 As expected, the main difference between plausibility action models and basic action models is that the agent-specific component (i.e., the function \(\geq\) giving the agent-specific relation \(\geq_a\)). In constructing new plausibility models based on plausibility action models, we may follow a construction similar to the  product update.  To make this work, our main task is to describe how the plausibility relation \(\geq_a\) in the resultant plausibility model \(M[A]\) is to be determined in terms of the plausibility relations coming from the given initial plausibility model M and the plausibility action model A. For this it will be helpful to consider an example. 