Group Corruption via Sequential Bargaining in a Hierarchical Organization

We develop a framework of group corruption via back-door negotiations between an outside initiator and an authority of decision-makers in a hierarchical organization. We examine the role played by the architecture of a multi-tier authority and determine under such a structure how bargaining proceeds, in what order, and when it breaks down. We verify that equilibrium bargaining sequence proceeds as a chain through decision-making agents, regardless of the hierarchy of the organization. We prove the existence of a compromised equilibrium, where the decision of the authority is compromised, and establish sufficient conditions under which the most natural bottom-up bargaining configuration arises in equilibrium where a proposer negotiates with an immediately higher ranked respondent, starting with the initiator bargaining with the lowest ranked decision-maker in the organization. We then show the circumstances under which a top-down or a non-monotonic equilibrium configuration may emerge, and those under which the deal may break down. This enables us to capture a rich array of group corruptive configurations as observed. We conclude by investigating the extension to multi-tier authorities with multiple agents of the same rank in each tier, such as in a tree hierarchy.