This books covers three topics in mathematical economics and economics theory which are solved by the use of methods from mathematical statistics. It starts with a mechanism design that covers themes such as: Vickrey-Clarke-Groves Mechanism, Vickrey auction, Mechanism Design Illustrated in a Walrasian Example,Constructing Decentralized Mechanisms, from Parameter Indexed Product Structures: Transition to Message-Indexed Product Structures. Than it continues with Prospect theory that covers themes such as: Prospect theory and Cumulative prospect theory, and their use in explanation of overbidding. And the final essay is: Myerson-Satterthwaite theorem and asymmetric FPA auctions, that includes numerical solution of the asymmetric auctions.