What are you basing your source of "market price"? And what kind of "high priced" good is this? real estate?
Regardless of what it is, the 'market price' is composed of ready buyers and sellers - but also is dependent on the region. Prices in New York City or San Francisco will be higher than prices in Topeka, Kansas (for pretty much any good). Also, every offer has qualifiers that have value - if real estate, is this a cash buyer ready to close in 30 days, buying "as-is" regardless of inspection? Is it contingent on them selling their house first? The former has much more "value" than the latter. If the OP is willing to wait 30, 60, 120 more days to get a higher price, then so be it - but a market is composed of ready buyers and sellers. Sometimes a market price will vary - there is no "set" market price on anything. Prices will fluctuate, so I'm curious what their source is for determine what the "market price" is.
Also, as another poster pointed out, the OP says that their "rock bottom" price is fair market value, and their asking price is 10% above that.
If this is real estate, I would probably offer less than asking price on a house, unless it is a fair value and just came on market - or perhaps they just lowered the price to a fair value and I expect it to get snapped up quickly. IN those instances, I would offer what they are asking - but in other cases, if the house has been sitting for several months, it's obvious that the market has not submitted an offer for a variety of reasons, so the market value was likely lower than what the seller thought, especially since many homes have offers taken very quickly (so if a house is sitting for 2-3 months or more, it means that it was overpriced given a variety of factors, and not what the seller thought.) But if I were buying a house, I'd offer more favorable financial terms than other buyers (it's not contingent on financing, it's only contingent on an inspection, I could close in 45 days), so that does have value.
Also, if this "big ticket" item is a collectible or some other luxury good (like a boat, a car, etc.), the pool of buyers may be fairly small. Sure, there may be an "average" market price - but how many transactions are occurring in a given 3 month period? Just 2? If 3 or 4 already sold, then the supply is higher than the market average, so you should expect less. But if there are typically 100 sales in a given quarter, and only a few dozen have sold in the quarter so far, then there are likely other buyers out there. Or perhaps there are seasonal demand factors - if you are selling a boat, expect to get a higher price in the spring vs at the end of Fall, when not many people are buying boats. Also, if not a house, look at what hte "new" prices are you are competing with with your "used" product - if (for example) it's a boat, maybe many manufacturers put on sales this time of year, so your used product might be not that much cheaper than buying new right now...but if you timed it at times of high demand, more people might pay more for a pre-owned product.