Distributed relay selection over multi-source and multi-relay wireless cooperative networks with selfish nodes

In this paper, an assignment game approach is proposed for relay selection and stimulating the cooperative behaviors of the relays in wireless networks. The sources should pay the relays for their cost energy in cooperative transmissions. The relays compete with each other to earn virtual currency from the assisted sources. The equilibrium concept in such games is called core. Such solutions correspond to the price-lists that competitively balance the benefits of all sources and relays. When the price assumes only discrete values, the core is transformed into discrete core. The non-empty core is ensured by the generalized condition named Gross Substitute (GS). We show that when one source is allowed to select at most one relay, GS always holds. However, if one source can select multiple relays, whether GS holds or not depends on the nature of the cooperative protocol and utility functions of the sources. We explore a scenario where GS does not hold for a multi-relay protocol. Subsequently, under GS condition, the Distributed Source-Relay Assignment (DSRA) Algorithm is proposed to get a discrete core solution of the game. With small enough measurement of price, the algorithm can achieve the optimal performance compared with centralized one in terms of total profit of the system.