Combining strength and uncertainty for preferences in the graph model for conflict resolution with multiple decision makers

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.     

Policy Stable States in the Graph Model for Conflict Resolution

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.     

Equilibrium and potential in coalitional congestion games

The model of congestion games is widely used to analyze games related to traffic and communication. A central property of these games is that they are potential games and hence posses a pure Nash equilibrium. In reality, it is often the case that some players cooperatively decide on their joint action in order to maximize the coalition’s total utility. This is modeled by Coalitional Congestion Games. Typical settings include truck drivers who work for the same shipping company, or routers that belong to the same ISP. The formation of coalitions will typically imply that the resulting coalitional congestion game will no longer posses a pure Nash equilibrium. In this paper, we provide conditions under which such games are potential games and posses a pure Nash equilibrium.     

On The Meaning Of Owen–Banzhaf Coalitional Value In Voting Situations

In this paper we discuss the meaning of Owen's coalitional extension of the Banzhaf index in the context of voting situations. It is discussed the possibility of accommodating this index within the following model: in order to evaluate the likelihood of a voter to be crucial in making a decision by means of a voting rule a second input (apart from the rule itself) is necessary: an estimate of the probability of different vote configurations. It is shown how Owen's coalitional extension can be seen as three different normative variations of this model.     

A note on the information content of a consistent pairwise comparison judgment matrix of an AHP decision maker

A decision maker using the Analytic Hierarchy Process (AHP) could be consistent, and still provide no information in the resulting vector of priorities. An extreme example would be a pairwise comparison judgment matrix filled with 1s which is totally consistent under the various definitions of consistency, but has provided no information about the prioritization of alternatives resulting from the decision maker's judgments. In this paper, the quality of a consistent decision maker's judgments using the Analytic Hierarchy Process is placed in the context of the entropy of the resulting vector of priorities. Indeed, it is the purpose of this paper to provide a formal definition of this notion ofentropy of a priority vector, and to provide a framework for a quantitative measurement of the information content of consistent pairwise comparison judgment matrices of a decision maker who is using the Analytic Hierarchy Process. We will prove that the entropy of the vector of priorities for consistent matrices follows a normal distribution and discuss some general considerations of this result.     

Mechanism robustness in multilateral bargaining

This paper discusses the relationship between coalitional stability and the robustness of bargaining outcomes to the bargaining procedure. We consider a class of bargaining procedures described by extensive form games, where payoff opportunities are given by a characteristic function (cooperative) game. The extensive form games differ on the probability distribution assigned to chance moves which determine the order in which players take actions. One way to define mechanism robustness is in terms of the property of no first mover advantage. An equilibrium is mechanism robust if for each member the expected payoff before and after being called to propose is the same. Alternatively one can define mechanism robustness as a property of equilibrium outcomes. An outcome is said to be mechanism robust if it is supported by some equilibrium in all the extensive form games (mechanisms) within our class. We show that both definitions of mechanism robustness provide an interesting characterization of the core of the underlying cooperative game.     

Coalitional stability and efficiency of partitions in matching problems

?zkal-Sanver (Theory Decis 59:193–205, 2005) studies stability and efficiency of partitions of agents in two-sided matching markets in which agents can form partitions by individual moves only, and a matching rule determines the matching in each coalition in a partition. In this study, we present the relationship between stability and efficiency of partitions that is analyzed for several matching rules and under various membership property rights codes, now allowing coalitional moves.     

Decision,irreversibility and flexibility: The irreversibility effect re-examined

In a seminal article C. Henry (1974) presented the irreversibility effect, which pointed out that under uncertainty, the optimal sequence of decisions depends on not only the payoffs, but also the flexibility, in terms of availability of future options, associated with each decision. But the irreversibility effect pertained to certain particular conditions and definitions. In this paper, a more general model is developed to re-examine the notion of an irreversible decision, its relation with flexibility and the irreversibility effect. It is shown through two propositions that the irreversibility effect need not hold always and the notion of irreversibiity can be used only under certain circumstances to derive the optimal sequence of decisions ex-ante.     

Olson VS. Coase: Coalitional Worth in Conflict

We analyze a model of conflict with endogenous choice of effort, where subsets of the contenders may force the resolution to be sequential: First the alliance fights it out with the rest and – in case they win – later they fight it out among themselves. For three-player games, we find that it will not be in the interest of any two of them to form an alliance. We obtain this result under two different scenarios: equidistant preferences with varying relative strengths, and varying vicinity of preferences with equal distribution of power. We conclude that the commonly made assumption of super-additive coalitional worth is suspect.     

Monotonicity of power in games with a priori unions

Power indices are commonly required to assign at least as much power to a player endowed with some given voting weight as to any player of the same game with smaller weight. This local monotonicity and a related global property however are frequently and for good reasons violated when indices take account of a priori unions amongst subsets of players (reflecting, e.g., ideological proximity). This paper introduces adaptations of the conventional monotonicity notions that are suitable for voting games with an exogenous coalition structure. A taxonomy of old and new monotonicity concepts is provided, and different coalitional versions of the Banzhaf and Shapley–Shubik power indices are compared accordingly.      

Teacher–Child Relationships from Kindergarten to Sixth Grade: Early Childhood Predictors of Teacher-perceived Conflict and Closeness

This article examined general trends in teacher-reported conflict and closeness among 878 children from kindergarten through sixth grade, and examined early childhood characteristics that predict differences in initial levels and growth of conflict and closeness over time. Results indicated modest stability of teacher-perceived conflict and closeness through sixth grade, with relatively greater stability in perceptions of conflict. Levels of conflict at kindergarten were higher for children who were male, Black, had greater mean hours of childcare, had lower academic achievement scores, and had greater externalizing behavior. Children identified as Black and those with less sensitive mothers were at greater risk for increased conflict with teachers over time. Levels of teacher-reported closeness were lower when children were male, had lower quality home environments, and had lower academic achievement scores. The gap in closeness ratings between males and females increased in the middle elementary school years. Additional analyses were conduced to explore differences in teacher ratings of conflict between Black and White students.     

A taxonomy of all ordinal 2 × 2 games

The 2 × 2 game is the simplest and most commonly employed representation of strategic conflict. The 78 strict ordinal 2 × 2 games have been used as conflict models extensively, and have been related in several different taxonomies. However, interest has recently focussed on the full set of 726 general ordinal games, in which one or both players may have equal preferences for two or more outcomes. This paper describes the development of a practical taxonomy of all 726 ordinal 2 × 2 games. The taxonomy provides for rapid identification of particular games, gives a convenient ordering, is as consistent as possible with previous work, and yet is not tied to any specific solution concepts. As well, definitions of several significant game properties are developed or extended to general ordinal games and applied in conjunction with the taxonomy.     

Probabilities and beliefs

Choice-theoretic definitions of subjective probabilities originated with the work of Ramsey and de Finetti and attained their definitive form in the work of Savage. These probabilities are intended to provide a numerical representation of a decision maker's beliefs regarding the likely realization of alternative events. In this article, I argue that the choice-theoretic definitions of subjective probabilities involve a tacit convention—namely, state-independent utility functions—that is not implied by the axioms, and, as a consequence, choice-theoretic subjective probabilities, even when they exist, do not necessarily represent the decision makers' beliefs.     

Stability and Efficiency of Partitions in Matching Problems

We define two versions of stability and efficiency of partitions and analyze their relationships for some matching rules. The stability and efficiency of a partition depends on the matching rule φ. The results are stated under various membership property rights axioms. It is shown that in a world where agents can freely exit from and enter coalitions, whenever the matching rule is individually rational and Pareto optimal, the set of φ-stable and φ-efficient partitions coincide and it is unique: the grand coalition. Then we define a weaker version of stability and efficiency, namely specific to a given preference profile and find some negative results for stable matching rules.     

Conflict and Creativity in Groups

Consultants and researchers have long recognized the debilitating effects that conflict between group members can have on both group and individual outcomes . Yet less attention has been paid to the important role that conflict may play in helping generate innovative solutions to ill-structured problems . Furthermore , conflict (properly managed) is critical to the avoidance of groupthink (i . e ., the tendency to sacrifice quality decision making and problem solving for the sake of consensus and conflict avoidance) . What strategies can group members use to incorporate conflict , or more specifically , dissent in group problem solving? We argue that the delivery of dissenting opinions (negative evaluations) affects the extent to which dissent fosters creativity . We report the results of an experiment in which the target of negative evaluations was varied (e . g ., source of an idea vs . idea itself ) and compared to a condition in which no negative evaluations were incorporated . The results show that (1) creativity is higher in the conditions involving idea-targeted negative evaluations than source-targeted or no negative evaluations; (2) negative evaluations from others increase in conditions in which there are source-targeted negative evaluations and idea-targeted negative evaluations , compared to no negative evaluations; and (3) group members report higher levels of satisfaction when working under conditions involving idea-targeted negative evaluations , compared to source-targeted or no negative evaluations . We discuss the implications of this research for organizational settings , with particular attention to how they might inform the design of group decision support systems .     

Effects of Outcome and Probabilistic Ambiguity on Managerial Choices

Information ambiguity is prevalent in organizations and likely influences management decisions. This study examines, given imprecise probabilities and outcomes, how managers make choices when they are provided with single-figure benchmarks. Seventy-nine MBA students completed two experiments. We found that, in a decision framed as a decision under certainty involving an ambiguous outcome, the majority of the subjects were ambiguity prone in the loss condition and switched to ambiguity aversion in the gain condition. However, in the presence of probabilistic ambiguity in a decision under risk, this expected switching pattern was shown only when the difference in riskiness between the two choice options (in the loss condition) was perceived to be relatively small. In a companion study, we used a written protocol approach to identify factors that affect decision makers' investment choices when faced with ambiguous outcomes. Protocols frequently mentioned that the ambiguous outcome option was risky, even in the case which was framed as a decision under certainty in the problem statement. In a decision under risk with ambiguous outcomes, the combination of probabilistic risk and outcome ambiguity was seen as even more risky.     

Simple Collective Identity Functions

A Collective Identity Function (CIF) is a rule which aggregates personal opinions on whether an individual belongs to a certain identity into a social decision. A simple CIF is one which can be expressed in terms of winning coalitions. We characterize simple CIFs and explore various CIFs of the literature by exploiting their ability of being expressed in terms of winning coalitions. We also use our setting to introduce conditions that ensure the equal treatment of individuals as voters or as outcomes.     

Coalitional Interval Games for Strategic Games in Which Players Cooperate

We propose a method to associate a coalitional interval game with each strategic game. The method is based on the lower and upper values of finite two-person zero-sum games. Associating with a strategic game a coalitional interval game we avoid having to take either a pessimistic or an optimistic approach to the problem. The paper makes two contributions to the literature: It provides a theoretical foundation for the study of coalitional interval games and it also provides, studies, and characterizes a natural method of associating coalitional interval games with strategic games.      

Socially Structured Games

We generalize the concept of a cooperative non-transferable utility game by introducing a socially structured game. In a socially structured game every coalition of players can organize themselves according to one or more internal organizations to generate payoffs. Each admissible internal organization on a coalition yields a set of payoffs attainable by the members of this coalition. The strengths of the players within an internal organization depend on the structure of the internal organization and are represented by an exogenously given power vector. More powerful players have the power to take away payoffs of the less powerful players as long as those latter players are not able to guarantee their payoffs by forming a different internal organization within some coalition in which they have more power. We introduce the socially stable core as a solution concept that contains those payoffs that are both stable in an economic sense, i.e., belong to the core of the underlying cooperative game, and stable in a social sense, i.e., payoffs are sustained by a collection of internal organizations of coalitions for which power is distributed over all players in a balanced way. The socially stable core is a subset and therefore a refinement of the core. We show by means of examples that in many cases the socially stable core is a very small subset of the core. We will state conditions for which the socially stable core is non-empty. In order to derive this result, we formulate a new intersection theorem that generalizes the KKMS intersection theorem. We also discuss the relationship between social stability and the wellknown concept of balancedness for NTU-games, a sufficient condition for non-emptiness of the core. In particular we give an example of a socially structured game that satisfies social stability and therefore has a non-empty core, but whose induced NTU-game does not satisfy balancedness in the general sense of Billera.