Weak isomorphism of extensive games

Abstract

Based on the Selten [Mathematical Social Sciences 5 (1983) 269] and Oh [Three Essays on Equilibrium Selection in Games, PhD Thesis, (1995) Graduate College of The University of Iowa] symmetries, we introduce weak isomorphism of extensive games that, in contrast to the Peleg et al. [The canonical extensive form of a game form: Symmetries. In: Alkan, A., Aliprantis, C., Yannelis, N. (Eds.), Current Trends in Economics: Theory and Applications, Springer, (1999) pp. 367–387] isomorphism, is compatible with the traditional extensive representation of strategic games. While being sufficiently ‘weak’ to ignore the order of moves to some extent, weak isomorphism is ‘strong’ enough not to violate sequential rationality considerations as incorporated in the concept of sequential equilibrium. In addition, there is some generic equivalence between weak isomorphism and isomorphism of the agent normal form.