Economic Behaviors In Social Networks

In the last twelve years, the study of complex networks is developing very fast, and has come into being an intersection science. As an important application area of complex networks, the network analysis of economy system also has been studied extensively and thoroughly, in recent years. There are some profound works about the relationship between economic behavior and social network, and the formation motivity of interactive networks in economic system, such as Bala and Goyal (2000), Jackson and Wolinsky (1996), and Goyal and Vega-Redondo (2007) and so on.Based on the the previous studies, this paper gives out some equilibrium supported networks, and the corresponding necessary and sufficient conditions, a bound of the link cost c. When c is large than or equal to the upper bound, some players will deviate for their payoffs are less than or equal to zero; when c is less than or equal to the lower bound, some players will deviate for profit. The ratio of total link cost to total surplus (network cost ratio?) is used to measure the immunity of an equilibrium supported network on the variation of c. The ratio of total intermediation rent to total surplus (network free-rider ratio?) is used to measure the structural holes in an equilibrium supported network. A probability model is proposed to analysis the risk of equilibrium networks. The risks of players on different positions of an equilibrium supported networks are compared, and the operation risks of different equilibrium supported networks are also compared.In chapter 2, base on the strict bilateral equilibrium (SBE), which allows for co-ordinated two-person deviations, two SBE-supported networks and their necessary and sufficient conditions are given out.In chapter 3, by considering the reliability of the bilateral deviation, the refinement conditions of equilibria are loosed. Base on the strict bilateral-proof equilibrium (SBPE), some SBPE-supported networks and their necessary and sufficient conditions are also given out.In a SB(P)E-supported network with many core players, if their is at most a core player, whose degree is less than?0, which is the upper bound of players capacity, then the lower bound of c goes down rapidly. So, the network immunity of the variation of c becomes stronger significantly. In a SBE-supported network, if the number of core players increases, then the network immunity of the variation of c becomes weak, but the structural holes increase. In a SB(P)E-supported network, the total link cost is mainly loaded by core players and players on a cycle with degree 2 (latency core players). If the total link cost is mainly composed of taxes and some other fees, and it is mainly used to utility and public welfare, then by increasing of c (or?) we can improve the fairness of network.In chapter 4, a probability model is proposed to analysis the risks of equilibrium networks.First, the coefficient of variation and devitation probability are both used to mea- sure the risks of players on different positions in a SB(P)E network, their results are almost coincident. If c is so close to its upper bound, then there is an amplification effect of the high cost to the risk from the randomness of transcations. In a SB(P)E network, when the rank of the difference between c and its upper bound decreases, the risks of periphery players are relatively stable, but the risk of core players and latency core players both increase, In a SB(P)E networks with latency core players, the mainly risk sources of the SB(P)E network is latency core players. That is to say, the players, who just enter the core cycle, always take the largest risk, which corresponds with the prac-tical situation. In a SB(P)E network without a latency core player, there is a threshold value?1/2 for a, where?1 is the rank of core players'degrees. If?>?1/2, then the mainly risk sources of the SB(P)E network is periphery players, else if?<?1/2, then the mainly risk sources of the SB(P)E network is core players. To leaders with degree?, the only way to reducing risks is to reduce c; to the other core players, the moderate degree is a firewall.Next, correlation coefficent is used to measure the relation between players payoffs. In a SB(P)E network, the rank of correlation coefficent of a random pair of players is decided by their degrees and their relatively positions, and it isn't irrelevant to other players degrees and c.Last, network devitation probability Q, network collapse probability Q, and net-work operation time T are all used to measure the whole operatoin risk of a SB(P)E network. When?1 decreases, the operation risk of a SB(P)E network increases. So, it is need guaranteed?1=1, that is to say the number of core players is?(1). When?1?1/2, the stability of a SB(P)E network is very terrible. So, it is must be guaranteed?1>1/2. For the different positions on a SB(P)E network, the deviations of different players have different influence. The deviation of some periphery players has a little influence, but the deviation of core players or latency core players will cause a collapse. In a SB(P)E networks with latency core players, the rank of T decreases as a decreasing. So, we can only take c as large as possible under the condition a=1. In a SB(P)E network whitout latency core players, if c gradually increases such that?<?1/2, then the mainly risk sources change form periphery players to core players. So, the operation risk of the whole SB(P)E network is blown up abruptly. If the rank?>?1/2, then the rank of T isn't irrelative with a, else if?<?1/2, then the rank of T decreases as a decreasing. So, we can take c as large as possible under the condition?>?1/2,That is exactly confirmed a practical situation, that large companies will go bankrupt, when the cost of economic operation is Irage. And it will bring a large fluctuation, even a disastrous influence on the whole economy system.