Shigeo Muto

On Cores and Stable Sets for Fuzzy Games

In this paper, cores and stable sets for games with fuzzy coalitions are introduced and their relations studied. For convex fuzzy games it turns out that all cores coincide and that the core is the unique stable set. Also relations between cores and stable sets of fuzzy clan games are discussed.

Farsighted Stability in an n-Person Prisoner’s Dilemma

Farsighted stability is examined in an n-person prisoner’s dilemma. It is shown that any individually rational and Pareto efficient outcome is a farsighted stable set and no other farsighted stable set exists; it is further shown that the largest consistent set consists of all individually rational outcomes.

Stable profit sharing in a patent licensing game: general bargaining outcomes

By considering coalition structures formed by an external licensor of a patented technology and oligopolistic firms, we investigate licensing agreements that can be reached as bargaining outcomes under those coalition structures. The following results hold in a generalized patent licensing game. The core for a coalition structure is always empty, unless the grand coalition forms. We give a necessary and sufficient condition for the nonemptiness of the core (for the grand coalition). If the number of licensees that maximizes licensees’ total surplus is greater than the number of existing non-licensees, each symmetric bargaining set for a coalition structure is a singleton, and the optimal number of licensees that maximizes the licensor’s revenue is uniquely determined.

A cooperative game of information trading: The core, the nucleolus and the kernel

A certain trade of the information about a technological innovation between the initial owner of the information andn identical producers is studied by means of a cooperative game theoretic approach. The information trading situation is modelled as a cooperative (n+1)-person game with side payments. The symmetrical strong ɛ-cores (including the core), the nucleolus and the kernel of the cooperative game model are determined. Interpretations of these game theoretic solutions and their implications for the information trading problem are given.

Fee Versus Royalty Policy in Licensing Through Bargaining: An Application of the Nash Bargaining Solution

In this paper, we consider a Cournot duopoly market in which the patent‐holding firm negotiates with its rival firm about payments for licensing a cost‐reducing innovation. Applying the Nash bargaining solution, we compare two licensing policies, a fixed fee and a royalty. Our results are as follows. Royalty licensing is better than fixed fee licensing for both firms if the innovation is not drastic. So, royalty licensing is always carried out. Moreover, though there exists a case in which consumers prefer fixed fee licensing, royalty licensing is always superior to fixed fee licensing from the social point of view.

GENERALIZED CORES AND STABLE SETS FOR FUZZY GAMES

Core elements (a la Aubin) of a fuzzy game can be associated with additive separable supporting functions of fuzzy games. Generalized cores whose elements consist of more general separable supporting functions of the game are introduced and studied. While the Aubin core of unanimity games can be empty, the generalized core of unanimity games is nonempty. Properties of the generalized cores and their relations to stable sets are studied. For convex fuzzy games interesting properties are found such as the fact that the generalized core is a unique generalized stable set.

Resale-proofness and coalition-proof Nash equilibria

Abstract This paper studies in detail the notion of resale-proofness proposed by Nakayama, Quintas, and Muto. It is shown that, in an information trading game with one initial owner of information, the following are attained as equilibrium outcomes of the game: the perfectly coalition-proof Nash equilibria due to Bernheim, Peleg, and Whinston. If a set of informed agents is resale-proof, information never diffuses further; the initial owner shares his information with a set of demanders such that the resulting set of informed agents forms one of the minimal resale-proof sets; and the initial owner gains the whole surplus produced by the information sharing.

Bargaining outcomes in patent licensing: Asymptotic results in a general Cournot market

We study asymptotic bargaining outcomes in licensing a patented technology of an external patent holder to firms in a general Cournot market. Our results are as follows: when the number of firms is large, the bargaining set for each permissible coalition structure suggests that the patent holder should extract the entire profits of all licensees. The outcome that the bargaining finally reaches exactly coincides with the non-cooperative outcome, and it cannot be improved upon even by any objections with almost zero cost. Thus, it is strongly stable. The fair allocation represented by the Aumann-Dreze value is, however, not realized as such a stable bargaining outcome.

Farsighted Coalitional Stability of a Price Leadership Cartel

This paper analyzes the farsighted behaviour of firms that form a dominant price leadership cartel. We consider stability concepts such as the farsighted core, the farsighted stable sets, and the largest consistent set. We show that: (i) the farsighted core is either an empty set or a singleton set of the grand cartel; (ii) any Pareto efficient cartel is itself a farsighted stable set; and (iii) the set of cartels in which fringe firms enjoy higher profits than the firms in the minimal Pareto efficient cartel is the largest consistent set.

Fuzzy clan games and bi-monotonic allocation rules

In this paper the class of fuzzy clan games is introduced. The cores of such games have an interesting shape which inspires to define a class of compensation-sharing rules that are additive and stable on the cone of fuzzy clan games. Further, the notion of bi-monotonic participation allocation scheme (bi-pamas) is introduced and it turns out that each core element of a fuzzy clan game is extendable to a bi-pamas.