ترجمه مقاله نقش ضروری ارتباطات 6G با چشم انداز صنعت 4.0
- مبلغ: ۸۶,۰۰۰ تومان
ترجمه مقاله پایداری توسعه شهری، تعدیل ساختار صنعتی و کارایی کاربری زمین
- مبلغ: ۹۱,۰۰۰ تومان
abstract
This note discusses the possibility of fair gain sharing in cooperative situations where players optimally partition themselves across a number of alternative channels. An example is group purchasing among a set of buyers facing with a range of suppliers. We introduce channel selection games as a new class of cooperative games and give a representation of their cores. With two channels (suppliers), the game has a non-empty core if the gain functions across every individual channel is supermodular.
Channel selection games
Suppose a non-empty finite set of channels M exists to select from. For a channel j ∈ M, let wj : 2 N → R+ be channel j’s gain function which gives the non-negative and finite gain obtained by every coalition of players that select channel j such that wj(∅) = 0. With the interpretation of channels as suppliers, a gain function specifies per coalition the cost savings from joint purchasing if all players in the coalition buy via this channel. A channel selection situation is (N, M, (wj)j∈M ) with its elements being defined previously. For every S ⊆ N, let (Tj)j∈M be a partition of S over the channels. That is, for every j, k ∈ M we have Tj ∩ Tk = ∅ and ⋃ j∈M Tj = S. Let S the set of all such partitions. The characteristic function of the channel selection game (N, v) assigns to each coalition S ⊆ N the value: v(S) = max (Tj )j∈M ∈S ∑ j∈M wj(Tj). Let (T S j )j∈M be an optimal partition of S over the channels. If all wj are supermodular functions, it is known that the optimization problem above for |M| = 2 is solvable in polynomial time [7], but for |M| ≥ 3 the optimization problem becomes NPhard [2]. Nevertheless, if all gain functions are supermodular then there would be economies of scale in cooperation and the characteristic function of the associated cooperative channel selection game would at least be superadditive.