Economists have become fond of lamenting irrational behavior, by which they refer to actions in actual reality which do not conform to to their models of optimal profitability.
For example, economists have done studies quantifying how much people overbid at auctions. By overbidding, the economists mean that people pay more to buy objects at auction than the amount their mathematical models say would result in the greatest cumulative profit.
Let us suppose that I wish to own object 'A' and that I am willing to pay as much as $100 to obtain it. Now at auction I may bid $80 to get object 'A'. The economic model may say, however, that I should bid $50 because if I bid $50 consistently I will get the $100 objects often enough to maximize my net value. Since I bid $80 rather than $50, I must be overbidding, or so the economic model would seem to show.
But why would paying 80% of an object's worth ever be irrational? What's wrong with this model?
Actual reality is more complex than the economic models. Remember the first supposition of my example: I wish to own object 'A'. For this imaginary me, the goal is not to buy and sell but rather to own. I value (for reasons not stated) possessing object 'A'; my story does not make the assumption that owning multiple objects 'A' will have a greater value. In my personal reality, in fact, duplicated objects are often just so much junk and have negative value. In addition, there may be a negative value attached to being without object 'A' between now and the next opportunity to bid.
I suspect that people typically do act rationally within their complete system of valuation and subject to the limitations of their current knowledge. As economists turn more to "behaviorial" economics, the study of how people actually behave rather than how they "ought" to behave, I expect that this rationality is what they will discover in our activity.
On the other hand, our current knowledge is subject to both ignorance and illusion. The recent economic downtown of 2008-2009 appears to illustrate this kind of irrationality in fairly clear terms.
A major part of the problem seems to have been risky mortgages which were resold without full information on the risk. One may think that loan officers were being deliberately ignorant of the risks they were undertaking, but they may also have quite rationally ignored risks which others were quite willing to assume. The issuers of the loans were under the illusion that they undertook no significant risk once the loan was sold. The loan purchasers were under the illusion that their individual risk was low because the overall risk was diluted among a large number of investors. In both cases, the specific behavior was rational in context. The problem was not irrationality but an illusion resulting from an oversimplification of the risk calculation which appeared rational in the absence of a comparison with a complex, difficult, and costly analysis.
Other illusions were also a part of the problem, such as the illusion that what is going up must continue up and (months later) that what is going down will fall forever. Some of these illusions arise naturally from the way our brains are constructed, which only means we should take extra care to avoid them.
Behavior which is based on reasonable errors in valuation or on unavoidable ignorance is not truly "irrational" behavior. Yet it is not fully rational, either; it is rational only within the illusory context.
Playing the actual reality game rationally requires both rational decisions and good knowledge of the actual reality within which we make our plays.