Harald Wiese

MEASURING THE POWER OF PARTIES WITHIN GOVERNMENT COALITIONS

The paper presents a coalition-structure value that is meant to capture outside options of players in a cooperative game. It deviates from the Aumann-Dreze value by violating the null-player axiom. We use this value as a power index and apply it to weighted majority games.

Entscheidungs- und Spieltheorie

Gegenstand dieses Buches sind die Entscheidungstheorie und die Spieltheorie. Die Entscheidungstheorie behandelt Entscheidungen eines einzelnen Agenten bei Unsicherheit, also entweder bei Risiko (dem Agenten sind Wahrscheinlichkeiten gegeben) oder bei Ungewissheit (Wahrscheinlichkeiten sind nicht gegeben). Die Spieltheorie wird angewendet, wenn man es mit mehreren Entscheidern (auch Spieler genannt) zu tun hat, beispielsweise in der Oligopoltheorie, bei Prinzipal-Agenten-Beziehungen oder bei der Analyse von Auktionen. Das Lehrbuch beruht auf der didaktischen Grundentscheidung, die Spieltheorie soweit als m glich auf der Basis der Entscheidungstheorie zu behandeln. Dies gilt f r die strategische wie f r die extensive Form. Diese Vorgehensweise erh ht das Verst ndnis f r den Stoff.

Reconstructing Granovetter's network theory

Abstract We employ concepts from graph theory and cooperative game theory to reconstruct Granovetters famous thesis concerning ‘the strength of weak ties’. In contrast to existing formal models related to this thesis, our approach captures the mechanisms Granovetter invokes in the derivation of his thesis. Notably, our model allows for an analytical distinction between the strength of ties and the value of ties – a distinction empirical research on the labor market has shown to be of great importance. We use our model to test the theoretical validity of Granovetters thesis and to evaluate its robustness if implicit assumptions in Granovetters argumentation are dropped.

Entry deterrence in the Schmalensee-Salop model

The question of entry deterrence in a Schmalensee type product differentiation market, that is in a market that can be depicted by a circle with circumference of 1, is investigated. It is normally assumed that incumbent firms or brands locate equidistantly whereas an entrant settles exactly in the middle between two firms. For questions of entry deterrence it has become customary to treat the n + 1 model with n incumbents and one entrant as if there were 2n firms located equidistantly. For this to hold, strong assumptions are needed. Using the Salop specification of the Schmalensee model, but without these strong assumptions, the number of entry deterring firms is calculated.

Scarcity, competition, and value

We suggest a value for finite coalitional games with transferable utility that are enriched by non-negative weights for the players. In contrast to other weighted values, players stand for types of agents and weights are intended to represent the population sizes of these types. Therefore, weights do not only affect individual payoffs but also the joint payoff. Two principles guide the behavior of this value. Scarcity: the generation of worth is restricted by the scarcest type. Competition: only scarce types are rewarded. We find that the types’ payoffs for this value coincide with the payoffs assigned by the Mertens value to their type populations in an associated infinite game.

Kauṭilya on Legal and Illegal Cancellations of Contracts

This article tries to clarify Arthaśāstra III.15.1–10 which is a difficult section on legal cancellations of contracts (anuśaya) for merchandise and on illegal ones. Previous translators apparently misunderstood the case of perishable goods and the expression anuśayaṃ dadāti. The view put forward in the present paper builds on the distinction between “Kauṭilya Recension” and “Śāstric Redaction”. However, the sections concerned may contain even more interpolations than previously thought. A related passage on immovable property (AŚ III.9.6–9), specifying fines for unlawful cancellations, is discussed as well.

The Need for Permission, the Power to Enforce, and Duality in Cooperative Games with a Hierarchy

A cooperative game with transferable utility (TU game) captures a situation in which players can achieve certain payoffs by cooperating. We assume that the players are part of a hierarchy. In the literature, this invokes the assumption that subordinates cannot cooperate without the permission of their superiors. Instead, we assume that superiors can force their subordinates to cooperate. We show how both notions correspond to each other by means of dual TU games. This way, we capture the idea that a superiors’ ability to enforce cooperation can be seen as the ability to neutralize her subordinate’s threat to abstain from cooperation. Moreover, we introduce the coercion value for games with a hierarchy and provide characterizations thereof that reveal the similarity to the permission value.

Indian Principal-Agent Theory, Or, How Varuṇa Helps the King to be Just

Abstract Economic principal-agent theory deals with asymmetric information. It has two aspects. (i) If one person is better informed than another one, the former may outwit the latter. Kauṭilya, the Arthaśāstra’s author, and other artha or dharma authors had a very good understanding of outwitting. (ii) Economic theory teaches that the person in command of superior knowledge may not always be able to benefit from this knowledge. He may need the uninformed side to agree to some mutually beneficial venture. The very fact of asymmetric information may then harm also the informed side. Judging from the literature surveyed by the author, the artha and dharma literature had no explicit (openly expressed) understanding of this second aspect. In the author’s mind, this discussion is related to the “Varuṇa rule”. This rule (specified in the Manusmṛti) stipulates that the king is to throw confiscated property into water. We explain this apparent waste of resources as an implicit solution to the second aspect of principal-agent theory mentioned above.

Four-king chess with dice is neither unrealistic nor messed up

Abstract Kauṭilya’s maṇḍala model has intrigued indologists and political scientists for some time. It deals with friendship and enmity between countries that are direct or indirect neighbours. (Ghosh; 1936) suggests a close relationship between this model and Indian four-king chess. We try to corroborate his claim by presenting a stylized game-theory model of both Indian four-king chess and Kauṭilya’s maṇḍala theory. Within that game model, we can deal with Kauṭilya’s conjecture according to which an enemy’s enemy is likely to be one’s friend. Arguably, this conjecture is reflected in the ally structure of four-king chess. We also comment on the widespread disapproval of dice in (four-king) chess.

B. Das Budget

Wir entwickeln die Budgettheorie fur zwei verschiedene Falle. In Abschnitt B.1 bezeichnen wir als Budget das Einkommen oder den Geldbetrag m eines Haushalts, mit dessen Hilfe bestimmte Guter gekauft werden konnen. Im dann folgenden Abschnitt ist das Budget als Anfangsausstattung gegeben. Dies bedeutet, dass der Haushalt ein bestimmtes Guterbundel besitzt. In beiden Fallen (Budget als Geldeinkommen und Budget als Anfangsausstattung) nennt man auch die Menge der Guterbundel, die mithilfe des Geldeinkommens bzw. mithilfe der Anfangsausstattung erstanden werden konnen, Budget oder Budgetmenge.