Effort profiles in multi-agent resource allocation

Abstract

Multi-agent systems are particularly appropriate for resource allocation, but configuring them for efficient operation requires understanding their dynamics. Concepts from statistical physics, such as phase transitions, can help. In decision problems such as constraint satisfaction, such transitions exhibit an easy-hard-easy effort profile, so that highly overconstrained problems are easier to solve than those near the transition. The conventional wisdom is that the profile in optimization problems such as resource allocation is monotonic, becoming more difficult as constraints increase. Contrary to this lore, we exhibit an easy-hard-easy profile in a multi-agent resource allocation problem. We compare problems that exhibit such a profile with others that do not and offer insights as to when such behavior can be expected and why it is desirable from a practical perspective.