Strategic uncertainty in markets for nonrenewable resources: a level-\(k\) approach (Q1784861)

Summary: 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.