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However, in such a case, fairness cannot be guaranteed since the TX, which can obtain a much higher utility in the non-cooperative scenario, can still obtain a much higher utility than the other in this cooperative scenario, which may lead to the failure of cooperation.
The treated health states were all rated at much higher utility and there were clear monotonic differences between the treatment vignettes (see Table 2).
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The treated health states were rated at much higher utilities and were statistically significantly different (p < 0.001) from each other: (1) 2-weekly: mean (median) utility = 0.61 (0.65); (2) 4-weekly: mean (median) utility = 0.65 (0.70); (3-monthlyhly: mean (median) utility = 0.70 (0.70).
Even though, comparing the competitive equilibrium and Nash equilibrium solutions, one can see that the competitive equilibrium provides a power distribution that not only meets physical power demand and supply constraints but also achieves a much higher social utility than the Nash equilibrium does.
Although much higher than utilities typically seen in advanced cancer [ 25], that values in multiple studies are similar may indicate that patients with advanced melanoma exhibit HRQL similar to age-matched members of the general population [ 10].
This reflected, in part, the distribution of data points illustrated in Figure 1 with the EQ-5D yielding utility scores as low as -0.077, whilst the minimum utility score generated by the SF-6D was much higher up the utility scale (0.374).
This can be seen by noting that the utility of a good school matching with a low experience teacher from a good school (0.7554) is much higher than the utility of a good school matching with a high experience teacher from a bad school (-0.6287).
In particular, low utilities were severely overestimated by the formula, and the mean predicted utility was 0.74, much higher than the measured utility of 0.45.
It is also worth noting that Pareto efficiency does not require an equitable distribution of wealth; the system may be Pareto efficient even if a small minority has the vast majority of the resources (as is the case with the drug companies in the U.S ., or benefits from a much higher level of its utility than the other actors.
While this PPA target is substantially lower than the USD $0.119 per kWh to USD $0.182 per kWh range seen in 2016 for CSP with storage3 [90], it is much higher than the recent utility-scale solar PV PPAs.
One can see that the competitive equilibrium significantly outperforms the Nash equilibrium in the social utility value and a much higher portion of users obtain higher individual utilities in the competitive equilibrium than those in the Nash equilibrium.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com