Computational Performance of Deep Reinforcement Learning to find Nash Equilibria
This work addresses the computational challenge of applying deep reinforcement learning to economic models of firm competition, though it is incremental as it focuses on parameter sensitivity rather than introducing a new method.
The study tested the performance of the deep deterministic policy gradient (DDPG) algorithm in learning Nash equilibria for firms competing in prices, finding that specific parameter configurations achieved convergence rates up to 99% to the analytically derived Bertrand equilibrium.
We test the performance of deep deterministic policy gradient (DDPG), a deep reinforcement learning algorithm, able to handle continuous state and action spaces, to learn Nash equilibria in a setting where firms compete in prices. These algorithms are typically considered model-free because they do not require transition probability functions (as in e.g., Markov games) or predefined functional forms. Despite being model-free, a large set of parameters are utilized in various steps of the algorithm. These are e.g., learning rates, memory buffers, state-space dimensioning, normalizations, or noise decay rates and the purpose of this work is to systematically test the effect of these parameter configurations on convergence to the analytically derived Bertrand equilibrium. We find parameter choices that can reach convergence rates of up to 99%. The reliable convergence may make the method a useful tool to study strategic behavior of firms even in more complex settings. Keywords: Bertrand Equilibrium, Competition in Uniform Price Auctions, Deep Deterministic Policy Gradient Algorithm, Parameter Sensitivity Analysis