I've asked the same question on the Economics Stack Exchange here to get answers from the perspective of applied economic theory.
I'm the managing director of a company in which we run appraisals every 6 months. Each time we negotiate salary I have in my mind's eye this picture...
Assuming the 'correct' salary for an employee is 70k, there's an incentive to offer slightly more. 'Slightly more' because there's some error in estimating the market rate and the costs of getting this wrong are high. I've added a staff churn costs of £20k/yr for getting this wrong based on loss of knowledge, morale, recruitment costs and what I refer to as a 'change incentive' for the replacement employee. The change incentive is the amount you must offer a new employee beyond their current rate (market rate?) to discount the loss of familiarity and to take on the risk of joining a new employee.
Belief 1 - Underpaying employees is much more costly over the long term once staff churn is taken into account.
Belief 2 - the employee has better information about their value - based on them being nearer the information about their skills, positive contributions and self interest in the literal sense.
Belief 3 - salary expectation in job adverts are positively skewed to discount against the risk and transaction costs to the employee of change. Nobody switches to an identical salary unless it's a sideways move. Anecdotally, I've heard advice to change jobs every few years in order to raise your salary faster. Humans tend to be unnecessarily risk adverse and you can give yourself a competitive edge by overcoming this bias.
Belief 4 - primary information source for market value are job adverts and job offers. These overvalue for the reasons in belief 3.
Belief 5 - Protracted and/or aggressive salary negotiation is costly in itself. If there's a big discrepancy it can create feelings of being undervalued.
Belief 6 - Employees will be content and thus likely to remain with the company if they feel they are receiving the market rate.
Assumptions: the company is otherwise a pleasant place to work.
In my particular industry, I'd consider low staff churn rates and high staff morale as being a distinct and powerful competitive advantage. The figure of 20k churn cost is probably conservative.
In England, where I live, the cultural norm is for the company to either start the negotiation or more commonly simply state what the pay rise is going to be. This is followed by a period of watching how much they squeak squirm with dissatisfaction. Given the beliefs above and an industry where staff churn is costly, I'm inclined to lean in the other direction and either let them begin the negotiation or even more radically, simply request what their salary should be; as is common for sellers of other types of good. Salary negotiation seems to me to be unique in that the buyer of the good (their labour) dictates the price and then watches to see if the supply vanishes (resigns).
Is it an optimal strategy in salary negotiations to let the employee decide?