A student in my Mergers and Acquisitions class asked that question. What a great question!
The classic articulation of the efficiency paradox comes from Grossman and Stiglitz, who were demonstrating the circularity of the efficient capital markets hypothesis. Their insight was that the very assumption of efficiency meant that no one would have an incentive to look for arbitrage opportunities (because embedded in the efficiency assumption is a no-arbitrage assumption). But the market can only arrive at efficiency if market players look for arbitrages and eliminate them. See Sanford J. Grossman & Joseph E. Stiglitz, On the Impossibility of Informationally Efficient Markets, 70 Am. Econ. Rev. 393, 404 (1980).
Stephen J. Choi & G. Mitu Gulati, Contract As Statute, 104 Mich. L. Rev. 1129, 1173 (2006).
The relationship of information to an efficient market is not as simple as this description makes it seem, however. Information is not magically reflected in the market price of shares. Efficient markets are efficient because there is a large number of analysts and traders in constant competition with each other over the acquisition of information.Whenever new information is revealed, these competitors will trade on it until any possibility of making an arbitrage profit is exhausted. The greater the number of market participants following a company, the more quickly new information will be reflected in that company's share price. By the same token, the larger the number of participants, the less likely it is that any one of them will be able to systematically profit on trading when information becomes available.
There is a well known paradox inherent in the Efficient Capital Markets Hypothesis. If market participants could not systematically profit from their investments in gathering information, then they would have no incentive to acquire information and trade on it. However, if all market participants decided not to acquire information, then the markets would not be efficient and there would be room for participants to acquire information and use it to make arbitrage profits. This paradox occurs because market efficiency arises from the competition among analysts and traders to acquire information and trade on it. In other words, capital markets will immediately reflect all available information only when analysts and traders ferret out information and trade on it before others acquire the same information. As a result, in any efficient market there must be market participants who will undertake to acquire information and trade on it instead of merely relying on the current market price as a true indicator of the value of shares.
Not all market participants will have the same incentives to purchase information, however. Large investors, such as institutional investors, will be more likely to purchase information because, on a portfolio dollar basis, they bear lower costs in purchasing this information. In addition, for certain types of information there may be large threshold amounts that must be purchased to make the information useful.
The above discussion yields several conclusions. First, even if capital markets are efficient, there will be a large number of market participants competing with each other to acquire and use information to make arbitrage profits. Second, while some of these market participants will be engaged in the acquisition of information because the benefits of doing so exceed the costs, others will do so out of the misguided belief that they can still beat the market, i.e. , that the market is inefficient. Both types of market participants will compete actively in the market for information ....
Manuel A. Utset, Disciplining Managers: Shareholder Cooperation in the Shadow of Shareholder Competition, 44 Emory L.J. 71, 94–95 (1995)