Optimal behavior and concurrent variable ratio-variable interval schedules

Concurrent variable ratio-variable interval (CONC VRVI) schedules of reinforcement, and the time-based analog of the same schedule (CONC VT*VT), have been used to determine if the matching law accounts for the distribution of choices between the behavior alternatives more accurately than the assumption that subjects distribute time between the alternatives to maximize total reinforcement rate. The results of those experiments leave room for interpretation. One problem is the lack of understanding of the theoretical outcomes associated with maximization in these schedules. A precise understanding of the characteristics of optimal behavior (OB) could help identify experimental evidence of OB. Here we derive equations that describe the optimal times the subject should spend on each alternative of the schedule. We provide a table of the optimal times for a wide range of parameter values of the schedule that experimenters can use to compare easily experimental results to the results expected if subjects behave optimally. We also derive a function m that relates matching and optimal performance and we prove interesting characteristics of the function. Finally, we describe features of OB with CONC VT*VT and with concurrent variable time schedules that can be used to identify evidence of OB.