Distributed load balancers exhibit thrashing where tasks are repeatedly moved between locations due to incomplete global load information. This paper shows that systems of Autonomous Mobile Programs (AMPs) exhibit the same behaviour, and identifies two types of redundant movement (greedy effect). AMPs are unusual in that, in place of some external load management system, each AMP periodically recalculates network and program parameters and may independently move to a better execution environment. Load management emerges from the behaviour of collections of AMPs.The paper explores the extent of greedy effects by simulating collections of AMPs and proposes negotiating AMPs (NAMPs) to ameliorate the problem. We present the design of AMPs with a competitive negotiation scheme (cNAMPs), and compare their performance with AMPs by simulation. We establish new properties of balanced networks of AMPs, and use these to provide a theoretical analysis of greedy effects.