This paper develops a method to compute the Stackelberg equilibria in sequential games. We construct a normal form game which is interactively played by an artiÿcially intelligent leader, GA L , and a follower, GA F. The leader is a genetic algorithm breeding a population of potential actions to better anticipate the follower's reaction. The follower is also a genetic algorithm training on-line a suitable neural network to evolve a population of rules to respond to any move in the leader's action space. When GAs repeatedly play this game updating each other synchronously, populations converge to the Stackelberg equilibrium of the sequential game. We provide numerical examples attesting to the e ciency of the algorithm.
This paper examines linkages between international trade, environmental degradation, and economic growth in a dynamic North-South trade game. Using a neoclassical production function subject to an endogenously improving technology, North produces manufactured goods by employing labor, capital, and a natural resource that it imports from South. South extracts the resource using raw labor, in the process generating local pollution.We study optimal regional policies in the presence of local pollution and technology spillovers from North to South under both non-cooperative and cooperative modes of trade. Non-cooperative trade is inefficient due to stock externalities. Cooperative trade policies are efficient and yet do not benefit North. Both regions gain from improved productivity in North and faster knowledge diffusion to South regardless of the trading regime.r oie_800 906..926
This paper proposes a novel method that enhances numerical approximation of infinite horizon optimal control problems. For direct numerical optimization, a continuous-time infinite horizon model needs to be first recast as a discrete-time, finite-horizon control problem. The very transformation itself may significantly degrade the quality of the optimization results, if due care is not taken to preserve the salient features in the original model. Michel (1994. Econometrica 62, 635-656, 2001. Journal of Economic Dynamics and Control 25, 1179-1191), for instance, propose time aggregation methods that minimize approximation errors at the steady-state. Using their scheme, we show that overall optimization performance can be further improved if the discretization of the transient phase is optimal as well. Three sample problems are numerically solved to demonstrate the potential benefits. r 2005 Elsevier B.V. All rights reserved.JEL classification: C61; C63
Nash equilibrium, Parallel genetic algorithms, Neural networks. 'For numerical computation, infinite-horizon differential games can be discretized as in [2] so that the discussions that follow can be extended without any loss of generality. 2See, among others, 13-71 for classes of games in which open-loop Nash equilibria are subgame-perfect.
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