Earning and utility limits in Fisher markets

摘要: Earning limits and utility limits are novel aspects in the classic Fisher market model. Sellers with earning limits have bounds on their income and lower the supply they bring to the market if income exceeds the limit. Buyers with utility limits have an upper bound on the amount of utility that they want to derive and lower the budget they bring to the market if utility exceeds the limit. Markets with these properties can have multiple equilibria with different characteristics. We analyze earning limits and utility limits in markets with linear and spending-constraint utilities. For markets with earning limits and spending-constraint utilities, we show that equilibrium price vectors form a lattice and the spending of buyers is unique in non-degenerate markets. We provide a scaling-based algorithm to compute an equilibrium in time O(n3ℓ log (ℓ + nU)), where n is the number of agents, ℓ ≥ n a bound on the segments in the utility …