Pricing Games with Incomplete Information in Parallel Relay Networks

We investigate the impact of incomplete information on the problem of pricing and incentives in a two-hop parallel relay network with one source and multiple relays. We consider a pricing game with incomplete information where the relays advertise traffic dependent charging functions to the source, which then allocates its traffic in a multipath manner and pays the relays according to the advertised charging functions. In our setting, the state of the links for a given relay is not observable by the source or the other relays, although the prior distribution of the types is observable. To provide a benchmark, we first show that in the pricing game with complete information, Nash equilibria exist and are all efficient. In particular, there exist efficient equilibria resulting from linear charging functions. On the other hand, we show that in the game with incomplete information, linear charging functions may lead to inefficiencies. In particular, we quantify the efficiency loss in the symmetric case, where the type distributions and cost structure are identical for all relays.