Currently OPM per diem rates for travel (TDY) are set so that the lodging rate is a 'use it or lose it' system whereby money not spent on lodging is returned to the government. This fosters an environment where most government travelers don't spend any time looking for the best rate. In fact, in many cases the upper limit is what travelers look for so that they can maximize their frequent traveler program points.
The lodging per diem rates can stay the same but make a hybrid solution of the current lodging and M&IE rules so that money spent under the maximum is split between the government and the traveler - perhaps a 50/50 split of the savings. For example, if the lodging in Area A is $100/night and a traveler finds a hotel for $50/night, he would keep $25/night and $25/night would be cost savings to the government.
Incentivize travelers to find more cost effective lodging with immediate and universal impact of hundreds of millions of dollars per year.