Market Equilibrium with Transaction Costs

Identical products being sold at different prices in different locations is a common phenomenon. To model such scenarios, we supplement the classical Fisher market model by introducing transaction costs. For every buyer i and good j, there is a transaction cost of cij ; if the price of good j is pj , then the cost to the buyer i per unit of j is pj + cij . The same good can thus be sold at different (effective) prices to different buyers. We provide a combinatorial algorithm that computes ǫ-approximate equilibrium prices and allocations in O 1 ǫ (n + log m)mn log(B/ǫ)
operations – where m is the number goods, n is the number of buyers and B is the sum of the budgets of all the buyers.