  Spending by the UK's National Health Service (NHS) on independent healthcare
treatment has been increased in recent years and is predicted to sustain its
upward trend with the forecast of population growth. Some have viewed this
increase as an attempt not to expand the patients' choices but to privatize
public healthcare. This debate poses a social dilemma whether the NHS should
stop cooperating with Private providers. This paper contributes to healthcare
economic modelling by investigating the evolution of cooperation among three
proposed populations: Public Healthcare Providers, Private Healthcare Providers
and Patients. The Patient population is included as a main player in the
decision-making process by expanding patient's choices of treatment. We develop
a generic basic model that measures the cost of healthcare provision based on
given parameters, such as NHS and private healthcare providers' cost of
investments in both sectors, cost of treatments and gained benefits. A
patient's costly punishment is introduced as a mechanism to enhance cooperation
among the three populations. Our findings show that cooperation can be improved
with the introduction of punishment (patient's punishment) against defecting
providers. Although punishment increases cooperation, it is very costly
considering the small improvement in cooperation in comparison to the basic
model.
