In this dissertation auction formats are developed and discussed that focus on three specific economic eironments. Regarding the impossibility results from mechanism design, the main task for the implementation of auction designs is to balance allocative efficiency and incentive compatibility – the main characteristics a mechanism should provide. Therefore, the dissertation iestigates the limits of conceivable relaxations of allocative efficiency and incentive compatibility for complex settings such as double auctions, interdependent-valuation eironments and electricity market designs. The overall aim is to carefully weigh up the advantages and disadvantages for either relaxing allocative efficiency or respectively incentive compatibility.