A model of risk and mental state shifts during social interaction

Abstract

Cooperation and competition between human players in repeated microeconomic games offer a window onto social phenomena such as the establishment, breakdown and repair of trust. However, although a suitable starting point for the quantitative analysis of such games exists, namely the Interactive Partially Observable Markov Decision Process (I-POMDP), computational considerations and structural limitations have limited its application, and left unmodelled critical features of behavior in a canonical trust task. Here, we provide the first analysis of two central phenomena: a form of social risk-aversion exhibited by the player who is in control of the interaction in the game; and irritation or anger, potentially exhibited by both players. Irritation arises when partners apparently defect, and it potentially causes a precipitate breakdown in cooperation. Failing to model one's partner's propensity for it leads to substantial economic inefficiency. We illustrate these behaviours using evidence drawn from the play of large cohorts of healthy volunteers and patients. We show that for both cohorts, a particular subtype of player is largely responsible for the breakdown of trust, a finding which sheds new light on borderline personality disorder.

Fig 1. Basic game and game data features.

A: Physical features of the multi round trust game. B: Recursive reasoning about a partner. At level 0 the blue player learns about the partner. At level 1 the blue players knows that the red player learns about them too (that is, that the red player is level 0). At level 2 the blue player knows that the red player knows they are learning about them (i.e. that the red player is level 1 and thinks of the blue player as level 0). This recurses up to higher levels. C) Averaged investments and repayments in the data set. Errorbars show standard errors of the mean. An asterisk denotes the largest difference (p = 0.05, two sided permutation t-test) corrected for multiple comparisons at the 10 steps. D) Average investment in real and in simulated exchanges based on best fit parameters. An asterisk denotes a significant difference (p < 0.05, two sided permutation t-test) in means between the original data and the generated exchanges. E) Average repayments in real and in simulated exchanges based on the actual parameters. F) Sample trajectory for an investor vs average of 200 generated exchanges with best fitting parameters, based on the earlier model (see [10]). Shaded area shows estimated standard deviations. G) Sample trajectory for a trustee vs average of 200 generated exchanges with best fitting parameters, based on the earlier model (see [10]). Shaded area shows estimated standard deviations.

Fig 2. Irritation mechanism and resulting data reproduction.

A) Simulated Repair Interaction. Single trajectory of two aware players (blue for investor, red for trustee). The golden line depicts the evolution of the investor irritation weight during the interaction. B) Simulated Break Interaction. Both players were irritability ignorant, thus they do not notice potential irritation. The gold line depicts the evolution of the investor irritation weight during the interaction (its value at the start of the relevant round is shown). For A;B the simulated investor/trustee had k = 2/1, ζ = 0.5/0, α = 0.4, P = 4, $\beta =\frac{1}{3}$. C) Average Investment profiles regenerated from estimated parameters in the full model. All errorbars are standard error of the mean. D) Average Repayment profiles regenerated from estimated parameters in the full model. All errorbars are standard error of the mean. E) Reproduction of sample investor trajectory using 200 simulated interactions with the best fitting parameters. Shaded areas are estimated standard deviation. F) Reproduction of sample trustee trajectory using 200 simulated interactions with the best fitting parameters. Shaded areas are estimated standard deviation.

Fig 3. Distributions of newly introduced parameters by group.

A) Risk Aversion distribution of investors BPD and HC. B) Risk Aversion distribution of trustees BPD and HC. C) Irritability distribution of investors BPD and HC. D) Irritability distribution of trustees BPD and HC. E) Awareness distribution of investors BPD and HC. F) Awareness distribution of trustees BPD and HC.

Fig 4. Model based data features.

A) Investment and return profile for subgroups of the BPD and HC data sets, defined by ζ^T > 0 or q^T(ζ) = 0. B) Investment and return profile for subgroups of the BPD and HC data sets, defined by ζ^T = 0 and q^T(ζ) > 0. C) Investment and return profile for subgroups defined by ω^I ≤ 1.0 (blue, red) or ω^I ≥ 1.2 (light blue, coral). D) Guilt distribution of trustees BPD and HC. All errorbars are standard error of the mean.