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Supply and demand


A matching engine for double auctions.

This program takes buy and sell (limit) orders, finds the market-clearing price and quantity and returns the remaining order book. This program is currently able of finding the equilibrium of hundreds of millions of orders in seconds.

Compile using


Usage and important notes

Run the program using ./doubleauction. If you add a filename as an argument, the order book will be read from that file. If you do not supply an argument, the order book is read from stdin.

Each order is a line like this:

B 100 15 71 5

The first field is either B or S, indicating whether it is a buy or sell order. The second field is the bid/ask. The third field is the corresponding quantity. The fourth field is the order ID: It is not directly used, but if you use doubleauction in conjunction with another program, this allows you to keep track of what happens with your order. The fifth field is the priority of the order. Importantly, a lower number here indicates higher priority. This means that if your order has the same bid/ask as another, but your order has a higher priority, your order will be fulfilled first. If you put in 0 as the priority, we set the priority to nanoseconds since Unix epoch, earlier arrival still implying preferred fulfillment.

The type of the second and third field are determined by you in the source code (currently uint64_t and int64_t, respectively). Please note the rampant difficulties that arise when using floating-point arithmetic, and consider avoiding the corresponding types. Also note that for computational reasons, quantites may become negative, while prices are always nonnegative. The type of the fourth and fifth field are always uint64_t.

After reading the order book, doubleauction will attempt to find a market equilibrium. If one is found, the market sides transact accordingly and fulfilled orders are deleted or altered (if there is only partial fulfillment). Thereafter, the resulting order book is output to stdout and some other information is output to stderr. (Thus, theoretically, you can pipe several instances of doubleauction together -- and if my code is correct, no equilibrium should ever be found after the first stage.)

This program asserts feasibility (i.e. individual rationality when transacting at some price) and approximate optimality (i.e. there is no higher feasible quantity) and aborts if they are not met. If quantity is integral, the optimality check is exact. Still, there is no guarantee and use of this program is entirely without warranty.

Example markets

Some example order books are supplied in the directory markets/.

For example, the market in the above graphic is available in markets/example.mkt. Running ./doubleauction markets/example.mkt gives the equilibrium. Visual inspection confirms that the market-clearing price is between p = 58 and p = 59, with quantity q = 697. Any higher quantity leads to a contradiction (not individually rational/feasible). If there is a range of feasible prices, we use split-the-difference. (Note, however, that the effectiveness of split-the-difference may be constrained by integral types. Thus, I suggest you run this example both with integral and floating-point types; see lines 37, 38 in main.cpp.)

There is also an example that does not have an equilibrium, markets/noeq.mkt.

There is also a script to generate markets, etc/genmkt.php and a script to plot curves like the above, etc/graph.R. Sadly, the latter still contains some bugs that will likely not be fixed.

doubleauction has been tested with up to 200 million orders (approximately half of which were buy orders). In this case, the correct equilibrium was found after 71 seconds.


This software is licensed under the GNU Affero General Public License v3.0. Any acknowledgment of use in academic research is appreciated but not technically required.


  • implement Nasdaq OUCH. This also implies:
    • market orders
    • immediate or cancel orders
    • proper messaging (to keep track of what happened to every order)
    • order deletion
  • parallelization?
  • implement the BCS FBA
  • more testing


A matching engine for double auctions




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