On simplifying ‘incremental remap’–based transport schemes

The flux-form incremental remapping transport scheme introduced by Dukowicz and Baumgardner [1] converts the transport problem into a remapping problem. This involves identifying overlap areas between quadrilateral flux-areas and regular square grid cells which is non-trivial and leads to some algorithm complexity. In the simpler swept area approach (originally introduced by Hirt et al. [2]) the search for overlap areas is eliminated even if the flux-areas overlap several regular grid cells. The resulting simplified scheme leads to a much simpler and robust algorithm.     

Reputation-based network selection mechanism using game theory

Current and future wireless environments are based on the coexistence of multiple networks supported by various access technologies deployed by different operators. As wireless network deployments increase, their usage is also experiencing a significant growth. In this heterogeneous multi-technology multi-application multi-terminal multi-user environment users will be able to freely connect to any of the available access technologies. Network selection mechanisms will be required in order to keep mobile users “always best connected” anywhere and anytime. In such a heterogeneous environment, game theory techniques can be adopted in order to understand and model competitive or cooperative scenarios between rational decision makers. In this work we propose a theoretical framework for combining reputation-based systems, game theory and network selection mechanism. We define a network reputation factor which reflects the network’s previous behaviour in assuring service guarantees to the user. Using the repeated Prisoner’s Dilemma game, we model the user–network interaction as a cooperative game and we show that by defining incentives for cooperation and disincentives against defecting on service guarantees, repeated interaction sustains cooperation.     

Quantum game interpretation for a special case of Parrondo’s paradox

By using the discrete Markov chain method, Parrondo’s paradox is studied by means of theoretical analysis and computer simulation, built on the case of game AB played in alternation with modulus M=4. We find that such a case does not have a definite stationary probability distribution and that payoffs of the game depend on the parity of the initial capital. Besides, this paper reveals the phenomenon that “processing in order produces non-deterministic results, while a random process produces deterministic results”. The quantum game method is used in a further study. The results show that the explanation of the game corresponding to a stationary probability distribution is that the probability of the initial capital has reached parity.     

Evolution of cooperation among mobile agents

We study the effects of mobility on the evolution of cooperation among mobile players, which imitate collective motion of biological flocks and interact with neighbors within a prescribed radius R. Adopting the the prisoner’s dilemma game and the snowdrift game as metaphors, we find that cooperation can be maintained and even enhanced for low velocities and small payoff parameters, when compared with the case that all agents do not move. But such enhancement of cooperation is largely determined by the value of R, and for modest values of R, there is an optimal value of velocity to induce the maximum cooperation level. Besides, we find that intermediate values of R or initial population densities are most favorable for cooperation, when the velocity is fixed. Depending on the payoff parameters, the system can reach an absorbing state of cooperation when the snowdrift game is played. Our findings may help understanding the relations between individual mobility and cooperative behavior in social systems.     

Costly punishment and cooperation in the evolutionary snowdrift game

The role of punishments in promoting cooperation is an important issue. We incorporate costly punishments into the snowdrift game (SG) by introducing a third punishing (P) character, and study the effects. The punishers, who carry basically a cooperative (C) character, are willing to pay a cost α so as to punish a non-cooperative (D) opponent by β. Depending on the initial fractions of the characters, α, β, and the cost-to-benefit ratio r in the SG, the three-character system evolves into a steady state consisting either only of C and P characters or only of C and D characters, in a well-mixed population. The former situation represents an enhancement in cooperation relative to the SG, while the latter is similar to the SG. The dynamics in approaching these different steady states are found to be different. Analytically, the key features in the dynamics and the steady states observed in simulations are captured by a set of differential equations. The sensitivity to the initial distribution of characters is studied by depicting the flow in a phase portrait and analyzing the nature of fixed points. The analysis also shows the role of P-character agents in preventing a system from invasion by D-character agents. Starting from a population consisting only of C and P agents, a D-character agent intended to invade the system cannot survive when the initial fraction of P agents is greater than r/β. Our model, defined intentionally as a simulation algorithm, can be readily generalized to incorporate many interesting effects, such as those in a networked population.     

Integrating neighborhoods in the evaluation of fitness promotes cooperation in the spatial prisoner’s dilemma game

A fundamental question of human society is the evolution of cooperation. Many previous studies explored this question via setting spatial background, where players obtain their payoffs by playing game with their nearest neighbors. Another undoubted fact is that the environment plays an important role in the individual development. Inspired by these phenomena, we reconsider the definition of individual fitness which integrates the environment, denoted by the average payoff of all individual neighbors, with the traditional individual payoffs by introducing a selection parameter u. Tuning u equal to zero returns the traditional version, while increasing u bears the influence of environment. We find that considering the environment, i.e., integrating neighborhoods in the evaluation of fitness, promotes cooperation. If we enhance the value of u, the invasion of defection could be resisted better. We also provide quantitative explanations and complete phase diagrams presenting the influence of the environment on the evolution of cooperation. Finally, the universality of this mechanism is testified for different neighborhood sizes, different topology structures and different game models. Our work may shed light on the emergence and persistence of cooperation in our life.     

q-Strategy spatial prisoner?s dilemma game

We generalize the usual two-strategy prisoner?s dilemma game to a multi-strategy game, in which the strategy variable s is allowed to take q different fractional values lying between 0 and 1. The fractional-valued strategies signify that individuals are not absolutely cooperative or defective, instead they can adopt intermediate strategies. Simulation results on 1D and 2D lattices show that, compared with the binary strategy game, the multi-strategy game can sustain cooperation in more stringent defective environments. We give a comprehensive analysis of the distributions of the survived strategies and we compare pairwise the relative strength and weakness of different strategies. It turns out that some intermediate strategies survive the pure defection because they can reduce being exploited and at the same time benefit from the spatial reciprocity effect. Our work may shed some light on the intermediate behaviors in human society.     

Evolution of cooperation among mobile agents with heterogenous view radii

In this paper, we study cooperative behavior among mobile agents; the agents have heterogenous view radii and they play the prisoner’s dilemma game with those being within their vision fields. It is found that the cooperation level is remarkably promoted when the heterogeneity of view radii is considered, and the degree distribution of the system is investigated to explain this interesting phenomenon. Moreover, we report that the cooperative behavior is best favored by low density, moderate view radius, and small moving speed. Our findings may be helpful in understanding cooperative behavior in natural and social systems consisting of mobile agents.     

Computational method for solving space fractional Fisher's nonlinear equation

This paper aims to present a general framework of the quadratic spline functions to develop a numerical method for solving the nonlinear space fractional Fisher's equation. Using Von Neumann method, the proposed method is shown to be conditionally stable. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm. The results reveal that the proposed approach is very effective, convenient, and quite accurate to such considered problems. Copyright © 2013 John Wiley & Sons, Ltd.     

Multi-player stopping games with redistribution of payoffs and BSDEs with oblique reflection

We examine the connections between a novel class of multi-person stopping games with redistribution of payoffs and multi-dimensional reflected BSDEs in discrete- and continuous-time frameworks. Our goal is to provide an essential extension of classic results for two-player stopping games (Dynkin games) to the multi-player framework. We show the link between certain multi-period m$m$-player stopping games and a new kind of m$m$-dimensional reflected BSDEs. The existence and uniqueness of a solution to continuous-time reflected BSDEs are established. Continuous-time redistribution games are constructed with the help of reflected BSDEs and a characterization of the value of such stopping games is provided.