Rohan Dutta

Bargaining with revoking costs

A simple two stage bilateral bargaining game is analyzed. The players simultaneously demand shares of a unit size pie. If the demands add up to more than one, the players simultaneously choose whether to stick to their demand or accept the otherʼs offer. While both parties sticking to their offers leads to an impasse, accepting a lower share than the original demand is costly for each party. The set of pure strategy subgame perfect equilibria of the game is characterized for continuously differentiable payoff and cost functions, strictly increasing in the pie share and the amount conceded, respectively. Higher cost functions are shown to improve bargaining power. The limit equilibrium prediction of the model, as the cost functions are made arbitrarily high, selects a unique equilibrium in the Nash Demand Game that corresponds to a Proportional Bargaining Solution of Kalai (1977).

ENTERTAINING MALTHUS: BREAD, CIRCUSES, AND ECONOMIC GROWTH

Motivated by the basic adage that man does not live by bread alone, we offer a theory of historical economic growth and population dynamics where human beings need food to survive, but enjoy other things, too. Our model imposes a Malthusian constraint on food, but introduces a second good to the analysis that affects living standards without affecting population growth. We show that technological change does a good job explaining historical consumption patterns and population dynamics, including the Neolithic Revolution, the Industrial Revolution, and the Great Divergence. Our theory stands in contrast to models that assume a single composite good and a Malthusian constraint. These models generate negligible growth prior to the Industrial Revolution. However, recent revisions to historical data show that historical living standards—though obviously much lower than todays—varied over time and space much more than previously thought. These revisions include updates to Maddisons dataset, which served as the basis for many papers taking long‐run stagnation as a point of departure. This new evidence suggests that the assumption of long‐run stagnation is problematic. Our model shows that when we give theoretical accounting of these new observations the Industrial Revolution is much less puzzling. (JEL B10, I31, J1, N1, O30)

Collusion constrained equilibrium

We study collusion within groups in non-cooperative games. The primitives are the preferences of the players, their assignment to non-overlapping groups and the goals of the groups. Our notion of collusion is that a group coordinates the play of its members among different incentive compatible plans to best achieve its goals. Unfortunately, equilibria that meet this requirement need not exist. We instead introduce the weaker notion of collusion constrained equilibrium. This allows groups to put positive probability on alternatives that are suboptimal for the group in certain razors edge cases where the set of incentive compatible plans changes discontinuously. These collusion constrained equilibria exist and are a subset of the correlated equilibria of the underlying game. We examine four perturbations of the underlying game. In each case we show that equilibria in which groups choose the best alternative exist and that limits of these equilibria lead to collusion constrained equilibria. We also show that for a sufficiently broad class of perturbations every collusion constrained equilibrium arises as such a limit. We give an application to a voter participation game showing how collusion constraints may be socially costly.

Dynamic commitment games, efficiency and coordination☆

An important form of commitment is the ability to restrict the set of future actions from which choices can be made. We study a simple two player dynamic game of complete information which incorporates this type of commitment. For a given initial game, the players engage in an endogenously determined number of commitment periods before choosing from the remaining actions. We show the existence of equilibria with pure strategies in the commitment periods. Partial characterization results for general games capture the tradeoff between commitment and deterrence. The equilibrium outcome is unique and efficient for two classes of games, including pure coordination and stag-hunt games.

Damned if You Do and Damned if You Don't: Two Masters

We study common agency problems in which two principals (groups) make costly commitments to incentives that are conditioned on imperfect signals of the agents action. Our framework allows for incentives to be either rewards or punishments. For our basic model we obtain a unique equilibrium, which typically involves randomization by both principals. Greater similarity between principals leads to more aggressive competition. The principals weakly prefer punishment to rewards, sometimes strictly. With rewards an agent voluntarily joins both groups; with punishment it depends on whether severe punishments are feasible and cheap for the principals. We study whether introducing an attractive compromise reduces competition between principals. Our framework of imperfect monitoring offers a natural perturbation of the standard common agency model of menu auctions, which results in sharper equilibrium predictions. The limit equilibrium prediction provides support to both truthful equilibria and the competing notion of natural equilibria, which unlike the former may be inefficient.