Using Hypergames to Model Difficult Social Issues: An Approach to the Case of Soccer Hooliganism

In this paper, Hypergame Analysis is used to produce predictive models of the social conflict of "soccer hooliganism". The purpose of this form of analysis is to help model interactions in which the parties involved may have quite different perceptions of the "game" being played. Soccer hooliganism is considered in terms of an interaction between two main parties-the "hooligan fans" and the "authorities". Recent empirical studies are used to help build up representations of some possible "games" that may be seen by each side. From the resulting hypergames, predictions are derived as to the likely outcome under various circumstances. Also considered are possible effects of taking the interaction through several "rounds". Finally, some practical conclusions are drawn, both about the problem of how best to respond to soccer hooliganism, and about the methodological question of how to approach the analysis of such social conflicts in a systematic way.     

Acceptance sampling in a producer—supplier conflicting environment: Risk neutral case

This paper considers a mutual inspection game which follows the signing of a quality delivery contract. The basic strategic decisions considered involve both the supplier and producer acceptance sampling procedure on the same lot. To solve the game, we consider the classical notions of ‘producer’ and ‘consumer’ risks and define a random payoffs game. To simplify our analysis, we assume risk neutrality by both the producer and the supplier. The approach of this paper provides a departure point from traditional acceptance sampling, to an approach which recognizes explicit motivations and the pursuit of self-interest as well as the cost of information for the parties involved. As a result, the traditional formulation of sampling plans, designed in terms of risk considerations based on Neyman—Pearson theory in hypothesis testing, is deemed limited. For demonstration purposes, an example is solved.     

Structural satisfaction in simple games

A fundamental maxim for any theory of social behavior is that knowledge of the theory should not cause behavior that contradicts the theory's assertions. Although this maxim consistently has been heeded in the theory of noncooperative games, it largely has been ignored in solution theory for cooperative games. Solution theory, the central concern of this paper, seeks to identify a subset of the feasible outcomes of a cooperative game that are ‘stable’ results of competition among participants, each of whom attempts to bring about an outcome he favors, rather than to prescribe ‘fair’ outcomes that accord with a standard of equity. We show that learning by participants about the solution theory can cause the outcomes identified as stable by certain solution concepts to become unstable, and discover that an important distinction in this regard is whether the solution concept requires each element of the solution set to defend itself against alternatives rather than relying on other elements for its defense. Finally, we develop a concept of ‘solid’ solutions which have a special claim for stability.The unifying theme of this paper concerns the sense in which certain outcomes of a cooperative game may be regarded as stable, and the extent to which this stability requires that the players are ignorant of the theory. Although the issues raised here have implications for the theory of cooperative games in general, Section 1 establishes the focus of the analysis on collective decision games. Section 2 develops some general perspectives on solution theory which are used in Sections 3 and 4 to evaluate the Condorcet solution, the core, the robust proposals set, von Neumann- Morgenstern solutions and competitive solutions. Section 5 presents the concept of a solid solution and relates this idea to the solution concepts reviewed earlier. We demonstrate that in general a solution concept has a strong claim to stability only if it is solid. Finally, Section 6 concludes by indicating that the basic argument also can be applied to Aumann and Maschler's bargaining sets and, more generally, to solution theory for any cooperative game.     

Risk and quality control in a supply chain: competitive and collaborative approaches

This paper provides a quantitative and comparative economic and risk approach to strategic quality control in a supply chain, consisting of one supplier and one producer, using a random payoff game. Such a game is first solved in a risk-neutral framework by assuming that both parties are competing with each other. We show in this case that there may be an interior solution to the inspection game. A similar analysis under a collaborative framework is shown to be trivial and not practical, with a solution to the inspection game being an ‘all or nothing’ solution to one or both the parties involved. For these reasons, the sampling random payoff game is transformed into a Neyman–Pearson risk constraints game, where the parties minimize the expected costs subject to a set of Neyman–Pearson risk (type I and type II) constraints. In this case, the number of potential equilibria can be large. A number of such solutions are developed and a practical (convex) approach is suggested by providing an interior (partial sampling) solution for the collaborative case. Numerical examples are developed to demonstrate the procedure used. Thus, unlike theoretical approaches to the solution of strategic quality control random payoff games, the approach we construct is both practical and consistent with the statistical risk Neyman–Pearson approach.     

Asymptotic structural characteristics of fuzzy measure and their applications

In fuzzy measure theory, as Sugeno's fuzzy measures lose additivity in general, the concept ‘almost’, which is well known in classical measure theory, splits into two different concepts, ‘almost’ and ‘pseudo-almost’. In order to replace the additivity, it is quite necessary to investigate some asymptotic behaviors of a fuzzy measure at sequences of sets which are called ‘waxing’ and ‘waning’, and to introduce some new concepts, such as ‘autocontinuity’, ‘converse-autocontinuity’ and ‘pseudo-autocontinuity’. These concepts describe some asymptotic structural characteristics of a fuzzy measure.In this paper, by means of the asymptotic structural characteristics of fuzzy measure, we also give four forms of generalization for both Egoroff's theorem, Riesz's theorem and Lebesgue's theorem respectively, and prove the almost everywhere (pseudo-almost everywhere) convergence theorem, the convergence in measure (pseudo-in measure) theorem of the sequence of fuzzy integrals. In the last two theorems, the employed conditions are not only sufficient, but also necessary.     

Complex Strategic Analysis: A Hypergame Study of the Fall of France

It is argued that a crucial element in decision-making in conflicts is the need for adequate conceptual complexity in problem formulation. This is illustrated by reference to a disastrous military failure—the fall of France in 1940. A formal model of the strategic situation is constructed using the Hypergame approach, in which the usual game-theoretic assumption that all "players" see the same "game" is discarded. Using this model, further features of the case are explored, and some general conclusions discussed. It is suggested that Hypergame analysis can be of assistance in achieving adequate levels of problem-perception in complex, conflict-prone environments, in particular by helping in the generation of multiple models.     

Decision resource management and practical intervention in conflicts — a model and its implications

One of the major problems for O.R. lies in providing decision-making assistance in complex conflicts. Too often in the past the approach has been concentrated on providing technical solutions to well-defined hypothetical problems, rather than on attempting to tackle the decision-makers' real problems of trying to make sense of the complex situations in which they find themselves. The paper is intended to contribute towards practical understanding by outlining a theory which explains the ways in which decision-makers' views of the environment are affected by conflicts, particularly under conditions of crisis.The theory attempts to integrate a series of pragmatic hypotheses derived from International Relations, by extending concepts originating in cognitive psychology. The theory's crucial concept is that of “resources” treated by the authors as the number of units of information processed over a given time period. By considering the impact of resources on the conscious analysis of problems a set of postulates is arrived at, which are applicable to a wide variety of decision-making situations.In particular the principle of “inappropriate resource saving” is proposed which suggests that resource considerations imply that unsuitable oversimplistic approaches are likely to dominate decision-making in precisely the situations where the necessity of a complex sophisticated approach is greatest.Finally the implications of the theory for decision-making in general, and for understanding other parties in conflicts, in particular, are discussed. The importance is stressed of; forward contingency planning (putting time in the bank), conscious resource management, and forming multiple models of complex situations.     

A combinatorial theory of minimal social situations

A minimal social situation is a game‐like situation in which there are two actors, each of them has two possible actions, and both evaluate the outcomes of their joint actions in terms of two categories (say, ‘success’ and ‘failure'). By fixing actors and actions and varying ‘payoffs’ the set of 256 ‘configurations’ is obtained. This set decomposes into 43 ‘structural forms’, or equivalence classes with respect to the relation of isomorphism defined on it. This main theorem and other results concerning related configurations (minimal decision situations) are derived in this paper by means of certain tools of group theory. Some extensions to larger structures are proved in the Appendix. In the introductory section after a brief explanation of the meaning given to the terms ‘structure’ and ‘isomorphism’ in mathematics (Bourbaki) it is shown how these terms can be used to formalize the concept of ‘social form’.     

The bargaining set for sharing the power

The evaluation of the power of the parties of a Parliament is usually carried out following a static approach, counting their numbers of seats and possible ideological relations among them. In this paper we propose a dynamic model in which parties may blackmail each other in order to increase their power at the expense of others. This model may be solved in terms of the Bargaining Set (Aumann and Maschler in Advances in game theory. Princeton University Press, Princeton, 1964), a set valued solution, in contrast to the classical power indices that are point valued; so it may be used to check the robustness of a power division taking into account possible blackmailing activities. The paper is mainly based on the idea of proposing an existing instrument, the Bargaining Set, as power index to analyze this blackmailing situation. The computational complexity limits the possibility of applying it to real-world situations, but the possibility of making the computation easier is shown using some examples.     

Optimal license fees for a new product

We compare how much profit an inventor of a patented new ‘superior’ product can realize by licensing its manufacture, for a fixed fee, to an oligopolistic industry producing an ‘inferior’ substitute. Our analysis is conducted in terms of a three stage noncooperative game involving n + 1 players: the inventor, acting as a Stackelberg leader, and the n firms. Analysis of subgame perfect equilibria in pure strategies of this game disclose the circumtances under which an inventor's optimal behavior ultimately leads to production of both products and when it allows for the production of the ‘superior’ product only. An extreme case of the latter possibility, namely when the ‘superior’ product is produced by a monopolist, is characterized also.     

Scenario analysis as a background for important energy policy decisions

This paper gives an example of how scenario analysis can be used in a decision-making context in the sphere of public debate. The example chosen to illustrate the process is the Norwegian Smelting Industry, an industry which uses about 25% of Norway's primary energy consumption. The paper describes an attempt at rationalising the energy policy decisions which are interwoven with the smelting industry's future. The analysis used a ‘Reference Group’ comprising leading members of the relevant interest groups to identify the goals of the different parties, and strategies for reaching these goals. The long-term consequences of following these paths were simulated and the results published in a popularised book [1].     

Two-party competition with many constituences

The paper considers a single member district, simple plurality political system with n districts. There are two political parties, each consisting of n candidates. Individual candidates seek to win their district per se, but voters appreciate that final policy outcomes will depend upon: (1) which party wins control of the legislature, and (2) how party policy is derived from the party members' policies. Candidates take account of such voter deliberations in choosing their election strategies. A set of minimal sufficient conditions for an equilibrium to exist in this game is provided and the equilibrium characterized. While party policies are shown to converge in equilibrium, candidate policies in general do not - either across or within parties.     

Le probleme d'etoiles pour graphes est np-complet

Nous appelons problème de ‘recollement de voisinages’ (RV) (‘star problem’ ou ‘problème d'ètoiles’) le problème qui consiste à savoir, étant donnée une famille $\text{V}$ de parties d'un ensemble S, s'il existe un graphe (non orienté et sans boucle) dont la famille de voisinages coïncide avec $\text{V}$. L'objectif de cet article est de montrer que le problème RV est NP-complet. La preuve s'appuiera sur l'èquivalence entre RV et le probléme de trouver un automorphisme d'ordre 2 dans un graphe quelconque (AUT2). La NP-complétude de AUT2 a été démontrée par Anna Lubiw [5].     

Odd and even hamming spheres also have minimum boundary

Combinatorial problems with a geometric flavor arise if the set of all binary sequences of a fixed length n, is provided with the Hamming distance. The Hamming distance of any two binary sequences is the number of positions in which they differ. The (outer) boundary of a set A of binary sequences is the set of all sequences outside A that are at distance 1 from some sequence in A. Harper [6] proved that among all the sets of a prescribed volume, the ‘sphere’ has minimum boundary.We show that among all the sets in which no pair of sequences have distance 1, the set of all the sequences with an even (odd) number of 1's in a Hamming ‘sphere’ has the same minimizing property. Some related results are obtained. Sets with more general extremal properties of this kind yield good error-correcting codes for multi-terminal channels.     

Measures of fuzzy sets and measures of fuzziness

The measures presented in this paper are defined by using Weber's concept of decomposable measures m of crisp sets, having in particular the Archimedean decomposable operations in view (Section 2). Measures $\text{m}$ of fuzzy sets are introduced as integrals with respect to m. For the Archimedean cases, Weber's integral will be used as alternative to Sugeno's and Choquet's concepts (Section 3). What ‘fuzziness’ means will be described by functions of fuzziness F (another name: entropy N-functions) with respect to a negation. In addition to the types of functions of fuzziness which are induced by concave functions, we discuss also the ones which are induced by fuzzy connectives (Section 4). Now, using m for measuring the ‘importance of items’ and F for the ‘fuzziness’ of the possible values of a fuzzy set ?, m?(F ° ?) serves us as a measure of the fuzziness $\text{F}$? of ?. The concepts of De Luca and Termini, Capocelli and De Luca, Kaufmann, Knopfmacher, Loo, Gottwald, Dombi and, under the restriction to the Archimedean cases, also the concepts of Trillas and Riera and Yager turn out to be special cases (Section 5).     

On non-binary social choice

In a recent paper Grether and Plott (1982) have extended Arrow's General Possibility Theorem to the case where choice over small (in particular ‘two-element’) sets may not be possible. This obviously raises the question whether the counterparts of other existing impossibility results will go through in the same framework. This note settles the question for the counterpart of the well-known impossibility theorem of Gibbard. By weakening the collective rationality condition of Arrow we show that all the social choice functions will be ‘oligarchical’ in Gibbard's sense, in the Grether and Plott (1982) framework.     

Arrow's theorem is not a surprising result

Arrow's theorem asserts that it is impossible to find a procedure which aggregates n given complete preorders into one complete preorder and which has ‘rational’ properties.Some authors have proposed to solve this problem in building what could be called ‘preaggregation methods’. The purpose of this paper is to study the Arrow's problematic in this context.The obtained results lead to an interpretation of Arrow's theorem which shows that it is rather natural, although many authors present it as a surprising result or even as a paradox.The last section compares the structures of the sets of decisive sets associated to aggregation and preaggregation procedures.     

Feedback Competitive Advertising Strategies with a General Objective Function

We introduce a general objective function, which incorporates competitive situations, such as conservative, punitive, and predatory advertising. Linking together the particular situations into a two-parameter family of max–min problems, and using the Lanchester model to describe the dynamics of the market, a bilinear-quadratic differential game is obtained. For this game, we find saddle-point feedback time-invariant advertising strategies and show when these strategies are Nash equilibrium strategies. In an empirical application involving duopolistic competition in the cola market, we find evidence of a punitive motivation for the advertising strategies.     

A model of a sudden-death field-goal football game as a sequential duel

A highly simplified ‘football’ game is constructed where individuals can run or kick for a field goal. It represents an attempt to extend the domain of the modeling of duels to a broader category than those previously studied. There are some worthwhile similarities (and important differences) in military, sports and economic tactics which are reasonably well modeled as zero sum games.The theory of duels for military application has been reasonably well developed but there are at least two other activities beyond war in which the zero-sum game duel is worth considering. They are in sports and in the tactics of advertising campaigns or other economic activities where the budgets of A and B are set and the fight is a non-price duel over a market of fixed size. In this paper we concentrate on the extension of dueling to sports.Rather than claim immediate relevance to football as it is played, a highly simplified version of ⌉sudden-death’ scoring is introduced. The basic game is as follows. With equal probability the team toss to see who gets the ball. The team with the ball can either run or try to kick a field goal. The first team to score wins the game.     

Stability and Shapley value for an n-persons fuzzy game

The aim of the paper is to explain new concepts of solutions for n-persons fuzzy games. Precisely, it contains new definitions for ‘core’ and ‘Shapley value’ in the case of the n-persons fuzzy games. The basic mathematical results contained in the paper are these which assert the consistency of the ‘core’ and of the ‘Shapley value’. It is proved that the core (defined in the paper) is consistent for any n-persons fuzzy game and that the Shapley values exists and it is unique for any fuzzy game with proportional values.