Dongshuang Hou

Procedural interpretation and associated consistency for the egalitarian Shapley values

An -egalitarian Shapley value is the convex combination of the Shapley value and the equal division value in terms of a social selfish coefficient [0,1] reconciling the two polar opinions of marginalism and egalitarianism. We present a procedural interpretation for every egalitarian Shapley value. We also characterize each -egalitarian Shapley value by associated consistency, continuity and the -dummy player property. The Jordan normal form approach is applied as the pivotal technique to accomplish the most important proof.

The general prenucleolus of n-person cooperative fuzzy games

Abstract In this paper, we define the concept of the general prenucleolus minimizing the player complaint vector in the lexicographic order over the preimputation set for the cooperative games with fuzzy coalitions. For the general prenucleolus, we get a sufficient condition that the complaints of all players are in equal amount under the case of linear complaint functions concluding the proposed player excess (Sakawa and Nishizaki (1994) [15] ). As a result, we can obtain the proposed fuzzy solutions with the corresponding linear complaint functions, such as the equalizer solution (Molina and Tejada (2002) [5] ) and Shapley function etc. We prove that the least square general prenucleolus minimizing the variance of the resulting player complaints, is the general prenucleolus. Thus, an optimal solution considered from two aspects of the lexicographic order and the least square criterion, is obtained. In addition, several general prenucleoli are proposed in terms of specific situations.

A-potential function and a non-cooperative foundation for the Solidarity value

Marginalism and egalitarianism are two main standpoints in economics. The Shapley value has been characterized in many ways from the view of marginalism. In this paper, we characterize the Solidarity value with respect to the egalitarianism by three approaches applied to the Shapley value. We introduce a revised potential function and deduce the recursive formula of the Solidarity value. It is also characterized by the property of quasi-balanced contributions. Finally, we provide a non-cooperative procedure leading to the Solidarity value.

Data Cost Games as an Application of 1-Concavity in Cooperative Game Theory

The main goal is to reveal the 1-concavity property for a subclass of cost games called data cost games. The motivation for the study of the 1-concavity property is the appealing theoretical results for both the core and the nucleolus, in particular their geometrical characterization as well as their additivity property. The characteristic cost function of the original data cost game assigns to every coalition the additive cost of reproducing the data the coalition does not own. The underlying data and cost sharing situation is composed of three components, namely, the player set, the collection of data sets for individuals, and the additive cost function on the whole data set. The proof of 1-concavity is direct, but robust to a suitable generalization of the characteristic cost function. As an adjunct, the 1-concavity property is shown for the subclass of so-called “bicycle” cost games, inclusive of the data cost games in which the individual data sets are nested in a decreasing order.

CONVEXITY OF THE "AIRPORT PROFIT GAME" AND k-CONVEXITY OF THE "BANKRUPTCY GAME"

The topic is two-fold. First, we prove the convexity of Owens Airport Profit Game (inclusive of revenues and costs). As an adjunct, we characterize the class of 1-convex Airport Profit Games by equivalent properties of the corresponding cost function. Second, we classify the class of 1-convex Bankruptcy Games by solving a minimization problem of its corresponding gap function.

The Core and Nucleolus in a Model of Information Transferal

Galdeano et al. introduced the so-called information market game involving n identical firms acquiring a new technology owned by an innovator. For this specific cooperative game, the nucleolus is determined through a characterization of the symmetrical part of the core. The nonemptiness of the (symmetrical) core is shown to be equivalent to one of each, super additivity, zero-monotonicity, or monotonicity.

The Shapley value for the probability game

Abstract The main goal of this paper is to introduce the probability game. On one hand, we analyze the Shapley value by providing an axiomatic characterization. We propose the so-called independent fairness property, meaning that for any two players, the player with larger individual value gets a larger portion of the total benefit. On the other, we use the Shapley value for studying the profitability of merging two agents.

Compromise for the complaint: an optimization approach to the ENSC value and the CIS value

AbstractThe main goal of this paper is to introduce a new solution concept: the optimal compromise value. We propose two kinds of complaint criteria based on which the optimistic complaint and the pessimistic complaint are defined. Two optimal compromise values are obtained by lexicographically minimizing the optimistic maximal complaint and the pessimistic maximal complaint, respectively. Interestingly, these two optimal compromise values coincide with the ENSC value and the CIS value, respectively. Moreover, these values are characterized in terms of equal maximal complaint property and efficiency. As an adjunct, we reveal the coincidence of the Nucleolus and the ENSC value of 1-convex games.

Stackelberg Oligopoly TU-Games: Characterization and Nonemptiness of the Core

In this paper, we consider the dynamic setting of Stackelberg oligopoly TU-games in γ-characteristic function form. Any deviating coalition produces an output at a first period as a leader and then, outsiders simultaneously and independently play a quantity at a second period as followers. We assume that the inverse demand function is linear and that firms operate at constant but possibly distinct marginal costs. First, we show that the core of any Stackelberg oligopoly TU-game always coincides with the set of imputations. Second, we provide a necessary and sufficient condition, depending on the heterogeneity of firms’ marginal costs, under which the core is nonempty.