  In the framework of transferable utility coalitional games, a scoring
(characteristic) function determines the value of any subset/coalition of
agents. Agents decide on both which coalitions to form and the allocations of
the values of the formed coalitions among their members. An important concept
in coalitional games is that of a core solution, which is a partitioning of
agents into coalitions and an associated allocation to each agent under which
no group of agents can get a higher allocation by forming an alternative
coalition. We present distributed learning dynamics for coalitional games that
converge to a core solution whenever one exists. In these dynamics, an agent
maintains a state consisting of (i) an aspiration level for its allocation and
(ii) the coalition, if any, to which it belongs. In each stage, a randomly
activated agent proposes to form a new coalition and changes its aspiration
based on the success or failure of its proposal. The coalition membership
structure is changed, accordingly, whenever the proposal succeeds. Required
communications are that: (i) agents in the proposed new coalition need to
reveal their current aspirations to the proposing agent, and (ii) agents are
informed if they are joining the proposed coalition or if their existing
coalition is broken. The proposing agent computes the feasibility of forming
the coalition. We show that the dynamics hit an absorbing state whenever a core
solution is reached. We further illustrate the distributed learning dynamics on
a multi-agent task allocation setting.
