Example Application of the b-Core: Buyer Coalition Problem with Beliefs - Belief-based Stability in Coalition Formation with Uncertainty - page 138

5.4 Experiment

We illustrate the concepts by conducting a two-part experiment to test
the performance of the distributed buyer coalition mechanism.
In part one, we first demonstrate that the mechanism is a stable
one, according to the criteria of the core, b-core and Pareto optimality,
no matter which of the b-strategy and nb-strategy is employed by
the agents, and we also check the scalability of the mechanism by
studying the number of messages sent in larger games, particularly,
for the belief-based mechanism. This way, we see that the mechanism
can achieve its goal, provided that the assumed strategy is incentive
compatible.
In part two of the experiment, we will provide evidences that our
mechanism is incentive compatible by showing our proposed strategy
is the best one to follow, among a number of reasonable approaches.

5.4.1 Performance of the Mechanism

In the first part of the experiment, we randomly generate a series of
scenarios with the number of agents ranging from four to ten. There
are three products on sale, and in each test case, the preferences of
each agent are randomly ordered, with the restriction that, among the
possible bids for the same products, a bid from a larger coalition is
always preferred to a bid from a smaller coalition, that is, we assume
( g i ,s 1 )

a ( g i ,s 2 ) for any given agent a if s 1 >s 2 ,otherwise,the
preferences are randomly ordered.
In each case, three agent compositions are tested: first with all
agents being b-agents, than with all agents being nb-agents, and finally
with an equal mix of b-agents and nb-agents. The belief accuracy of
the b-agents are set at 80%, meaning that for any two agents i and j
and any two bids b 1 and b 2 , there is a probability of 0 . 2 that agent i is