Efficiency of repeated network interactions

In this paper we consider a network with interactions by two users. Each of them repeatedly issues download requests on the network. These requests may be unsuccessful due to congestion or non-congestion-related errors. A user decides when to cancel a request (that is, what his impatience threshold is) and how long to wait before reissuing his request after cancellation of the previous request (that is, what his waiting time will be). This pair of impatience threshold and waiting time is his strategy. If a customer decides not to wait but to reissue his request immediately, that is, he sets his waiting time to zero, then he is said to use a so-called restart strategy. The goal of the user is to maximize the number of successful requests over a given time span.We study optimal strategies for the users in a game-theoretic framework. We find that in case congestion is the only cause of unsuccessful requests then each of the users will be very patient and any waiting time is optimal. Hence, restart strategies are among the optimal strategies. Second, in case non-congestion-related errors may occur, users will also set large impatience times, but now they will set waiting times to zero; in other words: they immediately reissue an unsuccessful download. In this case all optimal strategies are restart strategies. Hence, in both cases restart strategies are among the optimal strategies. Finally, implementing socially optimal strategies instead of individual optimal ones cannot improve the efficiency of the network usage.