Arbitrage in Combinatorial Exchanges

Combinatorial exchanges are trading mechanisms that allow agents to specify preferences over bundles of goods. When agents’ preferences exhibit complementarity and/or substitutability, this additional expressiveness can lead to more efficient allocations than is possible using traditional exchanges. In the context of combinatorial exchanges, this paper examines arbitrage, a risk-free profit opportunity. We show that some combinatorial exchanges allow agents to perform arbitrage and thus extract a positive payment from the market while contributing nothing, something that is not possible in traditional exchanges. We analyze the extent to which arbitrage is possible and computationally feasible in combinatorial exchanges. We show that the surplus-maximizing combinatorial exchange with free disposal is resistant to arbitrage, but without free disposal arbitrage is possible. For volume-maximizing and liquidity-maximizing combinatorial exchanges, we show that arbitrage is sometimes possible and we propose an improved combinatorial exchange that achieves the same economic objective but eliminates a particularly undesirable form of arbitrage. We show that the computational complexity of detecting winning arbitraging bids is NP-complete and that the ability for an agent to submit arbitraging bids depends on the type of feedback in the exchange. We also show that a variant of combinatorial exchanges in which arbitrage is impossible becomes susceptible to arbitrage if certain side constraints are placed on the allocation or if an approximating clearing algorithm is used.