Vierhaus, Ingmar Veldhuizen, Roel van Fügenschuh, Armin
[Journal:] Discrete Dynamics in Nature and Society [ISSN:] 1607-887X [Publisher:] Hindawi [Place:] London [Year:] 2017 (Article ID 2768045) [Pages:] 1-8
Existing models of nonrenewable resources assume that sophisticated agents compete with other sophisticated agents. This study instead uses a level-k approach to examine cases where the focal agent is uncertain about the strategy of his opponent or predicts that the opponent will act in a nonsophisticated manner. Level-0 players are randomized uniformly across all possible actions, and level-k players best respond to the action of player k - 1. We study a dynamic nonrenewable resource game with a large number of actions. We are able to solve for the level-1 strategy by reducing the averaging problem to an optimization problem against a single action. We show that lower levels of strategic reasoning are close to the Walras and collusive benchmark, whereas higher level strategies converge to the Nash-Hotelling equilibrium. These results are then fitted to experimental data, suggesting that the level of sophistication of participants increased over the course of the experiment.