Dynamic Games

Paper Session

Saturday, Jan. 7, 2017 8:00 AM – 10:00 AM

Hyatt Regency Chicago, Burnham
Hosted By: Econometric Society
  • Chair: Benjamin Brooks, University of Chicago

Costly Public Transfers in Repeated Cooperation Under Imperfect Monitoring

Mikhail Sergeyevich Panov
,
New York University

Abstract

We consider a continuous-time repeated game with imperfect monitoring of hidden production and the possibility that players can make public imperfect transfers between each other. Money transfers are costly: only a fraction k<1 of the money sent is received by the recipient (the case k=0 corresponds to pure money burning). We characterize the set of payoffs attainable in pure strategy public perfect equilibria (p-PPEs), as well as the dynamics in the efficient p-PPE. We show that adding the possibility of costly transfers increases the set of attainable p-PPE payoffs, because it allows one to provide incentives to one player with less cost to the other player. We also show that costly transfers are used rarely and only after extreme histories when promised utilities hit the individual rationality constraints.

Private Learning and Exit Decisions in Collaboration

Yingni Guo
,
Northwestern University
Anne-Katrin Roesler
,
University of Michigan

Abstract

We study a collaboration model in continuous time, with a positive arrival rate of a success in both the good and the bad state. If the project is bad, players may privately learn about it. At any time, players can choose whether to exit and secure the positive payoff of an outside option, or to stay with the project and exert costly effort. A player's effort not only increases the probability of success, but also serves as an investment in private learning. We identify an equilibrium with three phases. In all phases, uninformed players exert positive effort. Players who become informed and learn that the project is bad never exert effort. Because players benefit from the effort of the others, informed players may not exit immediately. In the first, no-exit phase, informed players do not exit. In the subsequent, gradual-exit phase, they exit with a finite rate. In the final, immediate- exit phase, informed players exit immediately. We find that effort levels may increase in the no-exit phase. Surprisingly, increasing the payoff of the outside option encourages collaboration.

Repeated Delegation

Elliot Lipnowski
,
New York University
Joao Ramos
,
New York University

Abstract

We study an ongoing relationship of delegated decision making. Facing a stream of projects to potentially finance, a principal must rely on an agent to assess the returns of different opportunities. The agent has lower standards, wishing to adopt every project. In equilibrium, the principal allows bad projects in the future to reward fiscal restraint by the agent today. We fully characterize the equilibrium payoff set, showing that Pareto optimal equilibria can be implemented via a two-regime ‘Dynamic Capital Budget’. We show that, rather than backloaded rewards—a prevalent feature of dynamic agency models with greater commitment power—our Pareto optimal equilibria feature an inevitable loss of autonomy for the agent as time progresses. This drift toward conservatism speaks to the life cycle of an organization: as it matures, it grows less flexible but more efficient.

When Does Predation Dominate Collusion?

Thomas Wiseman
,
University of Texas-Austin

Abstract

I study repeated competition among oligopolists. The only novelty
is that firms may go bankrupt and permanently exit: the probability that a firm survives a price war depends on its financial strength, which varies stochastically over time. With Bertrand competition, an anti-folk theorem holds: when firms are patient, every Nash equilibrium involves an immediate price war that lasts until only a single firm remains. Under some conditions, that result extends to Cournot and other forms of competition. Surprisingly, the possibility of entry may facilitate collusion, as may impatience. The model can explain observed patterns of collusion and predation, including recurring price wars and asymmetric market sharing.
JEL Classifications
  • C0 - General