Are the stocks of competitor companies negatively correlated? e.g. if Sony goes up in price, will Samsung fall?
Not especially. It depends on why sales have changed. If it's just consumer demand, that affects everyone in parallel rather than pushing in opposite direactions. If it's changes other than sales, that may have no effect on other companies. If it's because someone introduced the next must-have-it device and they're selling rapidly and drawing customers from the competing brands, maybe.
And that's all neglecting the fact that this may already have been incorporated into the competitor's share price long ago, in anticipation of this news.
Sorry, but the market just ain't simple.
It is important to first understand that true causation of share price may not relate to historical correlation. Just like with scientific experiments, correlation does not imply causation. But we use stock price correlation to attempt to infer causation, where it is reasonable to do so. And to do that you need to understand that prices change for many reasons; some company specific, some industry specific, some market specific. Companies in the same industry may correlate when that industry goes up or down; companies with the same market may correlate when that market goes up or down.
In general, in most industries, it is reasonable to assume that competitor companies have stocks which strongly correlate (positively) with each-other to the extent that they do the same thing.
For a simple example, consider three resource companies: "Oil Ltd." [100% of its assets relate to Oil]; "Oil and Iron Inc." [50% of its value relates to Oil, 50% to Iron]; and "Iron and Copper Ltd." [50% of its value relates to Iron, 50% to Copper].
For each of these companies, there are many things which affect value, but one could naively simplify things by saying "value of a resource company is defined by the expected future volume of goods mined/drilled * the expected resource price, less all fixed and variable costs". So, one major thing that impacts resource companies is simply the current & projected price of those resources.
This means that if the price of Oil goes up or down, it will partially affect the value of the two Oil companies above - but how much it affects each company will depend on the volume of Oil it drills, and the timeline that it expects to get that Oil. For example, maybe Oil and Iron Ltd. has no currently producing Oil rigs, but it has just made massive investments which expect to drill Oil in 2 years - and the market expects Oil prices to return to a high value in 2 years.
In that case, a drop in Oil would impact Oil Inc. severely, but perhaps it wouldn't impact Oil and Iron Ltd. as much. In this case, for the particular share price movement related to the price of Oil, the two companies would not be correlated. Iron and Copper Ltd. would be unaffected by the price of Oil [this is a simplification; Oil prices impact many areas of the economy], and therefore there would be no correlation at all between this company's shares.
It is also likely that competitors face similar markets. If consumer spending goes down, then perhaps the stock of most consumer product companies would go down as well. There would be outliers, because specific companies may still succeed in a falling market, but in generally, there would be a lot of correlation between two companies with the same market.
In the case that you list, Sony vs Samsung, there would be some factors that correlate positively, and some that correlate negatively. A clean example would be Blackberry stock vs Apple stock - because Apple's success had specifically negative ramifications for Blackberry. And yet, other tech company competitors also succeeded in the same time period, meaning they did not correlate negatively with Apple.
In theory, say we had two soft drink companies, and no other existed. On Jan 1, they report they each had 50% market share for the past year. Over the next year, one company's gain is the other's loss. But over the year, for whatever reason, the market has grown 10% (all the stories of bad water helped this), and while the market share ends at 49/51, the 49 guy has improved his margins, and that stock rises by more than the other.
In general, companies in the same industry will be positively correlated, and strongly so.
I offer my "spreadsheets are your friend" advice.
I took data over the last 10 years for Coke and Pepsi. Easy to pull from various sites, I tend to use Yahoo. In Excel the function CORREL with let you compare two columns of numbers for correlation. I got a .85 result, pretty high. To show how a different industry would have a lower correlation, I picked Intel. Strangely, enough, Intel and Pepsi had a .94 correlation. A coincidence, I suppose, but my point is that you can easily get data and perform your own analysis to better understand what's going on.