Pricing in Dynamic Advance Reservation Games

We analyze the dynamics of advance reservation (AR) games: games in which customers compete for limited resources and can reserve resources for a fee. We introduce and analyze two different learning models. In the first model, called strategy-learning, customers are informed of the strategy adopted in the previous iteration, while in the second model, called action-learning, customers estimate the strategy by observing previous actions. We prove that in the strategy-learning model, convergence to equilibrium is guaranteed. In contrast, in the action-learning model, the system converges only if an equilibrium in which none of the customers makes AR exists. Based on those results, we show that if the provider is risk-averse and sets the AR fee low enough, action-learning yields on average greater profit than strategy-learning. However, if the provider is risk-taking and sets a high AR fee, action-learning provably yields zero profit in the long term in contrast to strategy-learning.