Experiments over a variety of optimization problems indicate that scale-effective convergence is an emergent behavior of certain computer-based agents, provided these agents are organized into an asynchronous team (A-Team). An A-Team is a problem-solving architecture in which the agents are autonomous and cooperate by modifying one another‘s trial solutions. These solutions circulate continually. Convergence is said to occur if and when a persistent solution appears. Convergence is said to be scale-effective if the quality of the persistent solution increases with the number of agents, and the speed of its appearance increases with the number of computers. This paper uses a traveling salesman problem to illustrate scale-effective behavior and develops Markov models that explain its occurrence in A-Teams, particularly, how autonomous agents, without strategic planning or centralized coordination, can converge to solutions of arbitrarily high quality. The models also perdict two properties that remain to be experimentally confirmed: