Barter markets, indivisibilities, and Markovian core

We study a general barter market where every agent is endowed with several heterogeneous indivisible items and wishes to exchange. There is no medium of exchange like money. Agents have general preferences over their interested bundles of items and may acquire several items. We propose a practical and sensible solution called a Markovian core, generalizing the classical notion of the core. A Markovian core allocation is individually rational, Pareto‐efficient, and stable against any coalition deviation by comparison with their current assignments instead of their initial endowments and is shown to be a natural outcome of a decentralized market process.