Abstract. Infinite-horizon multi-agent control processes with nondeterminism and partial state knowledge have particularly interesting properties with respect to adaptive control, such as the non-existence of Nash Equilibria (NE) or non-strict NE which are nonetheless points of convergence. The identification of reinforcement learning (RL) algorithms that are robust, accurate and efficient when applied to these general multi-agent domains is an open, challenging problem. This paper uses learning pressure fields as a means for evaluating RL algorithms in the context of multi-agent processes. Specifically, we show how to model partially observable infinite-horizon stochastic processes (single-agent) and games (multi-agent) within the Finite Analytic Stochastic Process framework. Taking long term average expected returns as utility measures, we show the existence of learning pressure fields: vector fields