Vying for support: Lobbying a legislator with uncertain preferences

We consider a model where two opposing lobbyists bid for the support of a legislator with an integrity threshold and an uncertain bias towards either lobbyist. We find that higher winning valuations drive more aggressive lobbying, while higher legislator’s integrity thresholds pushes toward more conservative lobbying behaviour. Furthermore, although the legislator’s preferences influence the outcome, it does so only in relation to the difference between the winning valuation and the integrity threshold. When the degree of uncertainty about the legislator is low relative to this difference, lobbyists bid aggressively. Conversely, if the degree of uncertainty is high, the risk of overbidding is significant enough to have the lobbyists bid conservatively. When the degree of uncertainty is moderate, we find asymmetric equilibria where one lobbyist chooses to either bid conservatively or aggressively, and the other just enough to ensure that the average bid is equal to the legislator’s integrity threshold. Overall, in an environment where lobbying proceeds behind closed doors, we find that although cash is king, it does not always rule