I still don't see how that is the case with your examples.
Insider trading laws, for example, exist exactly because only a few people having the info reduces its value, there would be no point in having them if that wasn't the case. Obviously, the value to the few having the information is increased because they can use the information to their advantage - but the overall value of something has to consider externalities as well, which in this case would mean considering at least the losses that unsuspecting trading partners incur, which already would make it a zero-sum game, so there at least is no positive value in keeping the information secret. Now, another externality of keeping insider information secret is that it leads to the market making less rational decisions about asset allocation, for example allocating capital to a company that is actually less efficient at doing its job in society than its competitor that publishes such information immediately and honestly, thus likely wasting resources in comparison to the allocation that would happen in an honest market. I mean, after all, we put quite a lot of effort into making sure that price discovery in the stock market is not being manipulated, and into creating public exchanges with public price information in the first place, so presumably there is some value to society in making this information widely available?
You're only looking at half of the value, though. It's because it has value to others that it's worth keeping the secret. I'm asserting that the normal case is for the value to others to outweigh the individual's value. You are correct that it's asymmetric, of course. And yes, zero sum games would tend to be something of a limiting case. I'm not sure you can find a negative sum game for society as a whole, though you can for some particular group.
