Quantum Global Public Goods game implementation on Qiskit

[arthurostrauss]

Abstract

The well-being of our global ecosystem is dependent on the shared preservation of global public goods (GPGs). A GPG is a good which cannot be replaced with any other good, and that no one can be theoretically excluded from, such as air or climate change impact. One of the biggest threats to GPG integrity is the free-rider problem, which is a well defined problem in Game theory frame. Is it possible to develop another approach of this issue using quantum entanglement and hence demonstrate on a valuable problem quantum advantage? The answer seems to be yes and it might be possible to show it on a simple case building an efficient algorithm in Qiskit.

Description

Idea : Simplify GPG issue by converting it into a free-rider problem (Definition here) so we can use elements of game theory and quantum properties to deliver a new version, providing a better solution (under specific constraint) that would be of benefit for each participant (country in general). Defining efficiently Pareto optimality and Nash equilibrium criteria on this new version, can we find a configuration using entanglement that satisfies both conditions (note that this exists for the Prisoner's dilemma, article available here)?

Quantum protocol should have following properties:

• Take as inputs decisions of each country related to the desire to commit to preserve the good (i.e invest money in preservation of a good that will be a benefit from everyone, even potential free riders) or to defect (becoming the free-rider)

• Return an optimal amount of commitment for each participant analyzing and correlating decisions made by all others

• Add a constraint that induces a minimum amount of commitment (otherwise everyone could just defect and would be better off with this decision)

• Use entanglement to adapt the final outcome and perform optimization within the circuit

A possible modelling would be as follows:

1. Give each country one (or many) qubits, that are meant to be correlated with everyo other participant's qubits
2. Ask the country to encode his decision of commitment on its qubits (if yes, qubit state is tuned up to 1, if not tuned to 0)
3. Compute a quantum algorithm taking in input those qubits representing each actor's decision and giving as an output the optimal amount of commitment for each actor having decided to actually commit
4. Translate this result in a fairly calculated penalty condition on the free riders (those who decided not to commit)

Challenge would be to perform efficiently point 3 on a simple case on Qiskit. Main problem would be the defining of Pareto optimality and how to reach it (if it exists) using input qubits.

Inspiration of this problem mainly based on this article , but a free approach would be better to adapt the circuit to a simple model.

Members

• @githubhandle
• @githubhandle - Slack: @slackhandle email: example@example.com
• Qiskit Coach: @BryceFuller

Deliverable

GitHub repo

[VivienVandaele]

I'm interested ! Vivien Vandaele, Computer science

[shaimayshah]

I'm interested! Shaimay Shah, Computer Science/ Freelance

[arthurostrauss]

Wonderful! You can find me after pitches so I can explain the idea in more details!

[VivienVandaele]

Link to the code : https://github.com/VivienVandaele/Quantum-Global-Public-Goods-Game