Experiments of openBarter

For a first introduction to the barter market place follow the link openBarter.

ω is the ratio between the quantity provided and the quantity received. This ratio is expected by an order and produced by movements of exchange cycles.

Results presented were obtained to observe variations of foor indicators for different size of the order book:

• the mean execution time of an order (delay),
• the mean number of movements per cycle (nbcycle),
• fluidity of the market that is a measurement of it's capacity to drain values out of the order book (fluidity),
• the ratio between ω produced by movements and ω expected by the corresponding order, measuring the profit made by the transaction (gain).

Results presented here were produced by version 7.0.1 of openBarter instrumented for the purpose of the simulation.

Experimentation protocol

The order book is filled with N barter limit orders where ω is chosen randomly using a continuous uniform distribution between 0.5 and 1.5, and where the quantity provided is 10 000. The protocol used to explore different size of the book is the following:

A large external order book is created with the desired statistic. For each book size, the beginning of this external book is chosen to be the set of pending orders of the real order book of the given size. The table of movements is cleared. A set of barter limit orders is submitted to the book. The number of elements of this set is (S). Results presented are means of results obtained.

Constants defined by openbarter to limit computation load are:

• The maximum number of movement per cycle (Y),
• The maximum number of movement per transaction, since a transaction can wrap several cycles (M),
• The maximum number of cycle explored (P).

The fluidity of the market is defined as the ratio between the output flow of values produced by movements and the input flow of values offered by orders submitted to the order book. Flows of value are obtained by summing quantities of values for all qualities. The input flow is 10 000 (qtt_prov) * 1000 orders = 10 000 000, and the output flow is the sum of quantities brought by movements.

regular and barter market compared

An attempt is made to simulate the behaviour of a regular market with openbarter with the scenario money. It considers a special quality used by all orders, as on a regular order book where a sell order asks for € and a buy order offers €. The quality that is not € is chosen randomly with a uniform distribution between 99 other qualities. Cycles are limited to two partners with Y=2.

A second scenario 1e2uni is made of barter orders where the diversity of quality is 100 with a uniform distribution.

For the 1e2uni scenario, S=100,Y=64,P=1024*10,M=128; and for money scenario , S=100,Y=2,P=1024*10,M=128.

When no movement is produced, values are 0 and should not be considered. These measurements leads to the following comments:

• Fluidity is far better with 1e2uni than with the money scenario especially for low book volumes.
• The computation of the 1e2uni scenario is more expensive, but tend to decrease with the volume of the book.
• Larger cycles explored by the 1e2uni scenario give more gain and cooperation opportunities than for the money scenario.

A previous attempt of regular market simulation was made with Y=64, but produced non-bilateral cycles, showing that the regular market simulation was inaccurate. Cycles was found with four partners A,B,C,D exchanging qualities Q1,Q2,€ where A provides Q1 to B, B provides € to C, C provides Q2 to D and D provides € to A. This cycle should be better for partners than two separate bilateral cycles or was the single exchange possibility.

The better fluidity of the 1e2uni scenario can be explained by the fact that a single order brings both request and demand, while in the money scenario, an order just brings one of them. That's why the percolation threasold is reached by barter before the money scenario.

Large order book

This simulation was made to explore large order books with a diversity of quality of 10000 using a uniform distribution.

For this scenario, S=100,Y=64,P=1024*10,M=128.

These measurements leads to the following comments:

• The response time is low (between 130 and 160 ms) and independent of the volume.
• The fluidity is rapidly more than 1 after the percolation threasold, and gain and fluidity are stable afterward.
• The number of movements per cycle is high for low book volumes.

Diversity of qualities with uniform distributions

Different diversity of qualities are considered (100,1000 and 10000) noted (1e2,1e3,1e4) with uniform distributions.

Results was obtained with Y=64, P=1024*10 and a set of 100 orders (S=100) to show the percolation threasold when the volume of the book increases.

These measurements leads to the following comments:

• The fluidity of the market increases when de diversity decreases.
• Greater gain reveals higher competition for low diversity of qualities.
• The number of partners in cycles is large when the volume of the book is near a threasold depending on the diversity of qualities.

Diversity of qualities with non uniform distributions

Different diversity of qualities are considered (100,1000 and 10000) noted (1e2,1e3,1e4) with a beta distribution (alpha=2.0,beta=5.0) in order to simulate the fact that few qualities are used far more frequently that others. This beta distribution has a mean=0.29 and a variance=0.03.

Results was obtained with Y=64, P=1024*10 and a set of 100 orders.

These measurements leads to the following comments:

• Percolation threasolds remains even with a non uniform distribution,
• The threasold appears for lower volumes of the order book when compared to that of a uniform distribution.

Sensibility of limits

Different limits were used:

• X1: Y=64 P=1024*5 M=128
• X2: Y=32 P=1024*10 M=128
• X3: Y=64 P=1024*10 M=128
• X4: Y=64 P=1024*10 M=128*2

These measurements leads to the following comments:

• The execution time is sensible to P but not significantly dependant on other factors.
• Fluidity is slightly improved by P, but is independant of other limits.
• The number of movements per cycle is usually less than 16. Larger Y allow more exchanges with a small book size.
• The gain is always better than 1 due to the order type (LIMIT). The gain grows as the size of the book due to competition increase.

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