Policy Equilibrium and Generalized Metarationalities for Multiple Decision-Maker Conflicts

Abstract

A policy equilibrium is defined, and its properties investigated, for conflicts with more than two decision makers (DMs). A fundamental construction is the metarational tree, which expresses DMs' interactions as sequences of rounds, each consisting of an initial move by the focal DM followed by countermoves by the opponents. Using the metarational tree, the stability definitions of the graph model for conflict resolution can be adapted to apply to policies. These generalized metarational stabilities are shown to generalize Nash, general metarational, and symmetric metarational stabilities. Relationships among generalized metarationalities are derived, as are their connections with policy equilibria. Finally, the refinement that allows only credible moves (moves that are in the immediate interest of the mover) produces a new family of credible generalized metarational stabilities that generalizes the concept of sequential stability in the graph model.