Bounded Rationality with Subjective Evaluations in Enlivened but Truncated Decision Trees

In normative models a decision-maker is usually assumed to be Bayesian rational, and so to maximize subjective expected utility, within a complete and correctly specified decision model. Following the discussion in Hammond (2007) of Schumpeter's (1911, 1934) concept of entrepreneurship, as well as Shackle's (1953) concept of potential surprise, we consider enlivened decision trees whose growth over time cannot be accurately modelled in full detail. An enlivened decision tree involves more severe limitations than a mis-specified model, unforeseen contingencies, or unawareness, all of which are typically modelled with reference to a universal state space large enough to encompass any decision model that an agent may consider. We consider three motivating examples based on: (i) Homer's classic tale of Odysseus and the Sirens; (ii) a two-period linear-quadratic model of portfolio choice; (iii) the game of Chess. Though our novel framework transcends standard notions of risk or uncertainty, for finite decision trees that may be truncated because of bounded rationality, an extended form of Bayesian rationality is still possible, with real-valued subjective evaluations instead of consequences attached to some terminal nodes. Moreover, these subjective evaluations underlie, for example, the kind of Monte Carlo tree search algorithm used by recent chess-playing software packages.