Nonzero-sum games for continuous-time Markov chains with unbounded transition and average payoff rates

This paper attempts to study two-person nonzero-sum games for denumerable continuous-time Markov chains determined by transition rates,with an expected average criterion.The transition rates are allowed to be unbounded,and the payoff functions may be unbounded from above and from below.We give suitable conditions under which the existence of a Nash equilibrium is ensured.More precisely,using the socalled "vanishing discount" approach,a Nash equilibrium for the average criterion is obtained as a limit point of a sequence of equilibrium strategies for the discounted criterion as the discount factors tend to zero.Our results are illustrated with a birth-and-death game.     

Risk minimizing portfolios and HJBI equations for stochastic differential games

In this paper, we consider the problem to find a market portfolio that minimizes the convex risk measure of the terminal wealth in a jump diffusion market. We formulate the problem as a two player (zero-sum) stochastic differential game. To help us find a solution, we prove a theorem giving the Hamilton–Jacobi–Bellman–Isaacs (HJBI) conditions for a general zero-sum stochastic differential game in a jump diffusion setting. We then use the theorem to study particular risk minimization problems. Finally, we extend our approach to cover general stochastic differential games (not necessarily zero-sum), and we obtain similar HJBI equations for the Nash equilibria of such games.     

A Dynkin game with asymmetric information

We study a Dynkin game with asymmetric information. The game has a random expiry time, which is exponentially distributed and independent of the underlying process. The players have asymmetric information on the expiry time, namely only one of the players is able to observe its occurrence. We propose a set of conditions under which we solve the saddle point equilibrium and study the implications of the information asymmetry. Results are illustrated with an explicit example.     

Stochastic Differential Games With a Small Parameter

Much of stochastic game theory is concerned with diffusion models. Such models are often only idealizations of the actual physical process, which might be driven by a wide bandwidth process or be a discrete parameter system with correlated driving noises. For a two person zero-sum game, under quite general conditions, the optimal or nearly optimal strategies derived for the diffusion model are shown to be “nearly optimal” for the physical (say wideband noise driven) process. An approach based on occupation measures are used. We treat the problem of discounted cost, as well as the average cost per unit time problem. Weak convergence methods are utilized in the analysis     

公众参与下的企业环境行为演化研究

公众参与对环境治理非常重要并越来越受到社会各界的关注.本文采用演化博弈理论方法,建立了公众与排污企业行为交互过程的演化模型,用数值仿真展示了决策参数的不同取值和初始条件的改变对演化结果的影响.研究发现,公众参与下的企业环境行为路径演化系统既可以向良好状态演化,也可以“锁定”于不良状态;通过调节模型中的参数可以跳出不良“锁定”状态.本文的分析和结果可以为环境治理提供相应的参考.     

A density-dependent model describing age-structured population dynamics using hawk–dove tactics

In this paper we deal with a nonlinear two-timescale discrete population model that couples age-structured demography with individual competition for resources. Individuals are divided into juvenile and adult classes, and demography is described by means of a density-dependent Leslie matrix. Adults compete to access resources; every time two adults meet, they choose either being aggressive (hawk) or non-aggressive (dove) to get the best pay-off. Individual encounters occur much more frequently than demographic events, what yields that the model takes the form of a two-timescale system. Approximate aggregation methods allow us to reduce the system while preserving at the same time crucial asymptotic information for the whole population. In this way, we are able to describe the total population size as function of individual aggressiveness level and environmental richness. Model analysis shows a general trend with species that look for richer environment having smaller proportions of hawk individuals with larger costs.     

Characterizations ofk-Convex Games

The paper deals with the class of k-convex n-person transferable utility games which has clear affinities to the well-known class of convex n-person TU-games. Five new characterizations of a k-convex n-person game are presented in terms of the following key notions:(1) the unanimity coordinates, as determined by the algebraic representation of the game with respect to the particular basis consisting of all n-person unanimity games; (2) the second order partial derivatives of Owen's multilinear extension of the game; (3) the coremembership of the adjusted marginal worth vectors of the game (taking into account even or odd orderings of players); (4) a min-modular decomposition of an appropriately chosen cover-game (the decomposition of which is based on the adjusted marginal worth vectors of the initial game); (5) the concavity of the Lovász extension of the associated cover-game     

Selective investment promotes cooperation in public goods game

Most previous investigations on spatial Public Goods Game assume that individuals treat neighbors equivalently, which is in sharp contrast with realistic situations, where bias is ubiquitous. We construct a model to study how a selective investment mechanism affects the evolution of cooperation. Cooperators selectively contribute to just a fraction among their neighbors. According to the interaction result, the investment network can be adapted. On selecting investees, three patterns are considered. In the random pattern, cooperators choose their investees among the neighbors equiprobably. In the social-preference pattern, cooperators tend to invest to individuals possessing large social ties. In the wealth-preference pattern, cooperators are more likely to invest to neighbors with higher payoffs. Our result shows robustness of selective investment mechanism that boosts emergence and maintenance of cooperation. Cooperation is more or less hampered under the latter two patterns, and we prove the anti-social-preference or anti-wealth-preference pattern of selecting investees can accelerate cooperation to some extent. Furthermore, the theoretical analysis of our mechanism on double-star networks coincides with simulation results. We hope our finding could shed light on better understanding of the emergence of cooperation among adaptive populations.     

Heritability promotes cooperation in spatial public goods games

Heritability is ubiquitous within most real biological or social systems. A heritable trait is most simply an offspring’s trait that resembles the parent’s corresponding trait, which can be fitness, strategy, or the way of strategy adoption for evolutionary games. Here we study the effects of heritability on the evolution of spatial public goods games. In our model, the fitness of players is determined by the payoffs from the current interactions and their history. Based on extensive simulations, we find that the density of cooperators is enhanced by increasing the heritability of players over a wide range of the multiplication factor. We attribute the enhancement of cooperation to the inherited fitness that stabilizes the fitness of players, and thus prevents the expansion of defectors effectively.     

基于联合作战兵力配置的非合作博弈研究

基于联合作战实体定量分析的作战能力指数组合期望效用,研究了联合作战任务兵力配置问题,建立了二人零和参数博弈模型,并讨论了模型构建的理论依据与算法.