Yan-An Hwang

Fuzzy games: A characterization of the core

In this paper we extend to the cooperative fuzzy games case the reduced game introduced by Davis and Maschler [The kernel of a cooperative game, Naval Res. Logist. Quart. 12 (1965) 223-259]. We shall introduce two types of such a reduced game to cooperative fuzzy games and define the related properties of consistency and converse consistency. We further offer two axiomatizations of the core on the domain of all cooperative fuzzy games by means of consistency and its converse.

Max-consistency, complement-consistency and the core of fuzzy games

Recently, Hwang introduced two extensions of the max-reduced game to fuzzy games by reducing the number of the players. Based on these reduced games, he offered analogous axiomatizations of the core related to Serrano and Volij in the context of fuzzy games. Here, we continue and develop Hwangs work on similar topics. However, we turn to a different definition of the reduced game by simultaneously reducing both the number of the players and the participation levels. We propose such extensions of the complement-reduced game and of the max-reduced game to fuzzy games and define the related properties of consistency and converse consistency. Based on these properties, we offer several analogous characterizations of the core related to Peleg, Serrano and Volij and Tadenuma, respectively.

The consistent value of fuzzy games

In the framework of fuzzy games, we offer an extension of the reduced game introduced by Hart and Mas-Colell, which we name the self-reduced game. According to consistency which related to the self-reduced game, we provide a definition of the consistent value which is a generalization of the Shapley value of fuzzy games. We adopt three existing concepts from coalitional game theory and reinterpret them in the framework of fuzzy games. The first one is that there exists a unique potential function and the resulting payoff vector coincides with the consistent value. Second, based on the properties of balanced contributions and consistency, we offer several axiomatizations of the consistent value. Finally, we propose a dynamic process to illustrate that the consistent value can be reached by players who start from an arbitrary efficient payoff vector and make successive adjustments.

The multi-core, balancedness and axiomatizations for multi-choice games

This note extends the solution concept of the core for cooperative games to multi-choice games. We propose an extension of the theorem of Bondareva (Problemy Kybernetiki 10:119–139, 1963) and Shapley (Nav Res Logist Q 14:453–460, 1967) to multi-choice games. Also, we introduce a notion of reduced games for multi-choice games and provide an axiomatization of the core on multi-choice games by means of corresponding notion of consistency and its converse.

The core of multi-choice NTU games

Abstract.We propose a necessary and sufficient condition for the existence of core to the context of multi-choice NTU games.

The Harsanyi-Shapley solution and independence of irrelevant expansions

We characterize the Harsanyi-Shapley solution/value on essential and smooth games. An axiom – independence of irrelevant expansions of NTU games is introduced.

Closedness under Hart-Mas Colell reduction

Abstract. We will find 3 maximal subclasses with respect to essential, superadditive and convex games, respectively such that a game is in one subclass, so are its reduced games.

Two characterizations of the consistent egalitarian solution and of the core on NTU games

In this paper, we provide two characterizations in the context of NTU games: of the consistent egalitarian solution and of the core. The first characterization is based on reduced games and contraction and expansion independence. The second one is based on reduced games and sub-reduced games.

A dynamic approach to the Shapley value based on associated games

We propose a dynamic process leading to the Shapley value of TU games or any solution satisfying Inessential Game (IG) and Continuity (CONT), based on a modified version of Hamiaches notion of an associated game.

An NTU value under complement reduced game

The paper follows Kalai and Samet’s (Econometrica 53:307–327, 1985) construction to define a possible extension of the equal allocation of nonseparable costs (EANSC) to games without transferable utilities. We offer a characterization of the EANSC based on the axiom of independence of irrelevant monotonic transformation [Chang and Hwang (Int J Game Theory 32:253–271, 2003) introduced this axiom, and they named it independence of irrelevant expansions. The referee points out that the terminology is inappropriate. So, we change the name.] introduced by Chang and Hwang (Int J Game Theory 32:253–271, 2003) as well as on several familiar axioms. Specifically, we show that the EANSC is the only solution to satisfy Pareto optimality, translation covariance, anonymity, TU-bilateral consistency (or TU-converse consistency), aggregate monotonicity, and independence of irrelevant monotonic transformation.