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From Competition to Cooperation: Co-evolution In A Rewards Continuum

Submitted to CIG 12

### Daniel Ashlock, Wendy Ashlock, Spyridon Samothrakis, Simon Lucas, and Colin Lee

In this study the hypothesis that zero-sum (i.e strictly
competitive) games are more difficult targets for co-evolution than
non-zero-sum (i.e. games that are not strictly competitive nor
strictly cooperative) games is examined. Our method is to compare the
co-evolutionary behavior of a three move zero-sum game (rock paper
scissors) with that of a three move non-zero-sum game (coordination
prisoner's dilemma) as well as with intermediate games obtained using
weighted averages of the games's payoff matrices. The games are
compared by examining the way use of moves evolves, by using
transitivity measures on evolved agents, by estimating the complexity
of the agents and by checking for non-local adaptation. Two different
agent representations, finite state machines with 8 and 64 states, are
used. Unexpectedly, these two representations are found to have large,
qualitative differences. The results support the hypothesis that
co-evolving good strategies for zero-sum games is more difficult than
for non-zero-sum games. Many of the measurements used to compare
different games are found to exhibit a nonlinear responses to the
change in payoff matrix.