“Greedy” demand adjustment in cooperative games
研究合作博弈中一种简单的需求调整过程，玩家随机轮流提出尽可能高的需求，该过程收敛到期望集，在凸博弈中收敛到核心。引入扰动后，分离期望集对突变最稳健。
Abstract This paper studies a simple process of demand adjustment in cooperative games. In the process, a randomly chosen player makes the highest possible demand subject to the demands of other coalition members being satisfied. This process converges to the aspiration set; in convex games, this implies convergence to the core. We further introduce perturbations into the process, where players sometimes make a higher demand than feasible. These perturbations make the set of separating aspirations, i.e., demand vectors in which no player is indispensable in order for other players to achieve their demands, the one most resistant to mutations. We fully analyze this process for 3-player games. We further look at weighted majority games with two types of players. In these games, if the coalition of all small players is winning, the process converges to the unique separating aspiration; otherwise, there are many separating aspirations and the process reaches a neighbourhood of a separating aspiration.