Monotonic Core Allocation Paths for Assignment Games

We introduce a modification of Sprumont [9]'s population monotonic allocation scheme (PMAS), called monotonic core allocation path (MCAP) for assignment games, which is a sequence of allocations along an order on the set of players satisfying that (1) each allocation is in the core of the subgame of the corresponding players at that step, and (2) the payoffs for each player are non-decreasing through the sequence. The notion of MCAP preserves the population monotonicity of PMAS while avoids the difficulty that PMAS does not exist in many market games. We show that a MCAP exists for every assignment game. The terminals of MCAP form a re nement of the core. We also show that the terminals of MCAP coincide with the extreme core allocations in two subclasses of assignment games:gloves games and Bohm-Bawerk games. The strong connection of MCAP with extreme core allocations suggests some con ict between the stability of a coalition formation process and the fairness of the resulting outcomes.