In wireless networks, it is well-known that intermediate nodes can be used as cooperative relays to reduce the transmission energy required to reliably deliver a message to an intended destination. When the network is under a central authority, energy allocations and cooperative pairings can be assigned to optimize the overall energy efficiency of the network. In networks with autonomous selfish nodes, however, nodes may not be willing to expend energy to relay messages for others. This problem has been previously addressed through the development of extrinsic incentive mechanisms, e.g. virtual currency, or the insertion of altruistic nodes in the network to enforce cooperative behavior. This paper considers the problem of how selfish nodes can decide on an efficient energy allocation and endogenously form cooperative partnerships in wireless networks without extrinsic incentive mechanisms or altruistic nodes. Using tools from both cooperative and non-cooperative game theory, the three main contributions of this paper are (ⅰ) the development of Pareto-efficient cooperative energy allocations that can be agreed upon by selfish nodes, based on axiomatic bargaining techniques, (ⅱ) the development of necessary and sufficient conditions under which "natural" cooperation is possible in systems with fading and non-fading channels without extrinsic incentive mechanisms or altruistic nodes, and (ⅲ) the development of techniques to endogenously form cooperative partnerships without central control. Numerical results with orthogonal amplify-and-forward (OAF) cooperation are also provided to quantify the energy efficiency of a wireless network with sources selfishly allocating transmission/relaying energy and endogenously forming cooperative partnerships with respect to a network with centrally optimized energy allocations and pairing assignments.
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