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You're claiming that a smart person would seek a career with a more highly variable wage because that person has a higher potential to succeed. This argument fails on two points. First, let's assume that this argument is true, and that a smart worker pursues the more variable job because of the higher upper bound on the distribution. If this is the case, then it would be optimal for all smart workers to seek the more variable job and low workers to seek the less variable. As a result, the smart worker is now competition with only smart workers in the higher position, leading to increased competition. This means his expected profit with the more variable job is not increased by being smart. Meanwhile, the less variable job is full of not-smart workers, meaning he has an increased likelihood of reaching the upper bound in that distribution (he can be the big fish in the small pond). So as long as the distributions have reasonable overlap (and they do, in practice), there is incentive to deviate and no pure strategy Nash equilibrium forms, which is counter to your claim.
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<p>Actually, it is your logic that completely fails, for you are making the strong presumption that everybody is completely rational, yet that fact has been mercilessly debunked by an entire library's worth of papers in the last 30 years. The fact is, not only do people not behave rationally, not only do people also not expect others to behave rationally either, and furthermore, people don't even properly factor in responses of any kind (whether rational or not) to initial moves . Academics such as Daniel Kahneman and Vernon Smith have won Nobel Prizes for demonstrating that people's real-world behavior strongly deviates from rationality, and in fact, the entire fields of experimental and behavioral economics have been devised in order to study real-world behavior. </p>
<p>To give you just a hint of the literature, Taylor & Brown (1988) showed that people are overconfident about their own abilities relative to others and also about their own futures. Svenson (1981) showed that the vast majority of people say that they are above average on a wide variety of common skills such as driving a car, even though obviously, by definition, only half of them can be above average. Overconfidence levels are also strongly affected by not only whether the payoff is affected by their own (perceived) ability, but also whether they can choose to self-select to participate, regardless of the fact that others who participate have self-selected also. To quote Camerer & Lovallo (1999):</p>
<p>* "...when subjects' post-entry payoffs are based on their own abilities, individuals tend to over- estimate their chances of relative success and enter more frequently (compared to a condi- tion in which payoffs do not depend on skill). The more surprising finding is that overconfidence is even stronger when subjects self- select into the experimental sessions, knowing their success will depend partly on their skill (and that others have self-selected too)"</p>
<p>Joe Roth, chairman of Walt Disney Studios, when he was asked why so many expensive big-budget movies are re- leased on the same weekends (such as Me- morial Day and Independence Day). Roth replied: Hubris. Hubris. If you only think about your own business, you think, "I've got a good story department, I've got a good marketing department, we're going to go out and do this." And you don't think that everybody else is thinking the same way. In a given weekend in a year you'll have five movies open, and there's certainly not enough people to go around. (Emphasis ours)*</p>
<p>Similarly, Radzevick and Moore (2008) found that "people are more confident when their own side is strong, regardless of how strong the competition is" and that "people neglect to make adequate consideration of the competition". Ball, Bazerman, and Carroll (1991) and Bazerman & Carroll (1987) found that people continually and consistently fail to consider competitive responses to their own first moves. </p>
<p>The bottom line is that game theory is inapplicable here for the simple reason that game theory is not scientific. Sorry to break it to you, but it isn't. Game theory is a mathematical tool and a philosophy that perhaps describes how people should behave, but not how they actually do behave. I don't think any game theorist - even John Nash himself - has ever seriously claimed to be describing real-world behavior. </p>
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The second issue with your argument comes from looking at it as an adverse selection problem. You're claiming that an agent with lower disutility for effort (i.e. a smart agent) will take the more variable job with the higher upper bound. However, if the smart agent is risk adverse (which is very highly likely - prospect theory), then he very well would favor the less variable position. An easy example to show would be an infinitely risk adverse agent with the set of potential realizations from the low variable wage a subset of the potential realizations from the high variable wage.
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<p>Again, see the literature above. The behavioralists have demonstrated a strong connection between (perceived) ability and overconfidence, which means that prospect theory does not apply. Prospect theory has to do with the differential weighing of potential gains and losses, yet overconfident people don't really care about losses because they think they are going to win. </p>
<p>So, like I said, quality (or at least perceived quality) will tend to segregate based on the variability of outcomes. In this case, the perceptions of quality are not entirely unwarranted, because they are based on a true signal: those who can get into a top school like MIT or Stanford really do have good reason indeed to believe that they are probably more qualified than somebody who can only get into some average state school.</p>