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.

This paper studies an allocation procedure for coalitional games with veto players. The procedure is similar to the one presented by Arin and Feltkamp (J Math Econ 43:855-870, 2007), which is based on Dagan et al. (Games Econ Behav 18:55-72, 1997). A distinguished player makes a proposal that the remaining players must accept or reject, and conflict is solved bilaterally between the rejector and the proposer. We allow the proposer to make sequential proposals over several periods. If responders are myopic maximizers (i.e. consider each period in isolation), the only equilibrium outcome is the serial rule of Arin and Feltkamp (Eur J Oper Res 216:208-213, 2012) regardless of the order of moves. If all players are fully rational, the serial rule still arises as the unique subgame perfect equilibrium outcome if the order of moves is such that stronger players respond to the proposal after weaker ones.