Q:

Why do live crabs in a bucket prevent each other from escaping?

It has been observed that crabs in a bucket will stop others from easily escaping. This observation has lead to the English language colloquialism crabs in a bucket. Has this phenomena been studied? What are some animal psychology explanations of this?

A:

There should be a dictum somewhere that states, "Never ascribe to psychology what is caused by instinct." 
By that I mean, the captured crab has a survival instinct. It's not going anywhere on the bottom of the bucket; it needs (I don't even know if I would say, "It wants") to get out. Out means "up", since "sideways" doesn't get them out, which doesn't prevent them from trying that as well (as shown by scuttling around the bottom repeatedly.)
The sides of the bucket are slick; there's nothing to grab onto. So if one crab climbs atop another, suddenly there's something "above" (a shadow? An outcropping? Another crab?) to grab onto to hoist itself up the side. So the crab instinctually grabs onto something above it. Unfortunately for the higher crab, there's nothing for it to hold onto above it, so he falls back into the bucket.
If only they would work together, a few of them might make it out. If they were chivalrous, the females and the young ("women and children") would go first.
I don't really know crab psychology, nor do I know any crustacean psychologists. All kidding aside, however, there have been some attempts to study stress in crustaceans. Science Daily published an article about stress in declawed crabs. What you and I think of as "stress" may be different than how the author thinks of it, but from the article, it's pretty clear that Dr. Elwood means psychological stress. However, there is no evidence to support that; the increased mortality of declawed crabs is more likely to be due to physiological stress (as in the second cited paper.) He has been called out on this by fellow biologists.
Crabs are invertebrates. If you want to learn about invertebrate psychology, the octopus is your animal.
Declawing Crabs May Lead To Their Death
Assessing Stress and Predicting Mortality in Economically Significant Crustaceans

