  Gameplay under various forms of uncertainty has been widely studied. Feldman
et al. (2010) studied a particularly low-information setting in which one
observes the opponent's actions but no payoffs, not even one's own, and
introduced an algorithm which guarantees one's payoff nonetheless approaches
the minimax optimal value (i.e., zero) in a symmetric zero-sum game. Against an
opponent playing a minimax-optimal strategy, approaching the value of the game
is the best one can hope to guarantee. However, a wealth of research in
behavioral economics shows that people often do not make perfectly rational,
optimal decisions. Here we consider whether it is possible to actually win in
this setting if the opponent is behaviorally biased. We model several
deterministic, biased opponents and show that even without knowing the game
matrix in advance or observing any payoffs, it is possible to take advantage of
each bias in order to win nearly every round (so long as the game has the
property that each action beats and is beaten by at least one other action). We
also provide a partial characterization of the kinds of biased strategies that
can be exploited to win nearly every round, and provide algorithms for beating
some kinds of biased strategies even when we don't know which strategy the
opponent uses.
