Trigger strategy

Abstract: We study the problem of a risk-neutral decision-maker who has to choose among two alternative investment projects of different scales under output price uncertainty. We provide parameter restrictions under which the optimal investment strategy is not a trigger strategy and the optimal investment region is dichotomous. Whenever the decision-maker has the opportunity to switch from the smaller scale to the larger scale project, the dichotomy of the investment region can persist even when the volatility of the output price process becomes large.

Abstract: In the present paper we explore the set of equilibria in a game-theoretic model in which players can jointly exploit a productive asset. As in repeated games, we find that under certain circumstances there may be efficient as well as inefficient equilibria. In the model we study, efficient trigger-strategy equilibria may exist from some starting states (stocks of assets) but not others. More precisely, there is a stock level, sayy′, such that an efficient trigger-strategy equilibrium exists from starting stocks greater than or equal toy′, but not from those strictly less thany′. (This statement is meant to include the cases in whichy′ is zero or infinite.) Under some circumstances, there may exist a new kind of equilibrium, which we call aswitching equilibrium. We show that, in our model, whenever y′ is positive (and finite), there is an open intervalI with upper endpoint y′ such that, from any starting stock inI there is an equilibrium of the dynamic game with the following structure: the players follow an inefficient but growing path until the stock reaches the levely′, and then follow an (efficient) trigger strategy after that. The use of a continuous-time model enables us to conveniently decouple the delay of information from the time interval between decisions.

Abstract: To self-limit play, a player selects a trigger event and an associated action. During play, the game is monitored for the triggered event. If the triggered event occurs, the associated action is performed.

Abstract: This article examines optimal social linkage when each individual’s repeated interaction with each of his neighbors creates spillovers. Each individual’s discount factor is randomly determined. A planner chooses a local interaction network or neighborhood design before the discount factors are realized. Each individual then plays a repeated Prisoner’s Dilemma game with his neighbors. A local trigger strategy equilibrium (LTSE) describes an equilibrium in which each individual conditions his cooperation on the cooperation of at least one “acceptable” group of neighbors. Our main results demonstrate a basic trade-off in the design problem between suboptimal punishment and social conflict. Potentially suboptimal punishment arises in designs with local interactions since in this case monitoring is imperfect. Owing to the heterogeneity of discount factors, however, greater social conflict may arise in more connected networks. When individuals’ discount factors are known to the planner, the optimal design exhibits a cooperative “core” and an uncooperative “fringe.” “Uncooperative” (impatient) types are connected to cooperative ones who tolerate their free riding so that social conflict is kept to a minimum. By contrast, when the planner knows only the ex ante distribution over individual discount factors, then in some cases the optimal design partitions individuals into maximally connected cliques (e.g., cul-de-sacs), whereas in other cases incomplete graphs with small overlap (e.g., grids) are possible.