whether the topology of the underlying structures on which the games are played, possesses no role whatsoever in the determination of payoffs. Herein, we introduce the notion of cooperator graphs and defector graphs as well as a new form of game payoff, which is weakly dependent on the underlying network topology. These concepts are inspired by the well-known microbial phenomenon of quorum sensing. We demonstrate that even with such a weak dependence, the fundamental game dynamics and indeed the very nature of the game may be altered. Such changes in the nature of a game have been well-reported in theoretical and experimental studies.
We propose an extended spatial evolutionary public goods game (SEPGG) model to study the dynamics of individual career choice and the corresponding social output. Based on the social value orientation theory, we categorized two classes of work, namely the public work if it serves public interests, and the private work if it serves personal interests. Under the context of SEPGG, choosing public work is to cooperate and choosing private work is to defect. We then investigate the effects of employee productivity, human capital and external subsidies on individual career choices of the two work types, as well as the overall social welfare. From simulation results, we found that when employee productivity of public work is low, people are more willing to enter the private sector. Although this will make both the effort level and human capital of individuals doing private work higher than those engaging in public work, the total outcome of the private sector is still lower than that of the public sector provided a low level of public subsidies. When the employee productivity is higher for public work, a certain amount of subsidy can greatly improve system output. On the contrary, when the employee productivity of public work is low, provisions of subsidy to the public sector can result in a decline in social output.
We investigate the dynamics of a broad class of stochastic copying processes on a network that includes examples from population genetics (spatially-structured Wright-Fisher models), ecology (Hubbell-type models), linguistics (the utterance selection model) and opinion dynamics (the voter model) as special cases. These models all have absorbing states of fixation where all the nodes are in the same state. Earlier studies of these models showed that the mean time when this occurs can be made to grow as different powers of the network size by varying the the degree distribution of the network. Here we demonstrate that this effect can also arise if one varies the asymmetry of the copying dynamics whilst holding the degree distribution constant. In particular, we show that the mean time to fixation can be accelerated even on homogeneous networks when certain nodes are very much more likely to be copied from than copied to. We further show that there is a complex interplay between degree distribution and asymmetry when they may co-vary; and that the results are robust to correlations in the network or the initial condition.
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