  Many studies have shown that humans are "predictably irrational": they do not
act in a fully rational way, but their deviations from rational behavior are
quite systematic. Our goal is to see the extent to which we can explain and
justify these deviations as the outcome of rational but resource-bounded agents
doing as well as they can, given their limitations. We focus on the
well-studied ranger-poacher game, where rangers are trying to protect a number
of sites from poaching. We capture the computational limitations by modeling
the poacher and the ranger as probabilistic finite automata (PFAs). We show
that, with sufficiently large memory, PFAs learn to play the Nash equilibrium
(NE) strategies of the game and achieve the NE utility. However, if we restrict
the memory, we get more "human-like" behaviors, such as probability matching
(i.e., visiting sites in proportion to the probability of a rhino being there),
and avoiding sites where there was a bad outcome (e.g., the poacher was caught
by the ranger), that we also observed in experiments conducted on Amazon
Mechanical Turk. Interestingly, we find that adding human-like behaviors such
as probability matching and overweighting significant events (like getting
caught) actually improves performance, showing that this seemingly irrational
behavior can be quite rational.
