个体异质对纳什网络存在性的影响研究

1、    个体异质对纳什网络存在性的影响研究    刘念平摘 要 在bala and goyal (2000)提出的双向流网络形成模型基础上，研究当个体存在异质性时对纳什网络存在性的影响分别针对几种不同的环境设定下的个体异质性进行研究，发现个体的连接成本异质性是决定纳什网络存在性的重要因素；但相较于个体的连接成本而言，连接价值的异质性对纳什网络存在性的影响不大关键词 网络形成；纳什网络；异质性；非合作博弈abstract the importance of heterogeneity in the existence of nash networks wa

2、s explained by using the twoway flow model of network formation initiated by bala and goyal (2000). furthermore, the heterogeneity of link costs in different settings was examined and it is found find that the heterogeneity of link costs plays a crucial role in the existence of nash networks. howeve

3、r, the heterogeneity of values is not as important as that of link costs.key words network formation; nash networks; heterogeneity; noncooperative gamesf224.1 a1 introductionthere is substantial evidence to support the role that social and economic networks play in individual behavior and payoffs, a

4、nd in aggregate social outcomesnetwork effects on job search (montgomery(1991)2), trade (nishiguchi (1994)3), the granting of credit (mcmillan and woodruff (1999)4) and mutual insurance (bloch and genicot (2008)5). recent developments in this area have focused increasing attention on the theoretical

5、 analysis of network formation. in particular, bala and goyal (2000)1 proposed a noncooperative model of network formation, in which networks are categorized as either oneway or twoway flow, according to the flow of resources, while the addition and deletion of links are unilateral decisions that al

6、low players to access resources. in a twoway flow network, a link between two players allows both players to access the others resources, regardless of who pays for the link.this model has been extended in various directions. most studies have focused on the architecture of networks that result in e

7、quilibrium. compared with this issue, the existence of nash networks has been less systematically explored. this paper complements the existing literature on the existence of nash networks for the noncooperative model of network formation.bala and goyal (2000)1 proved that nash networks exist for bo

8、th oneway and twoway flow networks when the values and costs of links are both homogeneous. however, individual differences arise quite naturally in many contexts. for instance, some individuals possess skills that are scarce or the opportunity costs of maintaining their connections are lower, which

9、 makes them more valuable to others. indeed, the greek proverb “success has many friends” indicates that people prefer to connect with highly rewarded individuals. the heterogeneity of players plays an important role in network formation. in a oneway flow model, billand et al. (2008) endprintin this

10、 paper, we investigate the existence of nash networks in a twoway flow model with linear payoffs and different types of heterogeneity. we do not allow for decay and only consider pure strategies. we show that bala and goyals (2000) 1 results are not entirely robust when the link costs are heterogene

11、ous or partnerheterogeneous. in a number of different settings, we find that the heterogeneity of the link costs plays a major role in the existence of nash networks. however, the role played by the heterogeneity of values is not as important as the heterogeneity of the link costs. we also show that

12、 a nash network always exists when the link costs are ownerhomogeneous. we provide bounds on the link costs that guarantee the existence of nash networks when the link costs are partnerheterogeneous.this paper is organized as follows. in section 2 we set the basic twoway flow model with heterogeneou

13、s costs and values of the links. in section 3, we examine the existence of nash networks for this model. in section 4, we study this problem more precisely under various heterogeneity conditions for the link costs regardless of the heterogeneity of the values. section 5 concludes.2 model and notatio

14、ns5 conclusionthe literature on twoway flow models shows that over some parameter ranges, for instance when the link costs and values are both homogeneous or the link costs are homogeneous and the values vary freely, nash networks always exist. however, the question of whether nash networks exist ov

15、er the entire parameter range has not been resolved.this paper complements the existing literature on the existence of nash networks for a twoway flow model with linear payoff functions. we first find that the heterogeneity of the link costs plays a key role in the existence of nash networks in pure

16、 strategies, and link costs are obviously more important. indeed, if values vary freely but link costs are ownerhomogeneous, then nash networks always exist; however, they do not always exist when the link costs and values are both heterogeneous. second, we demonstrate that nash networks do not alwa

17、ys exist when the link costs are partnerheterogeneous unless we provide bounds on the link costs.references1 v bala,s goyal. a noncooperative model of network formation j.econometrica,2000, 68(5): 1181-1229. 2 james d montgomery. social networks and labormarket outcomes: toward an economic analysis.

18、jthe american economic review ,1991,81 (5): 1408-1418. endprint3 t nishiguchi. strategic industrial sourcing: the japanese advantagem.oxford:oxford university press, 1994.4 j mcmillan, c woodruff. interfirm relationships and informal credit in vietnamj. the quarterly journal of economics, 19991,14 (

19、4): 1285-1320. 5 f bloch, g genicot, d ray. informal insurance in social networksj. journal of economic theory ,2008,143(1): 36-58. 6 p billand, c bravard, s sarangi. existence of nash networks in oneway flow modelsj. economic theory, 2008,37(3): 491-507. 7 j derks, j kuipers, m tennekes,et al. exis

20、tence of nash networks in the oneway flow model of network formationj. modeling, computation and optimization, world scientific,2009forthcoming.8 j derks, m tennekes. a note on the existence of nash networks in oneway flow modelsj.economic theory ,2009,41 (3): 515-522. 9 h haller, j kamphorst, s sar

21、angi. (non) existence and scope of nash networksj. economic theory,2007, 31(3): 597-60410p billand, c bravard, s sarangi. existence of nash networks and partner heterogeneityj. mathematical social sciences ,2012,64(2): 152-158.11a galeotti, s goyal, j kamphorst. network formation with heterogeneous

22、playersj.games and economic behavior, 2006,54(2): 353-372.endprint3 t nishiguchi. strategic industrial sourcing: the japanese advantagem.oxford:oxford university press, 1994.4 j mcmillan, c woodruff. interfirm relationships and informal credit in vietnamj. the quarterly journal of economics, 19991,1

23、4 (4): 1285-1320. 5 f bloch, g genicot, d ray. informal insurance in social networksj. journal of economic theory ,2008,143(1): 36-58. 6 p billand, c bravard, s sarangi. existence of nash networks in oneway flow modelsj. economic theory, 2008,37(3): 491-507. 7 j derks, j kuipers, m tennekes,et al. e

24、xistence of nash networks in the oneway flow model of network formationj. modeling, computation and optimization, world scientific,2009forthcoming.8 j derks, m tennekes. a note on the existence of nash networks in oneway flow modelsj.economic theory ,2009,41 (3): 515-522. 9 h haller, j kamphorst, s

25、sarangi. (non) existence and scope of nash networksj. economic theory,2007, 31(3): 597-60410p billand, c bravard, s sarangi. existence of nash networks and partner heterogeneityj. mathematical social sciences ,2012,64(2): 152-158.11a galeotti, s goyal, j kamphorst. network formation with heterogeneo

26、us playersj.games and economic behavior, 2006,54(2): 353-372.endprint3 t nishiguchi. strategic industrial sourcing: the japanese advantagem.oxford:oxford university press, 1994.4 j mcmillan, c woodruff. interfirm relationships and informal credit in vietnamj. the quarterly journal of economics, 19991,14 (4): 1285-1320. 5 f bloch, g genicot, d ray. informal insurance in social networksj. journal of econo