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. The authors wish to thank the chief editor, anonymous referees, and participants in the 10th DC (Japan), the 3rd ICMA, and the 17th Stony Brook conference for helpful comments and suggestions. Thanks are extended to Ryo Kawasaki for editing English. They are partially supported by the MEXT Grant-in-Aid for 21 Century COE Program, Grant-in-Aid 18730517 (Watanabe), and Grant-in-Aid 16310107 (Muto).     

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-Drèze value is, however, not realized as such a stable bargaining outcome.     

Stable bargaining outcomes in patent licensing: A cooperative game approach without side payments

By formulating negotiations about licensing payments as cooperative games without side payments, we investigate stable bargaining outcomes in licensing a cost-reducing technology of an external patent holder to oligopolistic firms producing a homogeneous product under two policies: fee and royalty. The final bargaining outcome in fee licensing is uniquely determined, because the bargaining set for a coalition structure in which the patent holder can gain the maximum profit is a singleton. Under the royalty policy, the non-empty core for a coalition structure suggests that the patent holder should license his patented technology to all firms. Moreover, royalty licensing may be superior to fee licensing for the patent holder, when licensing is carried out through bargaining.     

双寡头垄断结构下的技术授权及社会福利分析——基于内生技术创新的视角

在具有水平差异且进行古诺竞争的双寡头结构中考虑技术拥有企业内生决定降低成本技术的创新程度,分析不同授权方式下技术拥有者利润、消费者剩余以及社会总福利的变化,并对不同授权方式下的技术创新程度进行比较。研究表明:技术拥有者通过双重收费、特许权收费方式总能实现利润增加,且双重收费方式能带来最大利润,而固定收费方式可能降低其利润;固定收费方式下消费者剩余、社会总福利高于双重收费,更高于特许权收费方式;技术创新程度与技术授权方式以及产品替代程度有关,且无论产品的替代程度如何,双重收费方式下的技术创新程度达到最大。     

The collective value: a new solution for games with coalition structures

In this study, we provide a new solution for cooperative games with coalition structures. The collective value of a player is defined as the sum of the equal division of the pure surplus obtained by his coalition from the coalitional bargaining and of his Shapley value for the internal coalition. The weighted Shapley value applied to a game played by coalitions with coalition-size weights is assigned to each coalition, reflecting the size asymmetries among coalitions. We show that the collective value matches exogenous interpretations of coalition structures and provide an axiomatic foundation of this value. A noncooperative mechanism that implements the collective value is also presented.     

Cooperative games with coalition structures

Many game-theoretic solution notions have been defined or can be defined not only with reference to the all-player coalition, but also with reference to an arbitrary coalition structure. In this paper, theorems are established that connect a given solution notion, defined for a coalition structure ? with the same solution notion applied to appropriately defined games on each of the coalitions in ?. This is done for the kernel, nucleolus, bargaining set, value, core, and thevon Neumann-Morgenstern solution. It turns out that there is a single function that plays the central role in five out of the six solution notions in question, though each of these five notions is entirely different. This is an unusual instance of a game theoretic phenomenon that does not depend on a particular solution notion but holds across a wide class of such notions.     

SHARING THE BENEFITS OF COOPERATION IN HIGH SEAS FISHERIES: A CHARACTERISTIC FUNCTION GAME APPROACH

In the current paper we examine a game-theoretic setting in which three countries have established a regional organization for the conservation and management of straddling and highly migratory fish stocks. A characteristic function game approach is applied to describe the sharing of the surplus benefits from cooperation. We demonstrate that the nucleolus and the Shapley value give more of the benefits to the coalition with substantial bargaining power than does the Nash bargaining scheme. We also compare the results that are obtained by using the nucleolus and the Shapley value as solution concepts. The outcomes from these solution concepts depend on the relative efficiency of the most efficient coalition. Furthermore, the question of fair sharing of the benefits is considered in the context of straddling stocks.     

A bargaining set for monotonic simple games based on external and internal stability

A new bargaining set based on notions of both internal and external stability is developed in the context of endogenous coalition formation. It allows one to make an explicit distinction between within-group and outside-group deviation options. This type of distinction is not present in current bargaining sets. For the class of monotonic proper simple games, the outcomes in the bargaining set are characterized. Furthermore, it is shown that the bargaining set of any homogeneous weighted majority game contains an outcome for which the underlying coalition structure consists of a minimal winning coalition and its complement.     

Bargaining set theory and stability in coalition governments

Various bargaining set theories are compared as predictors of coalition government portfolio distribution. While the kernel and B₁-bargaining set are known to exist in voting games with side payments, it is argued that the kernel, and thus B₁, are poor predictors. The B₂-bargaining set, a subset of B₁, when it exists is shown to be a good payoff predictor in a fractionalized and depolarized parliamentary situation (Finland: 1945ndash;1971). Moreover this predictor provides some explanation for the formation of surplus (winning but not minimal) coalitions.     

Noncooperative formation of coalitions in hedonic games

We study a bargaining procedure of coalition formation in the class of hedonic games, where players’ preferences depend solely on the coalition they belong to. We provide an example of nonexistence of a pure strategy stationary perfect equilibrium, and a necessary and sufficient condition for existence. We show that when the game is totally stable (the game and all its restrictions have a nonempty core), there always exists a no-delay equilibrium generating core outcomes. Other equilibria exhibiting delay or resulting in unstable outcomes can also exist. If the core of the hedonic game and its restrictions always consist of a single point, we show that the bargaining game admits a unique stationary perfect equilibrium, resulting in the immediate formation of the core coalition structure.     

市场力量、谈判能力与专利许可的Shapley值

分别在国内市场力量能否形成谈判能力的条件下,讨论了一个国外专利权人对两个国内厂商进行专利许可的两种谈判结果.若市场力量不能形成谈判能力,则国外专利权人将获得许可创造的全部利润;若市场力量能够形成谈判能力,则可能形成一种较为公平的、专利许可的Shapley值.结合现实中的专利许可实务,提出了将市场力量转化为谈论能力的建议.     

The kernel and bargaining set for convex games

It is shown that for convex games the bargaining set? ₁ ⁽ⁱ⁾ (for the grand coalition) coincides with the core. Moreover, it is proved that the kernel (for the grand coalition) of convex games consists of a unique point which coincides with the nucleolus of the game.     

Cooperative game analysis of retail space-exchange problems

We analyze retail space-exchange problems where two or more retailers exchange their excess retail spaces to improve the utilization of their space resource. We first investigate the two-retailer space exchange problem. In order to entice both retailers with different bargaining powers to exchange their spaces, we use the generalized Nash bargaining scheme to allocate the total profit surplus between the two retailers. Next, we consider the space-exchange problem involving three or more retailers, and construct a cooperative game in characteristic function form. We show that the game is essential and superadditive, and also prove that the core is non-empty. Moreover, in order to find a unique allocation scheme that ensures the stability of the grand coalition, we propose a new approach to compute a weighted Shapley value that satisfies the core conditions and also reflects retailers’ bargaining powers. Our analysis indicates that the space exchange by more retailers can result in a higher system-wide profit surplus and thus a higher allocation to each retailer under a fair scheme.     

The core and the bargaining set in glove-market games

In a glove-market game, the worth of a coalition is defined as the minimum, over all commodities in the market, of the total quantity that the coalition owns of each commodity. We identify a subclass of these games for which the core and the bargaining set coincide with the set of competitive equilibrium outcomes. We present examples showing that these solution concepts differ outside that subclass. We also illustrate a peculiar behavior of the bargaining set with respect to replication of a glove-market. These examples provide a simple economic setting in which the merits of the various solution concepts may be discussed and compared.Correspondence with Michael Maschler is gratefully acknowledged.This authors work was partly done while visiting the Department of Mathematics, Massachusetts Institute of Technology. Research supported by the Fund for the Promotion of Research at the Technion.     

The bargaining set of four-person balanced games

It is well known that in three-person transferable-utility cooperative games the bargaining set ℳⁱ ₁ and the core coincide for any coalition structure, provided the latter solution is not empty. In contrast, five-person totally-balanced games are discussed in the literature in which the bargaining set ℳⁱ ₁ (for the grand coalition) is larger then the core. This paper answers the equivalence question in the remaining four-person case. We prove that in any four-person game and for arbitrary coalition structure, whenever the core is not empty, it coincides with the bargaining set ℳⁱ ₁. Our discussion employs a generalization of balancedness to games with coalition structures. Received: August 2001/Revised version: April 2002     

On the Structural Stability of Values for Cooperative Games

It is generally assumed that any set of players can form a feasible coalition for classical cooperative games. But, in fact, some players may withdraw from the current game and form a union, if this makes them better paid than proposed. Based on the principle of coalition split, this paper presents an endogenous procedure of coalition formation by levels and bargaining for payoffs simultaneously, where the unions formed in the previous step continue to negotiate with others in the next step as “individuals,” looking for maximum share of surplus by organizing themselves as a partition. The structural stability of the induced payoff configuration is discussed, using two stability criteria of core notion for cooperative games and strong equilibrium notion for noncooperative games.

     

专利池形成中的厂商数量门槛值因素分析

专利池的主要功能在于降低专利许可的交易成本, 而该成本随着专利持有厂商数量增加而递增。针对这种专利持有厂商数量与专利池形成之间的关系, 在博弈论框架内, 分是否形成专利池、决定对外授权规模和产品市场竞争三个博弈阶段, 分析了交易成本、专利许可费率对专利池形成所要求的最低专利持有厂商数量的影响。研究结论表明专利池的形成对专利持有厂商数量有一个门槛值要求, 该门槛值随交易成本和专利许可费率反向变化。同时, 专利许可费率存在一个与专利持有厂商数量相关的边界值, 低于该边界值, 专利池最佳对外授权规模随着许可费率而递增, 高于该边界值, 最佳对外授权规模随着许可费率而下降, 在边界值处最佳对外授权规模达到最大值。     

关于研发机构非显著工艺创新的最优许可研究

研发机构创新成功后,应该重视知识资产的主动管理,在专利许可谈判中科学合理地确定专利许可策略,以追求收益最大化.本文的目的是进一步完善与具体化Kamien,Tauman与Oren(1992)的模型,深入研究研发机构在不同许可机制下对在位厂商的非显著创新许可收益,以及最优许可策略选择.主要结论是:给定厂商数量,当创新规模较小时,研发机构的最优策略为提成许可,其次是不限许可数量的F(F)许可与一级价格密封投标拍卖许可;当创新规模较大时,研发机构的最优策略为拍卖许可,提成许可次之,最后是不限许可数量的F(F)许可.     

A non-cooperative interpretation of the kernel

The purpose of the paper is to propose a bargaining game to interpret the kernel non-cooperatively. Based on the idea of the Davis-Maschler reduced game, a bilateral bargaining procedure is provided in our game model. We show that the set of all subgame perfect equilibrium outcomes of our non-cooperative game coincides with the kernel for transferable utility games.     

Coalitions and payoffs in three‐person sequential games: Initial tests of two formal models

In this paper we develop two formal models predicting coalitions and payoffs among rank striving players in a sequential three‐person game. We test the models’ predictions with data from a laboratory study of eleven male triads. Each triad plays a sequence of games; in each game a two‐person coalition forms and divides the coalition's point value between the two coalition partners. Participants know that the sequence of games will end without warning at a randomly chosen time; at the sequence's end each player's monetary payoff is a linear function of the rank of his accumulated point score, relative to those of the other members of his triad. The complexity of this situation prevents players and analysts from representing it as a single game; thus they are unable to use n‐person game theory to identify optimal strategies. Consequently, we assume that players, unable to develop strategies that are demonstrably optimal in the long run, adopt certain bargaining heuristics and surrogate short run objectives.

The two models follow the same basic outline; they differ, however, in the planning horizon they assume players to use. Proceeding from a priori assumptions concerning each player's decision calculus and the bargaining process, the two models state the probability that each coalition forms and predict the point divisions in the winning coalition. The laboratory data provide consistently strong support for the predictions of both models.