That makes all the sense there is. It is the basic function of a market. If you try to fix prices, you will either have to much or too little goods. For instance in a business, if you fix wages below the market, the business will have problems finding workers. if you fix the wages at a higher rate than the market, there will be a queue of workers outside. If there is no quota in the gates (two way pegged sidechain), all workers will be hired in that business.
I'm sorry but I don't see the correlation. You'll have to develop your scenario on how market participant decide unanimously to converge to either chains.