WP 2023-03 Mindshaping, Conditional Games, and the Harsanyi Doctrine
ABSTRACT: Much of the game theory literature concerns mechanisms by which players can infer information about the utilities, beliefs, and strategies of other players based on actions within games and pre-play signals. When game theory is applied to strategic interactions among people, such analysis interprets them as trying to “mindread”. Recent work in cognitive science, however, suggests that human coordination rests more centrally and necessarily on “mindshaping” processes, in which people resolve equivocal preference content jointly. This kind of process cannot be modeled using standard resources of game theory. However, as mindshaping is strategic, there is motivation to widen the game theory toolkit to accommodate it. Conditional Game Theory is a strategic theory of mindshaping. We show how it can be used to help players of standard games identify correlated equilibrium, and thus solve games. We then extend CGT to address a challenge to the relevance of correlated equilibrium to empirical choice data. This is based on the fact that correlated equilibrium requires the Harsanyi Doctrine, according to which Bayesian players share common priors; but the majority of observed empirical choice behavior under risk violates this Doctrine. We show how pre-play analysis using CGT can reconcile the Harsanyi Doctrine with rank-dependent choice as typically seen in economic experiments.