Dynamic Logic for Ungrounded Payoffs

Higher-order likes and desires sometimes lead agents to have ungrounded or paradoxical preferences. This situation is particularly problematic in the context of games. If payoffs are interdependent, the overall assessment of particular courses of action becomes ungrounded; in such cases, the game’s matrix is radically underdetermined. Paradigmatic examples of this phenomenon occur when players are ‘perfect lovers’ or ‘perfect haters’, in a sense to be explained. In this paper, I use a dynamic doxastic logic to mimic the search for a suitable matrix. Upgrades are triggered by conjectures about other players’ utilities, which can, in turn, be based on behavioural or verbal cues. We can prove that, under certain conditions, pairs of agents with paradoxical preferences eventually come to believe they cannot interact in a game. As a result, I hope to provide a better understanding of game-theoretic ungroundedness and, more generally, of the structure of higher-order preferences and desires.