106 C. Moreira and A. Wichert

It is interesting to notice that indeed the parameters used accommodate the violations of the Sure Thing Principle alone in the quantum-like Bayesian Network could also be used to maximise the utility of a Cooperate action. This was verified in all works of the literature analysed except in Game 6 in the work of Li and Taplin (2002). The reason is that Game 6 is not even reporting a violation to the Sure Thing Principle and could be explained by the classical theory with a minor error percentage. This means that in this experiment, a def ect action was favoured over a cooperate one.

8 Conclusion

In this work, we proposed an extension of the quantum-like Bayesian Network initially proposed by Moreira and Wichert Moreira and Wichert (2014, 2016) into a quantum-like influence diagram. Influence diagrams are designed for knowledge representation. They are a directed acyclic compact graph structure that represents a full probabilistic description of a decision problem by using probabilistic inferences performed in Bayesian networks (Koller and Friedman 2009) together with a fully deterministic utility function. Currently, influence diagrams have a vast amount of applications. They can be used to determine the value of imperfect information on both carcinogenic activity and human exposure (Howard and Matheson 2005), the are used to detect imperfections in manufacturing and they can even be used for team decision analysis (Detwarasiti and Shachter 2005), valuing real options (Lander and Shenoy 2001), etc.

The preliminary results obtained in this study show that the quantum-like Bayesian network can be extended 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. 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 quantum-like probabilistic graphical model where the utility node depends only on the probabilistic inferences of the quantum-like Bayesian network.

This notion of influence diagrams opens several new research paths. One can incorporate di erent utility nodes being influenced by di erent random variables of the quantum-like Bayesian Network. This way one can even explore di erent interference terms a ecting di erent utility nodes, etc. We plan to carry on with this study and further develop these ideas in future research.

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