The“core Equal treatment in the core: if X is an allocation in the r-core of a given economy, then any two agents of the same type must receive the same bundle Proof: if not LetsI\rxA1BrLj= B So∑x+∑1x=∑+∑ =16 That is x+XB=w+WB Every agent below the average will coalize to improve upon the allocationThe “core” • Equal treatment in the core: if x is an allocation in the r-core of a given economy, then any two agents of the same type must receive the same bundle. Proof: if not. Let , – So – That is – Every agent below the average will coalize to improve upon the allocation. 1 1 r A A r j x x = =  1 1 r B B r j x x = =  1 1 1 1 1 1 1 1 r r r r r r r r A B Aj Bj j j j j x x w x = = = =     + = + A B A B x x w w + = +