So is the real collusion here the fact that an index like that exists? Why are prices set by a centralized index rather than just normal supply and demand? (Genuinely asking; egg markets are far outside my area of expertise.)
In this case it looks like the price-setting market was the spot market for excess eggs but that market was a small percentage of the overall egg market: the majority of eggs are sold in private, years long contracts that are negotiated to adjust to the prices in that small excess egg market. The vulnerability of this kind of market to manipulation is obvious.
There was also some spoofing which apparently also affected the actual prices because the egg market index was not as sophisticated as stock market indexes are.