The talk starts with the brief introduction of Mechanism Design theory, with particular focus on dominant strategy incentive compatible mechanisms. Next, the joint work with Prof. Dr. J. Čopič and Dr. M. Castellani is presented. We study the bilateral trade problem under no subsidies constraint which has not been explored much due to its complexity. In our setting, there are two traders, i.e., a seller and a buyer, one indivisible good, and a market maker. The traders have private valuations over one indivisible good and have a scarce information. A market maker is in full command of the choice of market platform and has no private information. We consider market equilibrium mechanisms, among which a special attention is devoted to stochastic bid-ask mechanisms. We conclude with an example that shows that in general a mechanism that maximizes a social welfare function may lie outside the set of simple posted prices mechanisms.