Trump is the Principal and a Republican Congress member is the Agent. Trump wants their support and wants to compel them to support him. There is no money to align incentives and all Trump can do is shower with praise (e.g. people who cave in to him are “brave” like Megyn Kelly who went to visit him in Trump Tower after their dustup) or rain down abuse (e.g. the Republican Governor Martinez of New Mexico who dared to text during one of his speeches).
From the Agent perspective, since there is no money, there is only re-election probability. This leads to two cases. In one case, the Agents reelection probability is increasing in being seen as pro-Trump. Then, Trump should allocate praise and abuse in the natural way. In the other case, the Agent’s re-election probability is decreasing in being seen as pro-Trump but Trump would still like Republican support to increases his election chances. Then, Trump should visit the Agent’s district if the Agent does not support Trump. He should say the Agent is brave and lie and say the Agent does support him. This threat maximizes compellence.
Marco Rubio provides the most interesting example. He has lumped in with Trump as he decides whether to run for re-election. If he throws his hat into the ring and Trump’s polls tank in Florida, Donald should threaten to campaign there heavily if Rubio shows signs of weakening in his support of Trump.