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Supplementary Material A: A sample Prisonerβs Dilemma payoff matrix, agent, and available choices Supplemental Material B: Derivation of the transition matrix for the Type-indeterminate model In order to ensure that the probabilities of being in each state from the end of the promise game (which sum to 1) transition to a full type distribution in the Prisonerβs Dilemma game (probabilities in the PD game also must sum to 1), we use a unitary matrix U to represent the change of bases that occurs in this transition. A unitary matrix may have complex values, as may a particular state vector, but the TI model is restricted to the real coordinate space (Busemeyer & Lambert-Mogiliansky, 2009). Since the state vector is not complex, any complex rotation in the unitary could result in a complex-valued state vector in the Prisonerβs Dilemma. Therefore, we include the requirement that the unitary matrix have only real-valued elements. In addition, there are several other constraints on the unitary matrix. Given πΏ11 π(3) = οΏ½πΏ21 πΏ31 πΏ12 πΏ22 πΏ32 πΏ13 πΏ23 οΏ½ πΏ33 (11) We require that squared values of the rows and columns add up to 1; that is, βπ, βπ πΏππ 2 = 1 βπ, βπ πΏππ 2 = 1 (12) This is referred to as the double stochasticity constraint. In addition, U must meet the definition of a unitary matrix, indicating that UU* = U*U = I, where U* is the inverse of the unitary matrix U and I is the identity matrix. The full parameterization of a 3x3 unitary uses 16 parameters (see Dita, 1982); fortunately, due to the constraint of existing in the real space, the unitary matrix reduces to an orthogonal matrix and can be parameterized using only 3 Euler rotation angles (Hestenes, 1999). These Euler angles π1 , π2 , and π3 represent rotations around bases that weβre using. In this case, these are the x, y, and z axes. Note that the final result is also in the standard Cartesian coordinate space β this is mainly for convenience. In technicality, we could represent the PD game space in the same coordinates as the promise game space, but this would result in basis vectors that would be more difficult to interpret (though mathematically sound). Supplemental Material C: Data and model predictions based on best-fit parameters The conditions are described by [Type of Agent in Phase 1] / [Whether a promise was made to Agent A in Phase 1] / [Type of Agent in Phase 2]. For example, CoopA/NP/OppB (the second entry) would mean that the participant saw a cooperative agent in phase 1, made no promise (NP) to that agent, and then played with an opportunistic agent in phase 2, cooperating at the rate indicated by the bar. Supplemental Material D, References: Busemeyer, J. R., & Lambert-Mogiliansky, A. (2009). An exploration of Type Indeterminacy in strategic Decision-making. In Quantum Interaction (pp. 113-127). Springer Berlin Heidelberg. Dita, P. (1982). Parameterisation of unitary matrices. Journal of Physics A: Mathematics, General 15: 3465-3473. Hestenes, D. (1999). New Foundations for Classical Mechanics (2nd ed.). Springer. Supplemental Material E, other related reading: Cheon, T., & Tsutsui, I. (2006). Classical and quantum contents of solvable game theory on Hilbert space. Physics Letters A, 348(3β6), 147β152. doi:10.1016/j.physleta.2005.08.066 Khrennikov, A. I. (2004). Information Dynamics in Cognitive, Psychological, Social, and Anomalous Phenomena (Vol. 138). Kluwer Academic Publishers. Khrennikov, A. (2009). Quantum-like model of cognitive decision making and information processing. Biosystems, 95(3), 179β187. doi:10.1016/j.biosystems.2008.10.004