Blind FBA: Game Theory and Implications

Introduction

Frequent batch auctions clear every market participant in discrete batches at the same price, the one where there is the most overlapping volume.

Synchronicity Exchange implements Blind Frequent Batch Auctions (BFBA), meaning that individual orders are never published. The only information that is made public is the clearing price, clearing volume and liquidation volume in each batch, and the aggregate order book after the clearance.

BFBA creates the optimal game theory for traders to get the best possible price every trade because it creates the Nash equilibrium  for traders and clears orders in batches at the Walrasian (competitive) equilibrium .

For a full explanation of how Synchronicity implements frequent batch auctions, see Blind FBA: Implementation.

Creating the Nash Equilibrium

A Nash equilibrium is where no player can benefit by changing only their own strategy while the other players keep their strategies unchanged.

With FBA, liquidity providers are naturally rewarded for placing competitive bids and protected from over-bidding because their orders often fill at prices better than the limit price they set.

For example, consider BFBA Case 1.1 below. The buy volume exceeds the ask volume at intersection, resulting in a clearance at $107, $2 better than the price the best ask quoted, thus providing an effective rebate for sellers who quoted below the clearing price. This is in stark contrast with continuous clearing mechanisms where makers always clear at the price they quote.

The effective rebate can be calculated as follows.

• A buyer who bid above the clearing price (P*) was willing to pay more than the price they paid, so they got an effective rebate equal to bid - P*.

• A seller who offered below P* was willing to accept less than what they received, so they got an effective rebate equal to P* - ask.

The absence of information about what other market participants are bidding combined with the fact that if a participant overbids relative to the clearance price in a batch, they don’t actually overpay, means that the optimal behavior for every market participant is to make their best offer.

Thus, BFBA creates the Nash Equilibrium for market participants.

Clearing at the Walrasian Equilibrium

A Walrasian (a.k.a., competitive) equilibrium is where supply and demand are balanced across all markets simultaneously. The optimal market should clear at the Walrasian equilibrium. BFBA naturally does so.

Thus, by creating the Nash equilibrium for traders to place their best offers, and then clearing everyone at the Walrasian equilibrium, BFBA creates the optimal conditions for the tightest spreads, deepest liquidity and best fills possible.