This chapter deals with three specific studies conducted within the combinatorial optimization for competing agents (COCA) project. It also deals with optimization problems arising from the relationship between members of a social network. A game theoretic model of this relationship is introduced and widely discussed. The chapter then focuses on developing a mechanism able to incentivize the self-interested network members to play the profile maximizing the social welfare. It devotes to a simple connection game. It first reviews the main results, where the price of anarchy of the game is studied. Then two protocols are discussed, and the goal is to induce a socially optimal configuration. The chapter focuses the design of truthful algorithms with performance guarantee regarding the social welfare. It illustrates a facility location problem and an allocation problem.