The market maker is resolving or extending the curve (volatility surface) through some interpolative technique(s). The market maker doesn't set the price, he/she reacts to price agreed upon by other traders, including fellow market makers.
If there's zero volume in a strike, the market makers make their markets in that strike based on the IV of its "heavily traded brothers." But the IV in those "brothers" is set by supply and demand. This should be obvious. Imagine a day when IBM stock doesn't move all day. On this day the 100 calls are .45 bid at .55. Imagine further that some big house comes in and buys those calls all day long - a total of 20,000 calls by the end of the day. At the beginning, the market makers have a certain number they're willing to sell at their offer of .55. But do you think they're willing to sell an infinite number there? If so, they wouldn't be in business for long. No, they'll sell a certain number at .55. When they've sold all they're willing to sell at .55, they'll raise their offer to .60. When they've sold all they're willing to sell at .60, they'll raise their offer to .65. When they've sold all they're willing to sell at .65, they'll raise their offer to .70. Each time the 100 calls sell at the next higher price, the implied volatility jumps (remember in our example IBM stock is not moving). By the end of the day, those 20,000 buys will have driven IV significantly higher. How else do you think implied volatility goes up and down? It's in response to supply and demand. Plain and simple.
You are correct in your logic. Now you should [imo] figure out for yourself why there must be a skew/smile.
There is a tendency there to "drive" the price of the underlying security to the strike price that has the most OI, but it only happens if the prices are very close anyway. One can utilize it but overall it does not have required consistency to design an ongoing investing strategy.
I have a Ph.D. in electronics (Thyristor Cycloconverters) and a Ph.D. in Cybernetics (mathematical Psychology, a part of AI).
That is half correct. Models are used in two ways: One is to get theo prices, the other is to get greeks. Those two things are not always the same. This is discussed by Taleb in DH, under soft deltas etc.
Contamination principles have nothing to do with the spontaneous synchronization. If my "poor" explanations were not too clear, I apologize.
I understand this. But that's not what I am talking about. My question is, why would the IV change in an option which is not traded at all? Let's extend your example a bit further. Let's say, there is another option with different expiration date. There are no trades in that option. Can you give me an explanation, why would IV of this option change when someone is buying the other option?