Stability conditions for agents pursuing individual goals under uncertainty

A formal approach integrates the principles of optimality, stability, and the level of communication necessary in a decentralized system which has a high degree of uncertainty. The uncertainties are in state, strategy, and gain which arise from delays in communication, probabilistic strategies and stochastic gains, respectively. It is assumed that agents within the system establish individual goals for their probabilistic strategies and that each agent autonomously pursues its own goal, which then may change due to multi-agent interactions. The resultant dynamical equation is analyzed using techniques for delay differential equations. The results show that the parameters that lead the system to optimality also make the system more susceptible to delay-initiated instabilities, with the theory predicting the boundary between stability and instability. Agents which communicate sufficiently can avoid instabilities and maintain their search for optimality