Deciding to Disclose: A Decision Theoretic Agent Model of Pregnancy and Alcohol Misuse

Abstract

We draw together methodologies from game theory, agent based modelling, decision theory, and uncertainty analysis to explore the process of decision making in the context of pregnant women disclosing their drinking behaviour to their midwives. We employ a game theoretic framework to define a signalling game. The game represents a scenario where pregnant women decide the extent to which they disclose their drinking behaviours to their midwives, and midwives employ the information provided to decide whether to refer their patients for costly specialist treatment. This game is then recast as two games played against “nature”, to permit the use of a decision theoretic approach where both classes of agent use simple rules to decide their moves. Four decision rules are explored – a lexicographic heuristic which considers only the link between moves and payoffs, a Bayesian risk minimisation agent that uses the same information, a more complex Bayesian risk minimiser with full access to the structure of the decision problem, and a Cumulative Prospect Theory (CPT) rule. In simulation, we recreate two key qualitative trends described in the midwifery literature for all the decision models, and investigate the impact of introducing a simple form of social learning within agent groups. Finally a global sensitivity analysis using Gaussian Emulation Machines (GEMs) is conducted, to compare the response surfaces of the different decision rules in the game.