Pre-Distribution: A Model of Equity Bargaining with Endogenous Investments

Abstract

This article sets forth a model of multilateral negotiations with alternating offers and voting in which members bargain over the distribution of equity shares prior to making investment decisions that determine the surplus to distribute. We challenge the classical assumption embedded in the divide-the-dollar setting that the fund to distribute is exogenoulsy given. Bargaining over productive incentives is fundamentally a different problem that yields a distinct set of equilibrium payoffs. The proposer faces a trade-off between rent-sharing and rent-generation subject to the constraint of receiving a majority vote. If he attempts to offer small equity shares to coalition partners, the size of the pie might shrink, rendering his large ownership percentage unfruitful. In equilibrium, the proposer forms a minimum winning coalition by offering two types of shares. Some members are incentivized to invest in the common project and they receive a share that yields a payoff greater than the ex ante value of the game, thus the proposer's rent-seeking incentives are mitigated by the production constraints. The remaining coalition partners are offered a share that buys their vote without inducing investment. We provide a new view on efficiency in bargaining games which relates to the approved incentive scheme, and not only the timing of the approval.