The Graph Model for Conflict Resolution (GMCR) is a widely used technique for analyzing conflicts involving two or more decision makers (DMs), where each of them has a set of actions to be taken (the options) and different perceptions (the preferences) about the possible outcomes of the dispute (the states). In fact, preference information is essential for applying GMCR and its absence precludes the use of formal conflict analysis methods. This paper proposes a multi-criteria extension of the option prioritization technique for preference elicitation within the GMCR framework. In the standard approach, each DM is required to provide a complete ranking of preference statements expressed as Boolean combinations of conflict options. The proposed method relaxes this requirement by allowing indifference among preference statements. To illustrate the approach, it is applied to an Information Technology (IT) outsourcing conflict involving two DMs: the service provider and the client organization. The results highlight two main advantages: (i) the method supports DMs in formulating preference statements based on explicit criteria; and (ii) it produces more structured preference rankings.

This paper proposes a procedure to elicit lower and upper probabilistic preferences within the Graph Model for Conflict Resolution (GMCR) through a multicriteria perspective. This imprecise probability approach is especially recommended in situations where there is not enough information regarding how DMs evaluate or compare the feasible conflict states. Within this proposal, the elicitation process is carried out through three questions in which decision makers are asked to evaluate the performance of each viable state in each criterion. Uncertainty in this performance generates lower and higher probabilistic preferences among states. To illustrate the applicability of the new elicitation procedure, we present a real-world example from a construction project in Brazil.

In strategic conflicts, the behavior of decision makers (DMs) is affected by their beliefs about how their opponents will respond, how they will counter respond, and more generally by the number of action-reaction steps they consider. In this article, we propose several notions of stability with variable horizon that vary in whether the focal DM and her opponents are allowed to make moves that are immediately disadvantageous, called unilateral disimprovements. Credible maximin stability reflects the assumption that opponents will attempt to deter a focal DM from a move by imposing the strongest possible sanction. We analyze the effects of varying the horizon on this form of stability, and on the relationships among the solution concepts that result. Requiring the focal DM to make only unilateral improvements does not influence the stability of states, but restricting opponents’ responses to unilateral improvements reduces the set of stable states. An application to a water-pricing conflict illustrates the analysis of a graph model using credible maximin stabilities.

In this paper, we modify the graph model for conflict resolution (GMCR) to model interactive unawareness of decision makers (DMs) about the options available to them in the conflict. More specifically, we consider a GMCR with two DMs, where a DM, in some given state, can be unconscious about some of his options, or about the options of his opponent, and therefore, may have only a partial knowledge of the state space. By interactive unawareness, it is meant that a DM can reason about the awareness level of the other DM and about the awareness level of the other DM regarding his or her own awareness level and so on. We generalize standard solution concepts for this model and illustrate its usefulness by means of a hypothetical war conflict.

We present three problems found in this paper “Policy equilibrium and generalized metarationalities for multiple decision-maker conflicts,” by Zeng et al., published in IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 37, no. 4, pp. 456-463, Jul. 2007. More specifically, we show by means of counterexamples that: 1) the definition proposed for n-decision maker (DM) conflicts does not coincide with the existing generalized metarationality defined by these same authors for conflicts with 2 DMs; 2) the equivalence between generalized metarationality for 2 rounds and symmetric metarational stability is false; and 3) generalized metarational equilibrium does not imply policy equilibrium.

In this paper, our objective is to propose a stability concept within the graph model for conflict resolution (GMCR) that does not require knowledge about preferences of other decision makers (DMs) in the conflict and is flexible to analyze the conflict with variable horizon. For that we propose the use of the maximin decision rule within the GMCR. More specifically, we consider a GMCR with two DMs and introduce the concept of Maximinhstability with horizon h for a given DM. The Maximinhstability concept was inspired by the notion of limited-move stability with horizon h present in the GMCR literature and it is adequate for modeling cautious DMs in conflicts where they have no knowledge about the other DM's preferences. We establish what is the relationship among the Maximinhstabilities for different horizons and the relationship among Maximinhstability and other GMCR stability concepts. Finally, we present an application to illustrate the proposed stability concept, namely, a neuroscience technological selection conflict in China.

We present a generalization of the graph model for conflict resolution, introducing the possibility of decision makers (DMs) expressing their preferences among the possible scenarios through probabilistic preferences. In this new scenario, four stability definitions (solution concepts) are proposed: 1) α-Nash stability; 2) (α, β)-metarationality; 3) (α, β)-symmetric metarationality; and 4) (α, β, γ)-sequential stability. We deal with conflicts that involve two or more DMs. Relationships between these definitions are demonstrated, as well as an analysis of how the values of the parameters α, β, and y influence the set of stable states is made. Applications of the proposed model to conflicts involving two and three DMs are presented. The analysis of these applications highlights the advantages gained by allowing individuals to express their preferences probabilistically.

In earlier work [Halpern and Rêgo 2006b], we proposed a logic that extends the Logic of General Awareness of Fagin and Halpern [1988] by allowing quantification over primitive propositions. This makes it possible to express the fact that an agent knows that there are some facts of which he is unaware. In that logic, it is not possible to model an agent who is uncertain about whether he is aware of all formulas. To overcome this problem, we keep the syntax of the earlier paper, but allow models where, with each world, a possibly different language is associated. We provide a sound and complete axiomatization for this logic and show that, under natural assumptions, the quantifier-free fragment of the logic is characterized by exactly the same axioms as the logic of Heifetz, Meier, and Schipper [2008].

Most work in game theory assumes that players are perfect reasoners and have common knowledge of all significant aspects of the game. In earlier work [Halpern and Rêgo 2006], we proposed a framework for representing and analyzing games with possibly unaware players, and suggested a generalization of Nash equilibrium appropriate for games with unaware players that we called generalized Nash equilibrium. Here, we use this framework to analyze other solution concepts, with a focus on sequential equilibrium. We also provide some insight into the notion of generalized Nash equilibrium by proving that it is closely related to the notion of rationalizability when we restrict the analysis to games in normal form and no unawareness is involved.

There has been a great deal of work on characterizing the complexity of the satisfiability and validity problem for modal logics. In particular, Ladner showed that the satisfiability problem for all logics between K and S4 is PSPACE-hard, while for S5 it is NP-complete. We show that it is negative introspection, the axiom ¬Kp ⇒ K¬Kp, that causes the gap: if we add this axiom to any modal logic between K and S4, then the satisfiability problem becomes NP-complete. Indeed, the satisfiability problem is NP-complete for any modal logic that includes the negative introspection axiom.

We study the performance of a decision feedback decoder (DFD) for convolutional codes over an interleaved burst channel. The DFD adaptively estimates channel reliability information from previous decisions. The effect of error propagation, finite interleaving and the length of the initial training sequence is explicitly studied. A binary Gilbert-Elliott channel is used to model the correlation structure of the error process. Comparison of the DFD and the hard decision decoding with Hamming metric reveals a crossover between the performance curves, depending on the interleaving parameters and channel statistics.