On the impact of information disclosure on advance reservations: A game-theoretic view

Abstract

In many branches of the economy, customers can reserve resources in advance. Yet, service providers often differ in the information they disclose to customers. In this paper, we evaluate how information about server availability impacts the strategic behavior of customers in a loss system with N servers, where each customer can either reserve a server at a certain cost, or take the risk of finding no server available. We formulate the problem as a non-cooperative game with a random number of players. Our main contributions are to establish the existence, structure, and uniqueness (or lack thereof) of pure Nash equilibria, depending on the information disclosed to customers. Specifically, we first prove that if the number of available servers is always disclosed, then there exists exactly one pure Nash equilibrium. High reservation costs lead to an equilibrium in which all servers remain unreserved, while low reservation costs lead to an equilibrium that consists of N “time-thresholds.” A customer that observes n available servers, makes a reservation only if she makes her inquiry before the nth time-threshold. Next, we consider the case where the number of available servers is disclosed only when that number falls below a certain threshold. We show that, in this game, the same types of equilibria prevail. However, multiple Nash equilibria may exist. Finally, we numerically compare the performance of the different policies and we formulate the conjecture that it is preferable for a provider to hide information about the number of available servers.