model, while similar to our model in theme, bears little resemblance to Hotelling’s original game.

In 1987, De Palma et al. [@de1987existence] introduced randomness into the Hotelling game, though in a manner different than we do. Rather than uncertainty in the reliability of the environment or the players, their paper studied uncertainty in client behaviors. That is, clients normally shop at the closest vendor, but with some probability, due to unquantifiable factors of personal taste, they skip a seller and travel further to the next one. This paper has a similar approach to our paper, but considers a different problem than ours.

Other types Aside for location games, other types of fault tolerant games have recently been studied. For example, Gradwohl and Reingold [@GR14] studied the immunity and tolerance of games with many players. Immunity means that faults have a small affect on the utility of non-faulty players. Tolerance means that optimal strategies remain optimal when faults are introduced to the game (even though the utilities may be different from the case without faults). The authors show that the *games themselves* are resilient to faults and quantify the strength of their resilience. We, on the other hand, consider a game 