Any study on performance gap between optimal mechanism and linear mechanism? In mechanism design, the optimal mechanism is usually not linear in the agent's type. However, linear mechanisms are easy for implementation. Are there any studies on the performance comparison between optimal and linear mechanisms. I guess a theoretical comparison is probably hard, as the payoff in the linear mechanism does not have closed-form, but a numerical analysis is not very difficult. Thanks.
Robustness and linear contracts by Carroll says that linear is optimal (in his class of environments). Tim Roughgarden from Stanford also studies `the price of anarchy' related to using simple but suboptimal mechanisms.