We present a stochastic dynamics theory and analysis framework for studying a continuous time transparent visual game for pairs of agents we call continuous perceptual report (CPR) tasks.The CPR task is a pattern recognition task where subjects view a moving random dot pattern with a time-dependent veridical direction of motion and variable coherence. The task is transparent in that each subject receives information about the current estimate of the other. The difficulty of this type of task depends on the coherence and noise level of the stimulus, on the accessibility of information from the other subject, and on the dynamics with which the veridical direction changes.We construct a general kernel-based linear model that can both be used to simulate the behavior of ideal model subjects and to quantify the behavior of experimentally tested agents. We present a method for estimation of the kernels from measured time series, based on minimizing a cost function that was derived analytically, we split the data set into a training and test set, and we implemented an L1 regularization using the sklearn. linear_model.Lasso() python package.Synthetic time series perfectly recovers the underlying kernel. Even for realistic duration observations kernels are reproducible and correctly predicted as assessed by cross-validation. In addition, we derive an analytical solution to the conditional probability of one or two subjects' stimulus estimates. Using these methods and results we present an assessment of the data demands, and estimation power of this framework and use it to explore stimulus designs.