Dynamic consistency in games without expected utility

Within dynamic games we are interested in conditions on the players' preferences that imply dynamic consistency and the existence of sequentially optimal strategies. The latter means that the strategy is optimal at each of the player's information sets, given his beliefs there. To explore these properties we assume, following Gilboa and Schmeidler (2003) and Perea (2025a), that every player holds a conditional preference relation – a mapping that assigns to every probabilistic belief about the opponents' strategies a preference relation over his own strategies. We identify sets of very basic conditions on the conditional preference relations that guarantee dynamic consistency and the existence of sequentially optimal strategies, respectively. These conditions are implied by, but are much weaker than, assuming expected utility. Moreover, it is shown that non-expected utility is compatible with dynamic consistency and consequentialism in our framework.