While Matt is technically correct, it's much easier to maintain a conspiracy like this when you have a small number of participants with a high concentration of share.
If power is more diluted among a greater number of participants you are way more likely to see defectors, which would provide accurate pricing data to the market and cause the conspiracy to fail.
Can that be reduced to Prisoners Dilemma game theory?
Yes. Specifically in this case, "defect" is the good case and cooperate is price fixing cartel. So with more prisoners, the chances of someone choosing defect goes up. So then everyone else choose defect, breaking up the price fixing cartel, leading to market forces working and lower prices for consumers.
Or even better, folks actively trying to screw the market manipulators.