This paper models the indirect evolution of the preferences of a population of fully rational agents repeatedly matched to play a symmetric 2 x 2 game in biological fitnesses. Each agent is biased in favor of one of the strategies, and receives a noisy signal of his and his opponent`s bias. With sufficiently accurate signals, the resulting global game selects a unique outcome, allowing preference biases to be shaped by the replicator dynamics. Stability analysis in this setting requires the extension of recent techniques for evolution on infinite strategy spaces, introducing new setwise stability concepts. In coordination games, the interval of preference biases supporting the Pareto-dominant equilibrium is Lyapunov stable and weakly attracting, by virtue of constituting a "strongly uninvadable set". In Prisoners` Dilemmas that satisfy Kandori and Rob`s (Games and Economic Behavior 22, 1998, 30-60) "marginal bandwagon property", meanwhile, an interval of biases supporting efficient cooperation is a "neutrally uninvadable set", and thus Lyapunov stable.
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