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Joint cost-sharing and multi-relay selection for two-way relay networks using a pricing game

In this paper the joint cost-sharing and multi-relay selection problem in two-way relay networks is modeled as a repeated Bayesian Stackelberg game. In each Stackelberg stage, the two source nodes submit payment offers to the relays targeting the next best relay that maximizes the network power efficiency. Each relay, as a follower, will participate only if its cost will be covered by the payments promised. Assuming asymmetric source utility functions, a source may not always afford its fair share payment and the other source may benefit from covering the shortage in payment. However, because utility functions are private information to each source, Bayesian strategies that maximize the expected utility of players are derived along with a belief update system, which together are shown to constitute a perfect Bayesian equilibrium. Additionally, a means to trade off performance for complexity is realized through a stage game cost factor.