Rationalizable Foresight Dynamics: Evolution and Rationalizability

This paper considers a dynamic situation where rationality is common knowledge among infinitesimal agents, but beliefs may not be coordinated with each other. A rationalizable foresight path is a feasible path of behavior pattern along which every agent takes a strategy that maximizes his expected discounted payoff against another path which is in turn a rationalizable foresight path. A strategy distribution is accessible from another distribution under rationalizable foresight if there exists a rationalizable foresight path from the latter to the former. A strategy distribution is said to be a stable state under rationalizable foresight if no rationalizable foresight path departs from the distribution. A set of strategy distributions is said to be a stable set under rationalizable foresight if it is closed under accessibility. Stable sets under rationalizable foresight always exist. These concepts are compared with the corresponding concepts under perfect foresight. Every stable state under rationalizable foresight is shown to be stable under perfect foresight. But the converse is not true. An example is provided to illustrate that stability under rationalizable foresight gives a sharper prediction than that under perfect foresight.

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