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We study fragmentation of equity trading using a model of imperfect competition among exchanges. In the model, increased competition drives down trading fees. However, additional arbitrage opportunities arise in fragmented markets, intensifying adverse selection. Due to these opposing forces, the effects of fragmentation are context-dependent. To empirically investigate the ambiguity in a single context, we estimate key parameters of the model with order-level data for an Australian security. At the estimates, the benets of increased competition are outweighed by the costs of multi-venue arbitrage. Compared to the prevailing duopoly, we predict the counterfactual monopoly spread to be 23% lower.