THE EVOLUTION OF ALGORITHMIC LEARNING RULES: A Global Stability Result

This paper considers 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 in any way the dynamics of the system to be `monotonic in payo s' | those rules which do better in terms of payo s 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 payo s. JEL Classification: C70, C72, C79, D83.