Preference at First Sight

We consider decision-making and game scenarios in which an agent is limited by his/her computational ability to foresee all the available moves towards the future – that is, we study scenarios with short sight. We focus on how short sight affects the logical properties of decision making in multi-agent settings. We start with single-agent sequential decision making (SSDM) processes, modeling them by a new structure of ‘preference-sight trees’. Using this model, we first explore the relation between a new natural solution concept of Sight-Compatible Backward Induction (SCBI) and the histories produced by classical Backward Induction (BI). In particular, we find necessary and sufficient conditions for the two analyses to be equivalent. Next, we study whether larger sight always contributes to better outcomes. Then we develop a simple logical special-purpose language to formally express some key properties of our preference-sight models. Lastly, we show how shortsight SSDM scenarios call for substantial enrichments of existing fixed-point logics that have been developed for the classical BI solution concept. We also discuss changes in earlier modal logics expressing ‘surface reasoning’ about best actions in the presence of short sight. Our analysis may point the way to logical and computational analysis of more realistic game models.