Syllabus:

Linear and Dual Spaces, Optimization in Hilbert space, Optimization of functionals, Global theory of constraint optimization, Local theory of constraint optimization, Non-cooperative game theory: Nash equilibria, Cooperative game theory, Auction theory 

Reference texts:

Optimization by Vector Space Methods by David G Luenberger 

Convex Optimization, Stephen Boyd and Lieven Vandenberghe. Cambridge University Press 

Linear and Nonlinear Programming by David G. Luenberger 

Fun and Games: A Text on Game Theory, Ken Binmore 

A Course in Game Theory, Martin J. Osborne and Ariel Rubinstein 

Miscellaneous:

The course would involve two lectures a week of duration hour and a half each. The evaluation would be based on two exams, homeworks and a presentation.