The Theory of Dynamic Public Investment Games

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The project develops a theory of dynamic public investment games. These games are intended to model dynamic environments in which current actions have external effects that irreversibly alter future incentives. A canonical example is a fund drive to provide the capital that will produce a future public benefit such as public television programming or a new church complex. Important features of such a drive that characterize a public investment game are: (1) an individual's contribution affects (generally positively) all the other participants; (2) this benefit is irreversible, assuming contributions are nonrefundable; and (3) the contribution alters the incentives of future contributors by enlarging the amount of the public good to which they will contribute.Environments with similar features, and which hence may be usefully viewed through the lens of a public investment game, are far more pervasive than just charity fund drives. They include the following. Firms in an oligopoly invest over time in their own capital stocks, which thus grow and affect all firms via their effect on marginal cost and hence prices. Bargaining when there is no third party to enforce agreements, as in international negotiations over trade, peace, or pollution abatement treaties, often takes place piecemeal over time with future concessions depending on the affirmative steps taken at earlier dates. Payments made over time by lobbyists to legislators generate a bundle of public goods, the legislative outcomes. In a patent race, a firm's current R&D expenditures irreversibly affect the state of knowledge about an innovation that will affect all firms. In a strategic learning environment, the result of an agent's current action provides an informational externality to all agents, irreversibly changing beliefs and hence future incentives. Thus, very abstractly, a dynamic public investment game is intended to model any situation in which "social capital" is created by individual efforts, investments, contributions, or other influence activities that can be taken incrementally over time.This research formulates an appropriate general definition of such dynamic games. It characterizes as much as possible the sequential equilibria of these games, with the goal being to obtain results that rival in completeness those we now have for repeated games. The overall goal is to increase our understanding of these environments, and to provide guidance for how to alter them, e.g., by modifying the governance of lobbying, patents, or charity drives. The central issues to be addressed concern the inefficiencies caused by free riding and coordination failure that these environments exhibit.