Constrained games, intervening duality and experimenter–experiment interactions

In a previous paper I introduced the idea of intervening duality with a context of coin tossing games. In this paper I focus first on framing related specification issues in general and then on a class of intervening duality problems which model learning related interactions between an experimenter and a subject via an intervening die casting game. In this context it is easy to see how this particular game, which was considered by Howard to illustrate potential for Allais-like paradoxical outcomes, is potentially consistent with individually rational experimental behaviours. By specializing the example to a more restrictively framed class of relatively packed high–low games, I show how the intervening duality approach can provide straightforward motivations for the hypothesis by Tversky and Kahneman and others, that subjects' perceptions of probabilities relative to relatively packed outcomes will be weakly superadditive, if relatively favourable, and weakly subadditive if relatively unfavourable. Finally I use generalized strategic equivalence ideas both to introduce and analyse tracer games, which might rationally serve to formulate a game prior to subsequent play with payoffs of a higher order, and to generalize all of the preceding analyses and results to nonconstant sum payoff cases.