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See Proposition 6 on pg. 1600. The argument is purely economic and based on a simplified (but first-order reasonable) model of liquidity provisioning and price action. Price-priority uniform clearing price batch auctions (with or without randomized call times) transform competition over speed into competition over price.

Technical/practitioner notes:

1. Gaming is a bit of an overloaded term, and in this context, implies that agents are doing something wrong. Mechanism design assumes that agents will respond rationally and strategically to the mechanism they're presented with, so whatever happens is on the designer. Ideally, the mechanism chosen will result in an individual response that collectively optimize the designer's objective function, e.g., maximizing social welfare or the auctioneer revenues. Suppose the mechanism chosen isn't the "best" one for a specific set of agents & goods. In that case, agents might have individually rational behaviors that result in sub-optimal outcomes relative to what was achievable with another mechanism.

2. Prop 6 isn't entirely predicated on having a random call time (there will be competition over price as long as there are two "fast" types in the market). However, randomizing auction call times is still practically speaking useful.