One aspect of the current situation may cut against market power explanations: the empty shelves themselves. Standard monopoly theory says firms restrict quantity to drive up prices. If producers had significant market power, we’d expect to see high prices WITH eggs on shelves; they’d be maximizing profits by selling at elevated prices, not leaving money on the table with stockouts.
Empty shelves with signs saying “limit one dozen” suggest retailers aren’t letting prices rise enough to clear markets. That’s more consistent with competitive markets under a supply shock than monopolistic behavior.
I can buy a dozen eggs in around 1 dollar and 20 cents in India. Can you? I also don't remember if there has ever been a market out of supply for Eggs here.