Design of Social Agents - Foundations on Natural and Artificial Computation - page 196

depends on the length of the interaction. In particular it is meter if the conver-
gence is reached and, if is the case, at which phased of the periodic patter the
interaction is stopped. To get a representative performance of an agent we have
to make sure that the interaction between the agents is long enough to suppress
the dependency of the performance on the length of the interaction.
The performance of two agents can also depend on which agent started the
interaction first. To deal with this ambiguity, for any pair of agents we run two
sequences of interaction such that every agent starts one sequence.
For 29 agents we run the interactions containing 1000 steps. We found out
that for all considered agents the difference between the performances on the
step 999 and 1000 do not exceed 1 . 58 10 − 3 . This number is small in comparison
with the variation of the performances of different agents, indicating that 1000
steps are sucient to reach the convergence. Further on we will use this number
of games to calculate performance of agents, unless otherwise stated.
The performance of an agent also depends on the partner. Moreover, even
if agent A outperforms agent B while both playing with partner C it is still
possibe and agent A underperforms B while both playing with another partner
D . To get a representative performance of an agent we create a larger pool of
random partners and let the agent to play with every partner from the pool.
Then the performances of the agent with different partners are averaged to get
the representative performance. In our study we populated the pool by agents
that have no more than 12 internal states. The probability of an agent to be in
the pool does not depend on the number of internal states.
We chose the size of the pool of partners in the following way. For a given
random agent we have generated 10 different pools of the same size. Every pool
has been used to calculate the performance of the given agent and then the
difference between the maximal and minimal performance was calculated. If
this difference was larger than 0.1 we double the size of the pool and repeat
the same calculations. We start the procedure from the minimal possible pools
containing only one partner and grow the pool in the above described way until
the difference between the minimal and maximal performances of the considered
agent is smaller than 0 . 1. The above procedure has been performed for 7 different
random agents. We found out that for the all considered agents the range of the
performances became smaller than 0.1 with the pool containing less than 10
thousands agents. Further on pools containing 10 thousands agents are used,
unless otherwise stated.
We used the above given values for the length of the interaction and the size of
the pool to estimate the performance of the constructed social agent. We found
out that the score per game for this agent is equal to approximately 3.16. To
get an idea of how good this performance is we have calculated performances
of 4855 randomly generated agents. The distribution of the performances of
these agents is shown in the Fig.2. As we can see in the figure, the constructed
social agent outperform majority of randomly generated agents. In more details,
approximately 97.8 % of random agents were outperformed by the constructed
agent.