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).     

Fuzzy extensions of bargaining sets and their existence in cooperative fuzzy games

Recently, the concept of classical bargaining set given by Aumann and Maschler in 1964 has been extended to fuzzy bargaining set. In this paper, we give a modification to correct some weakness of this extension. We also extend the concept of the Mas-Colell's bargaining set (the other major type of bargaining sets) to its corresponding fuzzy bargaining set. Our main effort is to prove existence theorems for these two types of fuzzy bargaining sets. We will also give necessary and sufficient conditions for these bargaining sets to coincide with the Aubin Core in a continuous superadditive cooperative fuzzy game which has a crisp maximal coalition of maximum excess at each payoff vector. We show that both Aumann-Maschler and Mas-Colell fuzzy bargaining sets of a continuous convex cooperative fuzzy game coincide with its Aubin core.     

Equilibrium two-part cost structures

We consider an oligopolistic product market in which two competing firms instead of paying a competitive input price choose a two-part tariff. Costs for the input are divided up into upfront fixed costs independent of the output level and reductions in marginal costs. We explore under which competitive settings will such a two-part cost structure correspond to equilibrium behavior in a two stage game. We find that firms in a static model do have an incentive to choose a two-part cost structure when competition in the product market is not too strong and oligopoly rents can be shifted form the rival to the own firm. In a dynamic market when firms use Markov strategies competition is so intense that there are no rents to be shifted and firms do not benefit from two-part cost structures.     

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.     

拟凸对策的解

本文先引入拟凸对策的概念作为凸对策的推广,然后研究这种对策的各种解的性质。我们主要证得,当局中人数小于6或者对策的复盖严格凸时,谈判集与核心重合,核是单点集。另外,存在一个6人拟凸对策,其谈判集与核心不同。     

On a generalized Cournot oligopolistic competition game

We consider a model whereby players compete for a set of shared resources to produce and sell substitute products in the same market, which can be viewed as a generalization of the classical Cournot oligopolistic competition model, or, from a different angle, the Wardrop type routing model. In particular, we suppose that there are K players, who compete for the usage of resources as well as the sales of the end-products. Moreover, the unit costs of the shared resources and the selling prices of the products are assumed to be affine linear functions in the consumption/production quantities. We show that the price of anarchy in this case is lower bounded by 1/K, and this bound is essentially tight, which manifests the harsh nature of the competitive market for the producers.     

Infrastructure topology optimization under competition through cross-entropy

In this article, we study a two-level non-cooperative game between providers acting on the same geographic area. Each provider has the opportunity to set up a network of stations so as to capture as many consumers as possible. Its deployment being costly, the provider has to optimize both the number of settled stations as well as their locations. In the first level each provider optimizes independently his infrastructure topology while in the second level they price dynamically the access to their network of stations. The consumers’ choices depend on the perception (in terms of price, congestion and distances to the nearest stations) that they have of the service proposed by each provider. Each providers' market share is then obtained as the solution of a fixed point equation since the congestion level is supposed to depend on the market share of the provider, which increases with the number of consumers choosing the same provider. We prove that the two-stage game admits a unique equilibrium in price at any time instant. An algorithm based on the cross-entropy method is proposed to optimize the providers' infrastructure topology and it is tested on numerical examples providing economic interpretations.     

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.     

A two-person non-zero-sum game model of the world oil market

The world oil market is modelled as a two-person non-zero-sum game in normal form with each player having a continuum of strategies. The two players are the oil importing nations (OPIC) and the oil exporting nations (OPEC). The game is solved in the noncooperative sense using the equilibrium point solution concept due to Nash. The Nash equilibrium point solution yields an analytic expression for the optimal price per barrel of oil for OPEC and the optimal level of imports of oil for OPIC assuming noncooperation between the players. The cooperative solution to the game is also investigated using the von Neumann-Morgenstern negotiation set solution and Nash's bargaining point solution. Again, we give analytic expressions for the optimal price of a barrel of oil and the optimal level of imports of oil assuming that the players cooperate (negotiate, bargain, etc., for a binding agreement) in arriving at a solution.     

A simple procedure to obtain the extreme core allocations of an assignment market

Given an assignment market, we introduce a set of vectors, one for each possible ordering on the player set, which we name the max-payoff vectors. Each one of these vectors is obtained recursively only making use of the assignment matrix. Those max-payoff vectors that are efficient turn out to give the extreme core allocations of the market. When the assignment game has a large core, all the max-payoff vectors are extreme core allocations.     

交易流动性不对等环境下基于收入共享契约的供应链协调

供应链中存在单一生产商、单一零售商和一个交易流动性不对等的第三方B2B电子交易市场。在零售需求不确定的情况下,分别建立了供应链集中决策模型、传统固定合约均衡决策模型、收入共享契约分散决策模型,验证了收入共享契约在多渠道采购环境下仍可以协调供应链,分析了使供应链达到帕累托改进的收入共享契约的参数设定,最后分别从卖出流动性和买入流动性两个角度讨论了交易流动性对供应链的影响。研究结果表明,卖出流动性好的电子交易市场可以促使供应链达到最优生产量,实现整体收益的最大化;两种交易流动性的趋好都会提高供应链效率,但生产商更偏好卖出流动性好的电子交易市场。     

Optimal warranties,reliabilities and prices for durable goods in an oligopoly

This paper addresses the problem of durable goods manufacturers in an oligopoly seeking optimal values for three decision variables: product warranty, reliability and price. Each firm seeks a warranty-reliability-price combination that maximizes expected profit subject to quite general constraints on the firm's decision variables. Warranty serves as a signal of product reliability, which is not observable by consumers. We present a game-theoretic model of warranty-reliability-price competition in such a market and examine Nash equilibria for this game. We show that under fairly general assumptions each firm can optimally set its warranty and reliability independently of price and competitors' actions. In addition, we show that optimal warranties and reliabilities are complementary, and we explore the impact of different market factors on the optimal warranty and reliability. Finally, we show that optimal warranties are longer and products more reliable when consumers are risk averse.     

可再生能源价格政策在寡头竞争市场中的比较

在考虑可再生能源发电间歇性和电力企业两阶段决策过程的前提下,建立了度电补贴和配额制政策下的电力市场寡头垄断竞争模型并进行了分析。以以色列电力市场的数据进行数值实验,分析了电力企业数量、补贴价格、可再生能源电力配额、投资费用等关键因素对发电容量投资的影响。考虑到政策的福利效应,比较了度电补贴和配额制政策下电力价格、消费者剩余和社会福利的差异。     

On the bargaining set, kernel and core of superadditive games

We prove that for superadditive games a necessary and sufficient condition for the bargaining set to coincide with the core is that the monotonic cover of the excess game induced by a payoff be balanced for each imputation in the bargaining set. We present some new results obtained by verifying this condition for specific classes of games. For N-zero-monotonic games we show that the same condition required at each kernel element is also necessary and sufficient for the kernel to be contained in the core. We also give examples showing that to maintain these characterizations, the respective assumptions on the games cannot be lifted. Received: March 1998/Revised version: December 1998     

A three-person cooperative game formulation of the world oil market

The world oil market is modelled as a three-person cooperative game in characteristic function form with and without side payments. The three players are the oil importing countries, the group in OPEC led by Iran and the group in OPEC led by Saudi Arabia. Various solutions of the games are studied such as the core, the Shapley value, the bargaining set and the nucleolus.     

The maximum and the addition of assignment games

In the framework of two-sided assignment markets, we first consider that, with several markets available, the players may choose where to trade. It is shown that the corresponding game, represented by the maximum of a finite set of assignment games, may not be balanced. Some conditions for balancedness are provided and, in that case, properties of the core are analyzed. Secondly, we consider that players may trade simultaneously in more than one market and then add up the profits. The corresponding game, represented by the sum of a finite set of assignment games, is balanced. Moreover, under some conditions, the sum of the cores of two assignment games coincides with the core of the sum game.     

Nash bargaining solution under externalities

We define a Nash bargaining solution (NBS) of partition function games. Based on a partition function game, we define an extensive game, which is a propose–respond sequential bargaining game where the rejecter of a proposal exits from the game with some positive probability. We show that the NBS is supported as the expected payoff profile of any stationary subgame perfect equilibrium (SSPE) of the extensive game such that in any subgame, a coalition of all active players forms immediately. We provide a necessary and sufficient condition for such an SSPE to exist. Moreover, we consider extensions to the cases of nontransferable utilities, time discounting and multiple-coalition formation.     

Stationary perfect equilibria of an n-person noncooperative bargaining game and cooperative solution concepts

This paper characterizes the stationary (subgame) perfect equilibria of an n-person noncooperative bargaining model with characteristic functions, and provides strategic foundations of some cooperative solution concepts such as the core, the bargaining set and the kernel. The contribution of this paper is twofold. First, we show that a linear programming formulation successfully characterizes the stationary (subgame) perfect equilibria of our bargaining game. We suggest a linear programming formulation as an algorithm for the stationary (subgame) perfect equilibria of a class of n-person noncooperative games. Second, utilizing the linear programming formulation, we show that stationary (subgame) perfect equilibria of n-person noncooperative games provide strategic foundations for the bargaining set and the kernel.     

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.