Pair production is not something where the rule is 'go see what Wikipedia says'. Wikipedia just tries to summarize what is known, sometimes well, sometimes not.
Pair production is a well understood process in quantum field theory and quantum electrodynamics, and actually for particles other than electron-positron pairs, also from other parts of the standard model of quantum physics. There is nothing mysterious (anymore) about pair creation, pair annihilation or other interactions between charged particles and photons.
Quantum electrodynamics (QED) developed by Feynmann, Schwinger and others is the quantum field theory of the elctromagnetic interactions. In it you can calculate the cross sections, related to the probabilities of some creation, destruction and/or scattering event happening between charged particles (electrons and muons, and their antiparticles, plus other particles with internal structure when the internal structure effects can be approximated or ignored) and photons, the carrier of the electromagnetic force. It's a complex set of calculations using quantum field theory (QFT). Feynmann introduced his Feynmann diagrams as a way to make the setting up of the calculations easier. One example of a Feynmann diagram can be seen in the wiki article on Pair Production, at
One of the basic concepts in QFT, QED, and really all of relativistic quantum theory, is that particles (which are really excitations of quantum fields) can be created if there is enough energy for them to arise. Thus, it is really a many body problem, with all the different variations on which particles can be created and how likely those are. It is amazing that QFT and QED, a part of QFT, could figure it out. But that is the difference between non-relativistic and relativistic quantum theory, particles can appear and disappear.
Those cross section or probabilities, for instance of two photons creating an electron positron pair depends on the total photon energy in their, center of momentum frame of reference, and other factors. They've been demonstrated and measured in the laboratory. The same is true for the reverse process can also be calculated. But the difference is that an electron positron pair always has enough energy to create photons from their rest mass. Photons can only create massive particle pairs if they have the minimum energy to create two massive particles - for the electron positron pair it's 1.022 MeVs total.
Not every process you can think of can happen. Feynmann diagrams are a good methodology to see what processes can happen, and calculate their probabilities. Typically it is processes where, for QED, charged particles and or photons are involved, and energy, momentum and angular momentum can be conserved. It can be more complex for weak and stron interactions where you have to take into account the conservation of various quantum numbers also (such as flavor, in the strong interactions parity, etc).
At a high enough energies those processes of photon pair production will happen in large quantities, and they did in the early universe. But after it expanded and cooled some, their energies became lower and with many photons not having the minimum required energies pairs were not created. Pair annihilation kept happening until most positron disappeared. There was an abundance of electrons over positrons initially (why is a whole other story, it is not totally clear yet why there were and are much more particles than antiparticles. It may be to the broken parity and charge symmetry in the weak forces, but it is a work in progress)
The wiki article has more that that, it also has a brief summary of some of the calculations, and conservation laws, used, and what some of it means. QED was a huge accomplishment in physics, and it won its discoverers (or developers, it's just a word) Nobel prizes. It is something we know and should be proud of, there's still plenty we don't know.
More on QED at another wiki article at https://en.m.wikipedia.org/wiki/Quantum_electrodynamics
And a more detailed review of electrons and positrons in physics and astrophysics at http://www.icranet.org/misc/Scientific_Report_2009/Reports/08Xue_a.pdf
To really understand, and if you wish, to use, QED it is best to go through one of the Quantum Field Theory books. Wikipedia is just a quick view at thingS, and it may not always be right.