The weighted Shapley support levels values

This paper presents a new class of weighted values for level structures. The new values, called weighted Shapley support levels values, extend the weighted Shapley values to level structures and contain the Shapley levels value (Winter, 1989) as a special case. Since a level structure with only two levels coincides with a coalition structure we obtain, as a side effect, also new axiomatizations of weighted coalition structure values, presented in Levy and McLean (1989)

The weighted Shapley support levels values

This paper presents a new class of weighted values for level structures. The new values, called weighted Shapley support levels values, extend the weighted Shapley values to level structures and contain the Shapley levels value (Winter, 1989) as a special case. Since a level structure with only two levels coincides with a coalition structure we obtain, as a side effect, also new axiomatizations of weighted coalition structure values, presented in Levy and McLean (1989)

Two classes of weighted values for coalition structures with extensions to level structures

In this paper we introduce two new classes of weighted values for coalition structures with related extensions to level structures. The values of both classes coincide on given player sets with Harsanyi payoffs and match therefore adapted standard axioms for TU-values which are satisfied by these values. Characterizing elements of the values from the new classes are a new weighted proportionality within components property and a null player out property, but on different reduced games for each class. The values from the first class, we call them weighted Shapley alliance coalition structure values (weighted Shapley alliance levels values), satisfy the null player out property on usual reduced games. By contrast, the values from the second class, named as weighted Shapley collaboration coalition structure values (weighted Shapley collaboration levels values) have this property on new reduced games where a component decomposes in components of lower levels (these are singletons in a coalition structure) if one player of this component is removed from the game. The first class contains the Owen value (Shapley levels value) and the second class includes a new extension of the Shapley value to coalition structures (level structures) as a special case

Two classes of weighted values for coalition structures with extensions to level structures

In this paper we introduce two new classes of weighted values for coalition structures with related extensions to level structures. The values of both classes coincide on given player sets with Harsanyi payoffs and match therefore adapted standard axioms for TU-values which are satisfied by these values. Characterizing elements of the values from the new classes are a new weighted proportionality within components property and a null player out property, but on different reduced games for each class. The values from the first class, we call them weighted Shapley alliance coalition structure values (weighted Shapley alliance levels values), satisfy the null player out property on usual reduced games. By contrast, the values from the second class, named as weighted Shapley collaboration coalition structure values (weighted Shapley collaboration levels values) have this property on new reduced games where a component decomposes in the components of the next lower level if one player of this component is removed from the game. The first class contains as a special case the Owen value (Shapley levels value) and the second class includes a new extension of the Shapley value to coalition structures (level structures) as a special case

Two classes of weighted values for coalition structures with extensions to level structures

In this paper we introduce two new classes of weighted values for coalition structures with related extensions to level structures. The values of both classes coincide on given player sets with Harsanyi payoffs and match therefore adapted standard axioms for TU-values which are satisfied by these values. Characterizing elements of the values from the new classes are a new weighted proportionality within components property and a null player out property, but on different reduced games for each class. The values from the first class, we call them weighted Shapley alliance coalition structure values (weighted Shapley alliance levels values), satisfy the null player out property on usual reduced games. By contrast, the values from the second class, named as weighted Shapley collaboration coalition structure values (weighted Shapley collaboration levels values) have this property on new reduced games where a component decomposes in the components of the next lower level if one player of this component is removed from the game. The first class contains as a special case the Owen value (Shapley levels value) and the second class includes a new extension of the Shapley value to coalition structures (level structures) as a special case

Harsanyi support levels payoffs and weighted Shapley support levels values

This paper introduces a new class of values for level structures. The new values, called Harsanyi support levels payoffs, extend the Harsanyi payoffs from the Harsanyi set to level structures and contain the Shapley levels value (Winter, 1989) as a special case. We also look at extensions of the weighted Shapley values to level structures. These values, we call them weighted Shapley support levels values, constitute a subset of the class of Harsanyi support levels payoffs and coincide on a level structure with only two levels with a class of weighted coalition structure values, already mentioned in Levy and McLean (1989) and discussed in McLean (1991). Axiomatizations of the studied classes are provided for both exogenously and endogenously given weights

Harsanyi support levels payoffs and weighted Shapley support levels values

This paper introduces a new class of values for level structures. The new values, called Harsanyi support levels payoffs, extend the Harsanyi payoffs from the Harsanyi set to level structures and contain the Shapley levels value (Winter, 1989) as a special case. We also look at extensions of the weighted Shapley values to level structures. These values, we call them weighted Shapley support levels values, constitute a subset of the class of Harsanyi support levels payoffs and coincide on a level structure with only two levels with a class of weighted coalition structure values, already mentioned in Levy and McLean (1989) and discussed in McLean (1991). Axiomatizations of the studied classes are provided for both exogenously and endogenously given weights

Computational Aspects of Extending the Shapley Value to Coalitional Games with Externalities

Until recently, computational aspects of the Shapley value were only studied under the assumption that there are no externalities from coalition formation, i.e., that the value of any coalition is independent of other coalitions in the system. However, externalities play a key role in many real-life situations and have been extensively studied in the game-theoretic and economic literature. In this paper, we consider the issue of computing extensions of the Shapley value to coalitional games with externalities proposed by Myerson [21], Pham Do and Norde [23], and McQuillin [17]. To facilitate efficient computation of these extensions, we propose a new representation for coalitional games with externalities, which is based on weighted logical expressions. We demonstrate that this representation is fully expressive and, sometimes, exponentially more concise than the conventional partition function game model. Furthermore, it allows us to compute the aforementioned extensions of the Shapley value in time linear in the size of the input

Discourse network analysis: policy debates as dynamic networks

Political discourse is the verbal interaction between political actors. Political actors make normative claims about policies conditional on each other. This renders discourse a dynamic network phenomenon. Accordingly, the structure and dynamics of policy debates can be analyzed with a combination of content analysis and dynamic network analysis. After annotating statements of actors in text sources, networks can be created from these structured data, such as congruence or conflict networks at the actor or concept level, affiliation networks of actors and concept stances, and longitudinal versions of these networks. The resulting network data reveal important properties of a debate, such as the structure of advocacy coalitions or discourse coalitions, polarization and consensus formation, and underlying endogenous processes like popularity, reciprocity, or social balance. The added value of discourse network analysis over survey-based policy network research is that policy processes can be analyzed from a longitudinal perspective. Inferential techniques for understanding the micro-level processes governing political discourse are being developed