Unblockable k-Payoffs for Cooperative Games

The notion of unblockable k-payoff was introduced for investigation of stable allocations in unbalanced cooperative TU-games. In the paper, we propose a brief survey of the vector lattice approach relating to the nonadditive analogs of the standard core imputations. This approach was elaborated, mostly, for the infinite games of bounded polynomial variation. Here, we focus, basically, on the description of the appropriate ordered spaces of nonadditive set functions applied and some generalized core-existence results obtained. The paper contains also several new results concerning important properties of so-called polynomial k-cores in a finite case. In particular, it is shown that not like in classical situation ( \(k = 1\) ) polynomial k-cores and the sets of non-dominated k-imputations of any finite cooperative TU-game coincide for each \(k \geq 2.\) In conclusion, a short constructive proof of the non-emptiness of the polynomial 2-core of any finite cooperative game is given.