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In many two-sided search applications, autonomous agents can enjoy the advantage of parallel search, powered by their ability to handle an enormous amount of information, in a short time, and the capability to maintain interaction with several other agents in parallel. The adoption of the new technique by an agent suggests a reduction in the average cost per interaction with other agents, resulting in an improved overall utility. Nevertheless, when all agents use parallel search in Multi-Agent Systems (MAS) applications, the analysis must take into consideration mainly equilibrium dynamics which shape their strategies. In this paper we introduce a dual parallel two-sided search model and supply the appropriate analysis for finding the agents’ equilibrium strategies. As a framework application for our analysis we suggest and utilize the classic voice communication partnerships application in an electronic marketplace. By identifying the specific characteristics of the equilibria, we manage to supply efficient means for the agents to calculate their distributed equilibrium strategies. We show that in some cases equilibrium dynamics might eventually drive the agents into strategies by which all of them end up with a smaller expected utility. Nonetheless, in most environments the technique has many advantages in improving the agents expected utility.