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Based on Goyal and Joshi, we study a setting with many countries, in which there are firms that can sell in the domestic as well as foreign markets , and assumed that each firm compete to take the form of non-price, and analysis the incentive of country to sign FTA with other countries via Classical Competition Model. Our principal finding is that 1)two isolated countries have no incentive to sign an FTA, and the empty network is stable. 2) The complete trading network is stable if ; 3) There is no improving path from the empty network to the complete network . Introduction FTA as bilateral trade agreements between countries has played a huge advantage, and become an important means to achieve the globalization of trade. In order to investigate technical in the role of the FTA partner countries market makers occupation,the authors introduced the classic competition model. Each firm only concerns the market share in their own country and the FTA partner countries, and have complete information of other firms in technology spending. In the course of repeated games, technology spending of each firm finally reached equilibrium. In previous papers, Goyal and Joshi (2006) assumed that in each country there is a single firm producing a homogeneous good and competing as a Cournot oligopolist in all countries. A lot of follow-up research expand Goyal and Joshi(2006). Such as, Chen and Joshi(2010) considered the decision of the country to enter into an FTA is also crucially dependent on the participating countries' existing FTA relationships with third countries. In another example, Mauleon, Song and Vannetelbosch(2010) studied whether trade unions in different countries influence on global FTA network formation. In another example, Daisuke and Furusawa (2014) and Zhang, Cui and Zu (2014) studied dynamic evolution of FTA networks by introducing the dynamic analysis. Different from the existing literature, We assume that firms adopt technology investment strategy to compete in the same market. In their lay articles Goyal and Joshi find that if countries are symmetric, a complete network is consistent with the incentives of individual countries. In other words, the complete network is stable. Furusawa and Konishi based on Goyal and Joshi lay articles also find that the complete network is stable. Zhang, Cui and Zu analysis the dynamic FTA networks, and find that the complete network is stable, if 3 N ≥ . Cui and Gao studied a free trade agreement network formation game where bilateral free trade agreements imply unrestricted FDI, and finds that star FTA network is pairwise stable. In this article, we find that (1)any two independent states has no incentive to sign FTA and (2)the complete networks is stable, if 4 N ≥ . The basic model We consider a setting with N countries, each of which has one firm producing a homogeneous good, {1,2,3,..., } N = N , 3 N ≥ . Each firm can sell in the domestic market as well as in each of the foreign markets. We assume that any country offers a tariff-free access to its domestic market, if any two countries have bilaterally negotiated an FTA; otherwise, each country imposes a nonzero tariff on the imports from the other. Bilateral relations between any two countries is represented as follows: for any , i j N ∈ , the pairwise relationship between the two countries is captured by a binary variable, {0,1} ij g ∈ ; 1 ij g = means that FTA is established between countries i and j , whereas 0 ij g = means that no FTA is in effect. Additional, 1 ii g i N = ∀ ∈ . Let ( ) i j T g be the tariff faced by 2nd International Conference on Economics, Social Science, Arts, Education and Management Engineering (ESSAEME 2016) © 2016. The authors Published by Atlantis Press 499 firm i in country j in the network g . Note that ( ) ( ) 0 i j j i T g T g = = , if 1 ij g = . However, in general, impose prohibitive tariffs between countries i and country j , if 0 ij g = . Let { } ( ) : 1 i ij N g j g = ∈ = N , Each country in ( ) i N g is involved in an FTA with country i in the network g . Let ( ), ( ) ( ) i i i i N g g N g η ∈ = . e g represent the empty network; c g represent the complete network Therefore, ( ) e N g =Φ and ( ) c N g = N . Let ij g g + denote the network obtained by replacing 0 ij g = ; Similarly, let ij g g − denote the network obtained by replacing 1 ij g = in network g by 0 ij g = . For each new FTA partner country, it compete for market share through R&D investment. Let j i A represent R&D investment of firm i in country j . We let the output of firm j in country i be denoted by j i Q . We assume that each firm only concerned with its market share in FTA partner countries and in their own country. In general, in each country ( ) i i N g ∈ , each country faces an function of income given by

Free trade networks based on RaD perspective