Introducing Quantum-Like Influence Diagrams for Violations of the Sure Thing Principle
This work addresses decision-making anomalies in fields like economics or psychology, but it is incremental as it builds on existing quantum-like Bayesian networks.
The authors tackled the problem of modeling decision-making scenarios that violate the Sure Thing Principle by extending quantum-like Bayesian networks to incorporate maximum expected utility in influence diagrams, resulting in a model that maximizes utility for cooperative behavior over rational defection in the prisoner's dilemma game.
It is the focus of this work to extend and study the previously proposed quantum-like Bayesian networks to deal with decision-making scenarios by incorporating the notion of maximum expected utility in influence diagrams. The general idea is to take advantage of the quantum interference terms produced in the quantum-like Bayesian Network to influence the probabilities used to compute the expected utility of some action. This way, we are not proposing a new type of expected utility hypothesis. On the contrary, we are keeping it under its classical definition. We are only incorporating it as an extension of a probabilistic graphical model in a compact graphical representation called an influence diagram in which the utility function depends on the probabilistic influences of the quantum-like Bayesian network. Our findings suggest that the proposed quantum-like influence digram can indeed take advantage of the quantum interference effects of quantum-like Bayesian Networks to maximise the utility of a cooperative behaviour in detriment of a fully rational defect behaviour under the prisoner's dilemma game.