In classical game theory, optimal strategies are determined for games with
complete information; this requires knowledge of the opponent's goals. We
analyze games when a player is mistaken about their opponents goals. For
definitiveness, we study the (common) bimatrix formulation where both player's
payoffs are matrices. While the payoff matrix weights are arbitrary, we focus
on strict ordinal payoff matrices, which can be enumerated. In this case, a
reasonable error would be for one player to switch two ordinal values in their
opponents payoff matrix. The mathematical formulation of this problem is
stated, and all 78 strict ordinal 2-by-2 bimatrix games are investigated. This
type of incomplete information game has not -- to our knowledge -- been studied
before