Advancements in autonomous agents have led to an increasingly ubiquitous presence of robots in human environments where social and physical interaction is expected. Such environments are often composed of heterogeneous agents with disparate action capabilities, intentions, and motivations. Intra- and inter-agent dissimilarity often prevents enacting effective behavioral skills (e.g., collaboration, communication, coordination) towards dynamic task allocation objectives. We propose a Bayesian probabilistic inference approach, MultiRobot Belief Propagation with Identity constraints (MRPBI), for 1) decentralized task allocation in multi-agent systems and 2) modeling task affinity using personal identities. MRPBI leverages competing costs of individual and group capabilities that result in less error-prone convergence to steady state, scalability without loss of accuracy, and sensitivity to environmental dynamics. An implementation of MRBP-I as a distributed algorithm that weighs factors of both individual and cooperative perception in an energy-minimizing task allocation scheme is presented.