Stability and limit cycles in one-dimensional dynamic optimisations of competitive agents with a market externality

This paper considers low dimensional (more precisely, one state variable) dynamic optimisation problems of competitive agents. These individual decisions lead to a dynamic externality for the evolution of the system. However, the impact of an individual and competitive agent is negligible and thus each agent considers this evolution as exogenous data. This leads, assuming rational expectations (perfect foresight due to the deterministic set up), to motions in the three dimensional space of state, costate and externality. Considering the fact that such externalities are widespread, e.g., R&D in the literature on new growth theory, pollution in environmental economics, etc., the incorporation of such externalities due to competitive markets is important, yet this incorporation may alter the stability of the system. Indeed, complex policies such as stable limit cycles are sustainable in such a low-dimensional economy, even for a separable and strictly concave model.     

Numerical solution of dynamic oligopoly games with capital investment

Summary. This paper discusses how numerical techniques may be used to solve the simultaneous functional equations that arise in general dynamic stochastic games. Unlike the conventional linear-quadratic approach, our methods may be used to address general model specifications that may include non-quadratic objective functions, non-linear equations of motion, and constraints on decision variables. As an illustration, we apply our methods to a dynamic duopoly game in which competing firms play short-run quantity game subject to production cost that can be lowered through investment in capital stock in the long run. Received: June 1, 2000; revised version: December 27, 2000     

Learning from private information in noisy repeated games

We study the perfect type-contingently public ex-post equilibrium (PTXE) of repeated games where players observe imperfect public signals of the actions played, and both the payoff functions and the map from actions to signal distributions depend on an unknown state. The PTXE payoffs when players are patient are determined by the solutions to a family of linear programming problems. Using this characterization, we develop conditions under which play can be as if the players have learned the state. We provide a sufficient condition for the folk theorem, and a characterization of the PTXE payoffs in games with a known monitoring structure.     

Markov-perfect Nash equilibria in a class of resource games

Summary. A general model of non-cooperating agents exploiting a renewable resource is considered. Assuming that the resource is sufficiently productive we prove that there exists a continuum of Markov-perfect Nash equilibria (MPNE). Although these equilibria lead to over-exploitation one can approximate the efficient solution by MPNE both in the state space and the payoff space. Furthermore, we derive a necessary and sufficient condition for maximal exploitation of the resource to qualify as a MPNE. This condition is satisfied if there are sufficiently many players, or if the players are sufficiently impatient, or if the capacity of each player is sufficiently high.Received: November 1, 1996This revised version was published online in February 2005 with corrections to the cover date.     

Belief-free equilibria in games with incomplete information: Characterization and existence

We generalize the results of Hörner and Lovo (2009) [15] to N-player games with arbitrary information structure. First, we characterize the set of belief-free equilibrium payoffs under low discounting as the set of feasible payoffs that are individually rational, jointly rational, and incentive compatible. Second, we provide necessary and sufficient conditions on the information structure for this set to be non-empty.     

Simple Markovian equilibria in dynamic spatial legislative bargaining

The paper proves, by construction, the existence of Markovian equilibria in a dynamic spatial legislative bargaining model. Players bargain over policies in an infinite horizon. In each period, a sequential protocol of proposal-making and voting, with random proposer recognitions and a simple majority, produces a policy that becomes the next period's status-quo; the status-quo is endogenous. The construction relies on simple strategies determined by strategic bliss points computed by the algorithm we provide. A strategic bliss point, the dynamic utility ideal, is a moderate policy relative to a bliss point, the static utility ideal. Moderation is strategic and germane to the dynamic environment; players moderate in order to constrain the future proposals of opponents. Moderation is a strategic substitute; when a player's opponents do moderate, she does not, and when they do not moderate, she does. We provide conditions under which the simple strategies induced by the strategic bliss points computed by the algorithm deliver a Stationary Markov Perfect equilibrium, and we prove its existence in generic games with impatient players and in symmetric games. Because the algorithm constructs all equilibria in simple strategies, we provide their general characterization, and we show their generic uniqueness.     

The effects of tariffs on coalition formation in a dynamic global warming game

The prospects for cooperation on climate protection beyond 2012 are currently uncertain. Thus policy instruments which foster participation in International Environmental Agreements (IEA) are in demand. Among the instruments under discussion are trade sanctions. Multi-region optimal growth models are a state of the art tool for integrated assessment, but introducing trade sanctions distorts the competitive equilibrium, making it difficult to compute numerically. We introduce trade and trade sanctions into a model of coalition stability to assess the potential of trade sanctions to support an IEA. Trade is modeled by having all countries produce a generic output good, but adopting national product differentiation (Armington assumption). Coalitions are free to impose tariffs on imports from non-cooperating countries. We solve the model numerically using a refined version of Negishi's [Negishi, T., 1960. Welfare economics and existence of an equilibrium for a competitive economy. Metroeconomica 12, 92–97] basic algorithm. We then apply the model to analyze the influence of tariffs on international cooperation. The model suggests that there is indeed a significant potential to raise participation through trade sanctions, even when goods from different countries are nearly perfect substitutes. Furthermore we investigate the effect of trade sanctions on global welfare, environmental effectiveness, and the credibility of the tariff mechanism.