Table of Content

15 December 2012, Volume 16 Issue 4

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Original Articles

Local strategic interaction  in 2-neighborhood on the endogenous network  and its simulations

LI Kang, GAO Hongwei, SONG Li, HU Ping, WANG Kun, CHEN Chunrui

2012, 16(4):  1-10. 

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In the context of endogenous network formation, we study local strategic interaction among players within 2-neighborhood. We characterize the equilibrium networks and describe the impact of the link cost on the equilibrium networks and the impact of interaction radius. We illustrate and complement the analytical results by NetLogo simulation program, and the simulation results illustrate that the dynamics of the network formation plays an important role in the equilibrium outcomes. The results of this paper are helpful to solve the interactions in social economics and networks.

Study of bid evaluation behaviors for multi-attribute reverse auction based on game theory

LIU Xuwang, WANG Dingwei

2012, 16(4):  11-20. 

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There is usually strong negative relevance between technical and business attributes in current bid evaluation process. It will induce the antagonistic feelings and non-cooperation behavior between two groups. Administrative department's organizational administration is a key factor to fairness. Based on game theory, models about bid evaluation behaviors are constructed to analyze the conditions how to achieve equilibrium, one is about technical and business experts and the other is about experts and administrative department, and which is the Pure Strategies Nash Equilibrium. Then, the influencing factors to relative behaviors are analyzed. At last, the simulation system about the game is developed and runs on the platform of Matlab GUI with adjusting relevant parameters.

Incentive policy of retailer to supplier based on investment input

SU Yingsheng, WANG Xinhui, WANG Xianyu

2012, 16(4):  21-30. 

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The investment for cost saving is to improve the efficiency of unit cost. It guarantees that unit cost in each subsequent production process is in the lower level. However, the problems of hold-up and compensation tend to reduce supply chain investment enthusiasm. In order to solve this problem, this paper adopts the Stackelberg game analysis, and researches the incentive contract, respectively, when investments can be observed or not be observed. It can be concluded that the investment is not enough if the retailer invests, and that suppliers to the production investment levels even higher chain optimal investment level if the supplier invests.

The structure of the equilibrium network and the absorbing set based on strategic interaction on the endogenous infinite lattice

SONG Li, GAO Hongwei, CHEN Chunrui, LI Kang, HU Ping, WANG Kun

2012, 16(4):  31-40. 

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This paper deals with strategic interaction model based on the endogenous infinite lattice. The properties of the equilibrium and the tendency of players' strategy are the research objective. In every period of the dynamic process, players update their strategy at the same time. We study how the relationship between the cost of link formation and the payoff influences the equilibrium structure and the absorbing set. The main contribution of the paper is combining the endogenous network with the strategic interaction on the endogenous infinite lattice. We also give the accurate characteristics of the equilibrium structure and the absorbing set with different parameters.

M-S value for cooperative games with judgement worth

LIN Jian, ZHANG Qiang

2012, 16(4):  41-50. 

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With respect to cooperative n-person games with judgement worth, the Multiplicative-Shapley is proposed based on the 1-9 judgement scale. Firstly, the average payoff function is defined, and two types of consistent and their adjustment are introduced simultaneously. Secondly, some concepts of cooperative n-person games, such as domination, pseudoconvex, Multiplicative-Shapley value and unit element, are defined based on the corresponding characteristic function, and then the Multiplicative-Shapley value is proposed according to three axioms. Finally, a numeral example is illustrated to show the feasibility and availability of the Multiplicative-Shapley value.

Sequential search with anticipated regretting and rejoicing

WENG Zhiquan

2012, 16(4):  51-60. 

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This paper models how regret and rejoice arise in sequential search and shows that anticipation of regret can largely explain why people are found to "search too little" compared to the theoretical benchmarks. Due to the fundamental asymmetry in feedback structure in search, the model predicts: First, "search too little" is optimal as long as people are more sensitive towards regret than towards rejoicing. Second, if additional feedback is offered so that people expect to see the next price after search is stopped, behaviors become observationally indistinguishable from the benchmarks. The present model also explains why people occasionally recall past prices.

Extensive partial cooperative game with multi-coalition structure

WANG Lei, GAO Hongwei, ZHOU Changli

2012, 16(4):  61-68. 

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We define the new cooperative function and get the extensive partial cooperative game with multi-coalition structure. By backward induction we build the concept of solution in the partial cooperative game and get the corresponding optimal path. The model in this paper overcomes the limitation in the classic game models in which only simple coalition structure can be formed at any node on the game tree.

Random decentralization within multi-divisional organizations

WENG Xi, LI Siguang

2012, 16(4):  69-76. 

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This paper investigates random allocation of authority in a multidivisional organization in which decisions must be adapted to local conditions but also coordinated with each other. Our newly-proposed organizational structure introduces commitment to randomization of pure centralization and pure decentralization. Our result shows that random delegation indeed improves the organization's ability to govern adaptation and coordination in a strategic information transmission environment.  Thus the optimal organizational structure may involve random decentralization and the organization may add uncertainty on the power structure on purpose.

The average tree solution in graph games with  fuzzy coalitions

NIE Cuiping, ZHANG Qiang

2012, 16(4):  77-85. 

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In this paper, the generalization of the average tree solution is considered. It is the unique solution satisfying component fairness and component efficiency when the crisp graph game is cycle-free. We propose the fuzzy average tree solution that is an imputation for the graph game with fuzzy coalitions. Moreover, on a complete graph game with fuzzy coalitions the fuzzy average tree solution coincides with the fuzzy Shapely value. Finally, we give the relationship between the fuzzy average tree solution and the fuzzy core.

Coalitional solutions in differential games

Leon A. Petrosyan

2012, 16(4):  86-94. 

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The two-stage (level) coalitional solution for n-person differential game played over the time interval [t_0,∞) is proposed. The paper emerges from the
idea that it is natural not to assume that coalitions on the first level can form a grand coalition. At first level the Nash equilibrium in the game played by coalitions is computed. Secondly the value of each coalition is allocated according to the Shapley value. The results are illustrated by an example of n-person differential emission reduction model.

Multi-period complete-information games with self control: a dual-self approach

WANG Wei, ZHENG Jie

2012, 16(4):  95-104. 

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The existing literature on dual-self has focused on individual decision-making problems. We adopt the theoretical framework established by Fudenberg and Levine (American Economic Review, 2006, 96(5): 1449-1476) in 2006 to propose a new dual-self model that expands individual decision problems to multi-player strategic situations, better reflecting human interactions in reality. For the example of two-period complete-information game with multiple equilibria provided in this paper, we analyze it using our proposed dual-self model and compare the results we found with those of economic models without dual-self. Consistent with the Fudenberg-Levine axioms, our model defines a more general concept of self-control cost that takes into account multi-player interactions.

Global convergence of the Levenberg-Marquardt method with Goldstein line search

DU Shouqiang

2012, 16(4):  105-111. 

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In this paper, we consider the Levenberg-Marquardt method for solving nonlinear equations. We use Goldstein line search on every iteration to guarantee the global convergence of the Levenberg-Marquardt method. Under mild conditions, we prove that the Levenberg-Marquardt method is globally convergent. And we also apply the method to solve generalized complementarity problems.

Some results of convex programming complexity

LOU Ye, GAO Yuetian

2012, 16(4):  112-124. 

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Recently a number of papers were written that present low-complexity interior-point methods for different classes of convex programs. To guarantee the polynomiality of the procedure, in this paper we show that the logarithmic barrier function associated with these programs is self-concordant. In other words, we will present two different lemmas with different logarithmic barrier functions and apply them to several classes of structured convex optimization problems, using the self-concordancy.