Vote buying: Lobbying a legislator with uncertain preferences

We consider a dynamic model of lobbying with two opposing lobbyists vying for a legislator’s support, whose preferences are uncertain. The results show that the degree of uncertainty of legislator preferences has a direct effect on the bidding strategy of lobbyists. When the degree of uncertainty is low, lobbyists play in a one shot scenario. Conversely, we find that if the degree of uncertainty is high, the incentives of waiting outweigh its costs, and lobbyists proceed under a dynamic scenario. As the optimal policy function evolves as the state evolves, it is likely for lobbyists who start by bidding conservatively to end up in the one shot scenario. Interestingly, we also find multiplicity of equilibria when the degree of uncertainty is moderate. Under moderate levels of uncertainty, lobbyists can choose either to bid above or below the legislator’s integrity threshold, as well as decide to end the game today or continue playing in the subsequent periods