Knaster增益博弈中的Shapley值

Shapley-Snow kernels, multiparameter eigenvalue problems and stochastic games

We establish, for the first time, a connection between stochastic games and multiparameter eigenvalue problems, using the theory developed by Shapley and Snow (1950). This connection provides new results, new proofs, and new tools for studying stochastic games.

Shapley群值

The Shapley group value

根据Shapley值（Shapley，1953 a）的原始解释，作为对多人互动情况下参与者前景的先验评估，我们提出了一个组值，我们称之为Shapley组值，作为对联盟博弈中一组参与者作为一个单位时的前景的先验评估。我们研究了它的性质，并给出了一个公理化的刻画。依靠这个估值，我们分析了一个集团的盈利能力。我们激励我们的建议，通过一些相关的应用Shapley组值，当它被用作一个目标函数的决策者谁是试图确定一个最佳的代理人组的框架中，代理人相互作用和所获得的利益可以建模通过一个可转移的效用博弈。作为一个说明性的examplewe分析的问题，确定的关键代理人在一个恐怖网络。

Estimation of the Shapley Value of a Peer-to-Peer Energy Sharing Game using Coalitional Stratified Random Sampling

Various peer-to-peer energy markets have emerged in recent years in an attempt to manage distributed energy resources in a more efficient way. One of the main challenges these models face is how to create and allocate incentives to participants. Cooperative game theory offers a methodology to financially reward prosumers based on their contributions made to the local energy coalition using the Shapley value, but its high computational complexity limits the size of the game. This paper explores a stratified sampling method proposed in existing literature for Shapley value estimation, and modifi…

运输费用Shapley分配的代理研究

A Study of Proxies for Shapley Allocations of Transport Costs

我们提出并评估了一些解决方案的问题，计算成本，以服务于每个位置在一个单一的车辆运输设置。这种服务成本分析在运输中具有战略和操作上的应用。该问题是正式的旅行销售员游戏（TSG），合作的总效用游戏，其中代理商对应于旅行销售员问题（TSP）中的位置。服务于一个地点的成本是最优旅游成本的分配部分。Shapley值是合作博弈中最重要的规范划分方案之一，为TSG和更普遍的分配提供了原则和公平的分配。我们考虑了一些直接和采样为基础的程序来计算Shapley值，并提出了第一个证明，近似的Shapley值的TSG在一个常数因子是NP-困难的。将Shapley值视为理想的基线分配，然后为该值开发六个相对容易计算的代理。我们使用合成欧几里德游戏以及来自现实世界的旅游计算的快速消费品场景的游戏进行实验评估。我们的实验表明，几个计算上听话的分配技术对应于良好的代理的Shapley值。

The $κ$-core and the $κ$-balancedness of TU games

We consider transferable utility cooperative games with infinitely many players. In particular, we generalize the notions of core and balancedness, and also the Bondareva-Shapley Theorem for infinite TU-games with and without restricted cooperation, to the cases where the core consists of $κ$-additive set functions. Our generalized Bondareva-Shapley Theorem extends previous results by Bondareva (1963), Shapley (1967), Schmeidler (1967), Faigle (1989), Kannai (1969), Kannai (1992), Pinter(2011) and Bartl and Pintér (2022).

A Mathematical Programming approach to Overlapping community detection by cluster's Shapley value

We propose a new model to detect the overlapping communities of a network that is based on cooperative games and mathematical programming. More specifically, communities are defined as stable coalitions of a weighted graph community game and they are revealed as the optimal solution of a mixed-integer linear programming problem. Exact optimal solutions are obtained for small and medium sized instances and and it is shown that they provide useful information about the network structure, improving on previous contributions. Next, a heuristic algorithm is developed to solve the largest instances …