Narrow Results

In 1995 I introduced the idea of intervening duality with the context of matching pennies games between two persons. I subsequently extended that idea with papers relating first to experimenter-experiment interactions via an intervening — and explicitly specified — die casting experiment and, secondly, to farmer-landowner rent bargaining with intervening weather forecasts modelled as bargaining instruments. The purpose of the present paper is to provide general results which not only specialise to these three previous classes of applications, but which use the idea of strategic equivalence to provide a formal basis for the analysis of large classes of explicitly nonconstant sum bimatrix games, including the prisoners dilemma.

The overexploitation of common pool resources is frequently associated with open access regimes in which each resource user operates independently of all other resource users. The outcome is a Nash equilibrium of the prisoner’s dilemma. Restricted access regimes of the sort identified by Ostrom and colleagues typically ensure that individual resource users do not operate independently. Taking a quantum approach to the theory of games, we argue that the institutional arrangements involved in common pool resource management imply the “entanglement” of the strategies of resource users. For a very simple case — two firms exploiting a common pool fishery — we show that there exists an “entanglement” mechanism that assures the cooperative outcome.