Classifying mechanics has a lot to do with the way the mechanic is described. In other words, classifying mechanics is subject to a thematic bias.
The rules of No Thanks are blindingly simple. The game is for 3 to 5 players. The game consists of a deck of 33 cards numbers 3 to 35, and a sufficient number of tokens. Each player begins with 11 tokens.
The cards are shuffled and 9 cards are removed the deck. On a player's turn, if no card is currently flipped up, flip up a card. The player then either takes the card and all tokens on the card, or places one of his tokens on the card. If he takes the card, he goes again. If he places a token on the card, play passes to the next player.
At the end of the game, your score is the face value of your cards minus the number of tokens that you have. However, if you have any cards in sequence (e.g. 9-10, or 20-21-22-23) you count only the lowest valued card of each sequence (e.g. 9 or 20). Lowest score wins.
What mechanics does No Thanks use?
This is a matter for interpretation.
Action Points: Each player is given 11 action points to start with. During your turn, you can use one of your action points to avoid taking the current card. Or, you can take the card and gain additional action points from the tokens on the card.
Area Control: The game consists of 33 areas, 24 of which come into play each game. Each area you control is negative points. However, if you control contiguous areas, only the least negative area counts against your score.
Auction: Each time a card is up for sale, you raise the ante of how much you are willing to pay not to take the card. The first person to decline to up their bid takes the card, as well as all other players' bids. All other players lose their bids.
Betting: You pay money into the pot every time you don't want to take the current offering. If a low card comes up, or a card that fits into your sequence comes up, you can win the card and the pool.
Card Drafting: You are trying to form the best hand at the least cost. The best hand is an arrangement of sequences, where the lowest card of each sequence is less than anyone else's, combined with your remaining tokens.
Commodity Speculation: You are trying to buy cards of approximately equal values. A single card is worth its value. Sets of cards are worth only the lowest value among them. Buying these commodities comes with cash incentives. Each game has up to ten commodities, depending on which cards were removed before starting.
Delivery: Each player pays money to not deliver a load. If you don't pay the fee, you must deliver the load for however much payoff is allocated for that load.
Hand Management: You are trying to manage cards as you collect them, hoping to buy necessary cards with limited resources.
Pattern Building: You are trying to complete card patterns, the least number of, and the least valued, patterns.
Route Building: You are trying to create a travel itinerary on a budget. The cheapest itinerary, with the least number of jumps, while saving the most amount of money.
Set Collection: Collect sets of sequences cards at the least cost.
Stock Holding: Buy losing stocks. The least losing portfolios at the end wins.
Trading: Each player contribute tokens that they are willing to trade to whomever agrees to take the card. In return, they agree to take other cards in the future, once they agree to its price.
Unit Deployment: Battle opportunities arise, and you can fend them off or fight them, gaining all spent resources in the process.
Variable Phase Order: Each player gets a turn, but can take additional turns if they agree to take the face up card immediately after it is revealed.
Variable Player Powers: There isn't, but there should be.
Voting: Each player casts votes on issues with political penalties. A player can accept the issue, and gain all political influence spent by other players as a result.
No Thanks uses all of these mechanics? No. But there is a lot of overlap between what we think of as mechanics and the thematic description behind them. If I had to pick the most intuitive mechanics to assign to the game, I would probably choose auctions and set-collection. But it really depends on the theme.