Systems of Vector Quasi-equilibrium Problems and Their Applications

In this survey chapter, we present systems of various kinds of vector quasi-equilibrium problems and give existence theory for their solutions. Some applications to systems of vector quasi-optimization problems, quasi-saddle point problems for vector-valued functions and Debreu type equilibrium problems, also known as constrained Nash equilibrium problems, for vector-valued functions are presented. The investigations of this chapter are based on our papers: Ansari (J Math Anal Appl 341:1271-1283, 2008); Ansari et al. (J Global Optim 29:45-57, 2004); Ansari and Khan (Mathematical Analysis and Applications, edited by S. Nanda and G.P. Rajasekhar, Narosa, New Delhi, 2004, pp. 1-13); and Ansari et al. (J Optim Theory Appl 127:27-44, 2005).