Stability definitions for describing human behavior under conflict when coalitions may form are generalized within the Graph Model for Conflict Resolution and algebraic formulations of these definitions are provided to allow computer implementation. The more general definitions of coalitional stabilities relax the assumption of transitive graphs capturing movements under the control of decision makers, either independently or cooperatively, and allow the convenient expansion to the case of coalitions of the four basic individual stabilities consisting of Nash stability, general metarationality, symmetric (...) metarationality, and sequential stability. To permit the various coalitional stabilities to be efficiently calculated and conveniently encoded within a decision support system, algebraic expressions for the coalitional stabilities are provided in this research. Furthermore, a range of the theorems establish the mathematical credibility of employing the innovative algebraic approach to conflict resolution when coalitions are present. Finally, a conflict over the proposed exportation of bulk water from Lake Gisborne within the Canadian Province of Newfoundland and Labrador is modelled and analyzed to illustrate the practical application of the different coalitional stabilities and the strategic insights they provide. (shrink)

A hybrid preference framework is proposed for strategic conflict analysis to integrate preference strength and preference uncertainty into the paradigm of the graph model for conflict resolution (GMCR) under multiple decision makers. This structure offers decision makers a more flexible mechanism for preference expression, which can include strong or mild preference of one state or scenario over another, as well as equal preference. In addition, preference between two states can be uncertain. The result is a preference framework that is more (...) general than existing models which consider preference strength and preference uncertainty separately. Within the hybrid preference structure, four kinds of stability are defined as solution concepts and a post-stability analysis, called status quo analysis, which can be used to track the evolution of a given conflict. Algorithms are provided for implementing the key inputs of stability analysis and status quo analysis within the extended preference structure. The new stability concepts under the hybrid preference structure can be used to model complex strategic conflicts arising in practical applications, and can provide new insights for the conflicts. The method is illustrated using the conflict over proposed bulk water exports from Lake Gisborne in Newfoundland, Canada. (shrink)

1. Introduction The policy of deterrence, at least to avert nuclear war between the superpowers, has been a controversial one. The main controversy arises from the threat of each side to visit destruction on the other in response to an initial attack. This threat would seem irrational if carrying it out would lead to a nuclear holocaust – the worst outcome for both sides. Instead, it would seem better for the side attacked to suffer some destruction rather than to retaliate (...) in kind and, in the process of devastating the other side, seal its own doom in an all-out nuclear exchange. Yet, the superpowers persist in their adherence to deterrence, by which we mean a policy of threatening to retaliate to an attack by the other side in order to deter such an attack in the first place. To be sure, nuclear doctrine for implementing deterrence has evolved over the years, with such appellations as “massive retaliation,” “flexible response,” “mutual assured destruction”, and “counterforce” giving some flavor of the changes in United States strategic thinking. All such doctrines, however, entail some kind of response to a Soviet nuclear attack. They are operationalized in terms of preselected targets to be hit, depending on the perceived nature and magnitude of the attack. Thus, whether U.S. strategic policy at any time stresses a retaliatory attack on cities and industrial centers or on weapons systems and armed forces, the certainty of a response of some kind to an attack is not the issue. (shrink)

This paper proposes a revised Theory of Moves (TOM) to analyze matrix games between two players when payoffs are given as ordinals. The games are analyzed when a given player i must make the first move, when there is a finite limit n on the total number of moves, and when the game starts at a given initial state S. Games end when either both players pass in succession or else a total of n moves have been made. Studies are (...) made of the influence of i, n, and S on the outcomes. It is proved that these outcomes ultimately become periodic in n and therefore exhibit long-term predictable behavior. Efficient algorithms are given to calculate these ultimate outcomes by computer. Frequently the ultimate outcomes are independent of i, S, and n when n is sufficiently large; in this situation this common ultimate outcome is proved to be Pareto-optimal. The use of ultimate outcomes gives rise to a concept of stable points, which are analogous to Nash equilibria but consider long-term effects. If the initial state is a stable point, then no player has an incentive to move from that state, under the assumption that any initial move could be followed by a long series of moves and countermoves. The concept may be broadened to that of a stable set. It is proved that every game has a minimal stable set, and any two distinct minimal stable sets are disjoint. Comparisons are made with the results of standard TOM. (shrink)

A new approach to policy analysis is formulated within the framework of the graph model for conflict resolution. A policy is defined as a plan of action for a decision maker (DM) that specifies the DM’s intended action starting at every possible state in a graph model of a conflict. Given a profile of policies, a Policy Stable State (PSS) is a state that no DM moves away from (according to its policy), and such that no DM would prefer to (...) change its policy given the policies of the other DMs. The profile of policies associated to a PSS is called a Policy Equilibrium. Properties of PSSs are developed, and a refinement is suggested that restricts DMs to policies that are credible in that they are in the DM’s immediate interest. Relationships with existing stability definitions in the graph model for conflict resolution are then explored. (shrink)