The Evolution of Algorithmic Learning Rules: A Global Stability Result

This paper consider the dynamic evolution of algorithmic (recursive) learning rules in a normal form game. It is shown that the system - the population frequencies - is globally stable for any arbitrary N-player normal form game, if the evolutionary process is algorithmic and the `birth process' guarantees that an appropriate set of `smart' rules is present in the population. The result is independent of the nature of the evolutionary process; in particular it does not require the dynamics of the system to be `monotonic in payoffs' - those rules which do better in terms of payoffs grow faster than those who do less well. The paper also demonstrates that any limit point of the distribution of actions in such an evolutionary process corresponds to a Nash equilibrium (pure or mixed) of the underlying game if the dynamics of the system are continuous and monotonic in payoffs.