  There is general agreement that some form of regulation is necessary both for
AI creators to be incentivised to develop trustworthy systems, and for users to
actually trust those systems. But there is much debate about what form these
regulations should take and how they should be implemented. Most work in this
area has been qualitative, and has not been able to make formal predictions.
Here, we propose that evolutionary game theory can be used to quantitatively
model the dilemmas faced by users, AI creators, and regulators, and provide
insights into the possible effects of different regulatory regimes. We show
that creating trustworthy AI and user trust requires regulators to be
incentivised to regulate effectively. We demonstrate the effectiveness of two
mechanisms that can achieve this. The first is where governments can recognise
and reward regulators that do a good job. In that case, if the AI system is not
too risky for users then some level of trustworthy development and user trust
evolves. We then consider an alternative solution, where users can condition
their trust decision on the effectiveness of the regulators. This leads to
effective regulation, and consequently the development of trustworthy AI and
user trust, provided that the cost of implementing regulations is not too high.
Our findings highlight the importance of considering the effect of different
regulatory regimes from an evolutionary game theoretic perspective.
