I didn't encounter much in the way of quantitative stuff other than DeMesquita's "Logic of Political Survival," and related papers and code, which is what people should understand after they have read the foundational books like Getting To Yes, Influence, Never Split the Difference, the guidebook to negotiations A-Z from The Economist, etc.

People who haven't read laterally in it tend to only have one or two tools that have worked for them up to their level. Haggling, bargaining, and auction models aren't really negotiation. Reality is, it's the process of price discovery, often with people who are looking for rules they can break and points of leverage.