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Most starting points resulted in convergence to the symmetric Nash equilibrium point (underline {p}^= [3.53,3.53,3.53]) as shown in Figure 2. Additionally, we numerically found other symmetric Nash equilibrium points forming a line segment, as shown in Figure 3.
Considering equal allocations at symmetric price point (underline {p}) as above, define B_{i,1} = left{p:~pfrac{D p)}{|G|}-a_{i}left(frac{D p)}{|G|}right)^{2} geq u_{B,i}'(p),~ hat{p}_{i} geq p right}.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com