Nash implementation for resource allocation network problems with production

An Efficient Game Form for Unicast Service Provisioning

“…Philosophically, our work is most closely related to [30], but it is distinctly different from [30] for the following reasons: (1) the game form proposed in our paper is distinctly different from that of [30]. (2) The mechanism of [30] is not balanced off equilibrium.…”

“…(2) The mechanism of [30] is not balanced off equilibrium. (3) In the mechanism of [30] there is no coupling among the games that are being played at different links. In our mechanism such a coupling exists (see section III), and results in a balanced-budget off equilibrium.…”

“…First we note that an optimal solution (x * , t * ) = (x * 1 , x * 2 , · · · , x * N , t * 1 , t * 2 , · · · , t * N )(where t i , i = 1, 2, · · · , N , are defined by (15), (16), (30), (31) and (32)) of Problem Max exists. This follows from: (i) the fact that each U i , i ∈ N , is concave and the space of the constraints described by Eqs.…”

“…they are not price-takers, they do not necessarily obey the rules of the mechanism but have to be induced to follow the rules). Within the context of wired networks, decentralized resource allocation mechanisms have been proposed and analyzed in [6], [8], [23]- [30] and [31]. A more detailed discussion of these references and comparison with the results of this paper will be presented in section I-C.…”

Power Allocation and Spectrum Sharing in Multi-User, Multi-Channel Systems With Strategic Users

“…However, such an approach would result in an infinite dimensional message/strategy space for the corresponding game. We don't follow Maskin's approach; instead we adopt the philosophy of [5], [8], [12], [13]. Specifically, by quoting [12], "we interpret our analysis as applying to an unspecified (message exchange) process in which users grope their way to a stationary message and in which the Nash property is a necessary condition for stationarity".…”