Working Papers

Cooperation in the Repeated Prisoner's Dilemma Game with Local Interaction and Local Communication (2008). [pdf]

   This paper considers a repeated prisoner's dilemma game in a network in which each agent interacts with his neighbors and cannot observe the actions of other agents who are not directly connected to him. If there is global information processing through public randomization and global communication, it is not difficult to construct a sequential equilibrium which supports cooperation and satisfies a refinement, called stability, which requires that cooperation resumes after any history. In this paper, we allow agents to locally communicate with their neighbors and show that it is possible to construct such an equilibrium without global information processing. Here, the role of local communication is to resolve the discrepancy of agents' expectations about their neighbor's future actions.


Public Randomization in the Repeated Prisoner's Dilemma Game with Local Interaction (2007). [pdf]

   The paper considers the situation where each agent interacts with his neighbors by playing repeated prisoner's dilemma games and he cannot observe the actions of others who are not directly connected to him. In this environment, a trigger strategy or Ellison (1994)'s modification of the trigger strategy, depending on the loss from neighbor's defection, can be a sequential equilibrium which supports cooperation. However, these equilibria have an undesirable property that a small possibility of mistake to play defection causes a complete breakdown of cooperation. In this paper, agents are assumed to observe a public randomization and we construct a sequential equilibrium for sufficiently patient agents which supports cooperation and in which cooperation is eventually recovered from any history. If there is a small possibility of mistakes, the equilibrium we construct can result in more efficient outcome than the trigger strategy equilibrium, even though they give the same payoffs in the limit.


Endogenous Formation of Networks for Local Public Goods (2008). [pdf]

   The paper studies a situation in which agents can make a binding agreement both on the amount of local public goods and on the structure of networks through which they share the benefits of public goods. An agent enjoys the benefit of public goods produced by others who are (directly or indirectly) connected to him. There is a cost to maintain a link as well as to produce a public good. Since agents can choose the amount of public goods, the value of a link is endogenously determined. First, we consider two different models of sequential bargaining games through which a contract on allocations is established. In the first model, we allow agents to propose a pure allocation and show that there is no symmetric stationary perfect equilibrium for sufficiently patient agents. In the second model, agents are allowed to propose a distribution on allocations. As a result, we find a symmetric stationary perfect equilibrium in which probabilistic choices are made on an equivalent class of allocations. Next, we characterize core allocations, which consist of a minimally connected network and an effort profile in which at most one agent does not produce the maximum amount of public good.


Efficient Structure of Organization with Heterogeneous Workers (2008). [pdf]

   The paper studies the problem of organizational design in a setting in which workers differ in their abilities and each worker is required to be monitored to prevent shirking. The need for monitoring workers generates a hierarchical structure in an organization, which can be represented as a rooted tree. The value of an organization is determined by the wage cost, the total number of productive tasks carried out, and the length of chain of supervision in the organizational hierarchy. % In this setting, we construct and characterize an efficient structure of hierarchy which maximizes the value of the organization. In addition, we show that a hierarchy with the optimal size has the form of balanced rooted tree.