Fitness Function

Defining an appropriate fitness measure to rank our agents has proven difficult. In principle we defined a variant of fitness sharing [8] by giving points for doing better than average against a human player, and negative points for doing worse than average. The fitness of agent a was defined as:

$$F(a)=\sum _{\{h:p(h,a)>0\}}\left( \frac{s(h,a)}{p(h,a)}-\frac{s(h)}{p(h)}\right) \left( 1-e^{\frac{p(h)}{10}}\right)$$ (3.1)

where s(h,a) is the number of games lost minus the number of games won (score) by a human opponent h against a; p(h,a) is the total number of games between the two; s(h) is the total score of h; and p(h) is the number of games that h has played. All games played are counted, not just those that belong to the current generation. The factor is a confidence measure that devalues the average scores obtained against humans who have played only a small number of games.

A second part of the experiment assayed a new definition of fitness, based on our statistical analysis of players' strengths. This problem is discussed in detail in section 3.6.