On the core of dynamic cooperative games (Q384054)

The paper concerns dynamic cooperative games where a sequence of allocations uniquely induces a sequence of stage games. After considering in Section 2 a motivating example based on the classical majority game, in Section 3 the authors introduce a Markovian dynamic game and the notion of an allocation plan. In Section 4 the intertemporal and \(\varepsilon\)-intertemporal core are defined. ``A sequence of allocations is in the intertemporal core if no coalition can deviate and get on its own a greater share than the one proposed by the sequence.'' When a coalition deviates, then the game is no longer played with the original set of players but the deviating coalition becomes the new grand coalition which induces a new dynamic game. In Section 5 the main theorem that characterizes the nonemptyness of the \(\varepsilon\)-intertemporal core is proved. While the authors assume a common discount factor, in the final remarks presented in Section 6 they mention different discount rates as one of the issues for further studies. Also investigating a different core definition, the fair core, and considering a stochastic dynamic game where the stage games are endogenously determined are listed as possible further research.