Designing Agent Collectives For Systems With Markovian Dynamics

The "Collective Intelligence" (COIN) framework concerns the design of collectives of agents so that as those agents strive to maximize their individual utility functions, their interaction causes a provided "world" utility function concerning the entire collective to be also maximized. Here we show how to extend that framework to scenarios having Markovian dynamics when no re-evolution of the system from counter-factual initial conditions (an often expensive calculation) is permitted. Our approach transforms the (time-extended) argument of each agent's utility function before evaluating that function. This transformation has benefits in scenarios not involving Markovian dynamics, in particular scenarios where not all of the arguments of an agent's utility function are observable. We investigate this transformation in simulations involving both linear and quadratic (nonlinear) dynamics. In addition, we find that a certain subset of these transformations, which result in utilities that have low "opacity (analogous to having high signal to noise) but are not "factored" (analogous to not being incentive compatible), reliably improve performance over that arising with factored utilities. We also present a Taylor Series method for the fully general nonlinear case.