Sensitivity to Context in Human Interactions

Oliver Waddup,Emmanuel M Pothos,Bartosz W Wojciechowski,James M Yearsley,Pawel Blasiak

doi:10.3390/math9212784

Oliver Waddup, Emmanuel M Pothos + Show 3 more

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https://doi.org/10.3390/math9212784

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Abstract

Considering two agents responding to two (binary) questions each, we define sensitivity to context as a state of affairs such that responses to a question depend on the other agent’s questions, with the implication that it is not possible to represent the corresponding probabilities with a four-way probability distribution. We report two experiments with a variant of a prisoner’s dilemma task (but without a Nash equilibrium), which examine the sensitivity of participants to context. The empirical results indicate sensitivity to context and add to the body of evidence that prisoner’s dilemma tasks can be constructed so that behavior appears inconsistent with baseline classical probability theory (and the assumption that decisions are described by random variables revealing pre-existing values). We fitted two closely matched models to the results, a classical one and a quantum one, and observed superior fits for the latter. Thus, in this case, sensitivity to context goes hand in hand with (epiphenomenal) entanglement, the key characteristic of the quantum model.

Highlights

Introduction and Basic DefinitionsPrisoner’s dilemma (PD) games involve two players with a binary action each, typically denoted as cooperate (C) vs. defect (D)
PD games have been extensively studied in psychology, partly because they can lead to apparent discrepancies with classical probability theory [1,2,3,4]
Sensitivity to context is an important insight concerning the representation of information, whether in physics, data science, or psychology

Summary

Introduction

Introduction and Basic DefinitionsPrisoner’s dilemma (PD) games involve two players with a binary action each, typically denoted as cooperate (C) vs. defect (D). Prisoner’s dilemma (PD) games involve two players with a binary action each, typically denoted as cooperate (C) vs defect (D). A usually symmetrical payoff matrix determines the reward of each player, depending on their combined action. Payoffs are set so that it is most advantageous to D, if the other player Cs, but the mutual gain is highest if they both C (defection is the Nash equilibrium). In the pioneering study by [4], participants were put in the shoes of one of the players in a PD game and were presented with three kinds of trials: first, trials for which participants were told the other player would defect; second, trials for which participants were told the other player would cooperate; third, trials for which participants were not given information about the other player. Results indicated that Prob(DParticipant , unknown) was outside the bounds of Prob(DParticipant |known C) and

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