Economic deliberations are slow, effortful and intentional searches for solutions to difficult economic problems. Although such deliberations are critical for making sound decisions, the underlying reasoning strategies and neurobiological substrates remain poorly understood. Here two nonhuman primates performed a combinatorial optimization task to identify valuable subsets and satisfy predefined constraints. Their behavior revealed evidence of combinatorial reasoning—when low-complexity algorithms that consider items one at a time provided optimal solutions, the animals adopted low-complexity reasoning strategies. When greater computational resources were required, the animals approximated high-complexity algorithms that search for optimal combinations. The deliberation times reflected the demands created by computational complexity—high-complexity algorithms require more operations and, concomitantly, the animals deliberated for longer durations. Recurrent neural networks that mimicked low- and high-complexity algorithms also reflected the behavioral deliberation times and were used to reveal algorithm-specific computations that support economic deliberation. These findings reveal evidence for algorithm-based reasoning and establish a paradigm for studying the neurophysiological basis for sustained deliberation.