  The Prisoner's Dilemma game (PDG) is one of the simple test-beds for the
probabilistic nature of the human decision-making process. Behavioral
experiments have been conducted on this game for decades and show a violation
of the so-called \textit{sure thing principle}, a key principle in the rational
theory of decision. Quantum probabilistic models can explain this violation as
a second-order interference effect, which cannot be accounted for by classical
probability theory. Here, we adopt the framework of generalized probabilistic
theories and approach this explanation from the viewpoint of quantum
information theory to identify the source of the interference. In particular,
we reformulate one of the existing quantum probabilistic models using density
matrix formalism and consider different amounts of classical and quantum
uncertainties for one player's prediction about another player's action in PDG.
This enables us to demonstrate that what makes possible the explanation of the
violation is the presence of \textit{quantum coherence} in the player's initial
prediction and its conversion to probabilities during the dynamics. Moreover,
we discuss the role of other quantum information-theoretical quantities, such
as quantum entanglement, in the decision-making process. Finally, we propose a
three-choice extension of the PDG to compare the predictive powers of quantum
probability theory and a more general probabilistic theory that includes it as
a particular case and exhibits third-order interference.
