The robustness of a Nash equilibrium simulation model: Game-theoretic approach using variable metric projection method

This paper proposes a Nash equilibrium model that applies continuous time replicator dynamics to the analysis of oligopoly markets. The robustness of the proposed simple Nash equilibrium model under the simultaneous constraints of allocation of product and market share using a simulation method to derive an optimal solution for production decisions by rival firms in oligopoly markets is tested by changing profit and cost function parameters, as well as the initial production values and market shares of the firms examined in this study. The effects of differences in conjectural variation and initial allocation of market share on the convergent values are considered, particularly in the case of corner solutions. This approach facilitates the understanding of the robustness of attaining equilibrium in an oligopoly market.     

基于演化博弈论的p-坚持CSMA网络接入控制研究

考虑到存在无线信道差错,针对p-坚持CSMA网络的非合作系统行为,建立了p-坚持CSMA演化博弈模型,推导了唯一的演化稳定策略,以饱和吞吐量最大、平均能耗最小为目标求解了最优演化稳定策略。然后,进一步研究了收益时延、成功收益以及比特差错概率对最优演化稳定过程的影响。数值仿真结果表明,当比特差错概率一定、收益时延较小时,选择合适的成本和收益,使多路访问博弈在最优传输概率处演化稳定,可获得一个稳定且性能最优的p-坚持CSMA网络。     

Optimal replicator factor control in wireless sensor networks

For TDMA MAC protocols in wireless sensor networks (WSNs), redundancy and retransmission are two important methods to provide high end-to-end transmission reliability. Since reliable transmissions will lead to more energy consumption, there exists an intrinsic tradeoff between transmission reliability and energy efficiency. For each link, we name the number of its reserved time slots in each MAC superframe as a replicator factor. In the following paper, we propose a reliability-lifetime tradeoff framework (RLTF) for WSNs to study replicator factor control problem. First, for the redundancy TDMA MAC, we formulate replicator factor control problem as convex programming. By the gradient projection method, we develop a fully distributed algorithm to solve the convex programming. Second, for the retransmission TDMA MAC, we set the retransmission upper bound for each link according to the optimal replicator factors under the redundancy MAC and compute the total communication overhead for the retransmission MAC. Finally, we compare the communication overhead of these two MAC protocols under different channel conditions.     

A Nash equilibrium solution in an oligopoly market: The search for Nash equilibrium solutions with replicator equations derived from the gradient dynamics of a simplex algorithm

The present analysis applies continuous time replicator dynamics to the analysis of oligopoly markets. In the present paper, we discuss continuous game problems in which decision-making variables for each player are bounded on a simplex by equalities and non-negative constraints. Several types of problems are considered under conditions of normalized constraints and non-negative constraints. These problems can be classified into two types based on their constraints. For one type, the simplex constraint applies to the variables for each player independently, such as in a product allocation problem. For the other type, the simplex constraint applies to interference among all players, creating a market share problem. In the present paper, we consider a game problem under the constraints of allocation of product and market share simultaneously. We assume that a Nash equilibrium solution can be applied and derive the gradient system dynamics that attain the Nash equilibrium solution without violating the simplex constraints. Models assume that three or more firms exist in a market. Firms behave to maximize their profits, as defined by the difference between their sales and cost functions with conjectural variations. The effectiveness of the derived dynamics is demonstrated using simple data. The present approach facilitates understanding the process of attaining equilibrium in an oligopoly market.     

What evolutionary game theory tells us about multiagent learning

This paper discusses If multi-agent learning is the answer, what is the question? [Y. Shoham, R. Powers, T. Grenager, If multi-agent learning is the answer, what is the question? Artificial Intelligence 171 (7) (2007) 365-377, this issue] from the perspective of evolutionary game theory. We briefly discuss the concepts of evolutionary game theory, and examine the main conclusions from [Y. Shoham, R. Powers, T. Grenager, If multi-agent learning is the answer, what is the question? Artificial Intelligence 171 (7) (2007) 365-377, this issue] with respect to some of our previous work. Overall we find much to agree with, concluding, however, that the central concerns of multiagent learning are rather narrow compared with the broad variety of work identified in [Y. Shoham, R. Powers, T. Grenager, If multi-agent learning is the answer, what is the question? Artificial Inteligence 171 (7) (2007) 365-377, this issue].     

Criticality of cooperative society

Generally speaking, there are two types of interaction, synchronous interactions (N members interact simultaneously) and asynchronous interactions (each member interacts withN neighboring agents individually). The purpose of this paper is to consider the dynamics of the evolution of a cooperative society with synchronous interaction by focusing on the spatial size of the interaction. Asynchronous interaction is dealt with in the cumulative payoff of individual 2-interated prisoner's dilemma (2-IPD) games. The result has shown that an adequate spatial size for interaction promotes a highly cooperative society, but it gets more difficult for agents with synchronous interactions to achieve a cooperative society as it increases in size. This work was presented, in part, at the Sixth International Symposium on Artificial Life and Robotics, Tokyo, Japan, January 15–17, 2001     

Replicator Dynamics in the Iterative Process for Accurate Range Image Matching

Iterative algorithms are often used for range image matching. In this paper, we treat the iterative process of range image matching as a live biological system: evolving from one generation to another. Whilst different generations of the population are regarded as range images captured at different viewpoints, the iterative process is simulated using time. The well-known replicator equations in theoretical biology are then adapted to estimate the probabilities of possible correspondences established using the traditional closest point criterion. To reduce the effect of image resolutions on the final results for efficient and robust overlapping range image matching, the relative fitness difference (rather than the absolute fitness difference) is employed in the replicator equations in order to model the probability change of possible correspondences being real over successive iterations. The fitness of a possible correspondence is defined as the negative of a power of its squared Euclidean distance. While the replicator dynamics penalize those individuals with low fitness, they are further penalised with a parameter, since distant points are often unlikely to represent their real replicators. While the replicator equations assume that all individuals are equally likely to meet each other and thus treat them equally, we penalise those individuals competing for the same points as their possible replicators. The estimated probabilities of possible correspondences being real are finally embedded into the powerful deterministic annealing scheme for global optimization, resulting in the camera motion parameters being estimated in the weighted least squares sense. A comparative study based on real range images with partial overlap has shown that the proposed algorithm is promising for automatic matching of overlapping range images.     

基于有限理性的个体出行路径选择进化博弈

首先,从出行者的信息集和理性层次的差异两个方面给出两种改进的“最优反应动态”模型,并将其应用于一个算例,得到了与利用复制者动态方程所求得的进化稳定策略一致的结果;然后,为验证结论的普遍性,将出行者和路径数量扩充,构造了相应的算法,并将此算法及其复制者动态方程应用于一个规模较大的路网;最后,将不同机制下的实验结果进行了比较,并对其实际意义进行了分析．     

A dynamic replicator model of the players’ bids in an oligopolistic electricity market

In this paper, the replicator dynamics of the power suppliers’ bids in an oligopolistic electricity market are derived for both the fixed and variable demand cases. The replicator dynamics stability analysis is also performed. The dynamics of the electricity markets are the results of players’ decisions. The physical parameters of the power systems (such as the lines capacities, voltage limitations, etc.) also affect the market dynamics indirectly, through the changes in players’ behaviors. Assuming rational players, an optimal bidding strategy for constructing the supply function (SF) of a generating firm is presented and based on that, the dynamics of the bid replicators are studied. Both fixed demands and price sensitive demands are taken into account. The replicator model is presented in the well-known state space structure. A case study is presented to show the applicability of the developed dynamic replicator bid model, and also to show how the Nash–SFE equilibrium evolves over time.