Bargaining on whales: A differential game model with pareto optimal equilibria

A two-country differential game model of whaling is used for analysing a dynamic bargaining problem. At a given initial time, the two countries may either continue on a noncooperative mood of play characterized by an open-loop Nash-equilibrium, or negotiate a bargaining solution which we define as the Kalaï-Smorodinsky solution. The cooperative solution calls for a restraint in the whaling efforts which leaves a temptation to cheat for any player. The model shows how, by announcing a credible threat, namely to make whaling an ‘open-access’ fishery, a country can eliminate this temptation to cheat and transform the cooperative solution into an equilibrium.     

Multiple-issue bargaining and axiomatic solutions

We study two-person, multiple-issue bargaining problems and identify four procedures by which the bargaining may take place. Drawing on some logic from non-cooperative game theory, we propose axioms which relate the outcomes of the procedures. We also promote a weak monotonicity axiom on solutions, called issue-by-issue monotonicity, which is geared toward multiple-issue bargaining. Our main result concerns the relationship between a sequential bargaining procedure — with the rule that agreements are implemented only after all issues are resolved — and global bargaining (in which all issues are negotiated simultaneously). If a bargaining solution predicts the same outcome with these two procedures, then we say that it satisfiesagenda independence. We prove that a solution satisfies axioms of efficiency, symmetry, scale invariance, issue-by-issue monotonicity, and agenda independence if and only if it is the Nash solution. This result provides new intuition for Nash's independence of irrelevant alternatives axiom. Among other results, we show that a solution is invariant to all four of the procedures and satisfies efficiency and symmetry if and only if it is the utilitarian solution with equal weights. We comment on the results of other authors who address multiple-issue bargaining.     

Bargaining order and delays in multilateral bargaining with heterogeneous sellers

We consider a complete-information multilateral bargaining game in which a single buyer negotiates with two heterogeneous sellers selling perfect complementary units. While bilateral negotiations take place through a sequence of offers and counteroffers, the bargaining order is exogenously given. We solve for the conditions under which (a) the buyer prefers to negotiate with the lower-valuation seller first and (b) efficient (inefficient) outcomes emerge for the two bargaining orders. We find that the buyer prefers to negotiate with the lower-valuation seller first whenever the players are relatively impatient or the sellers are sufficiently heterogeneous. We show that there exists a unique efficient outcome when the buyer negotiates first with the lower-valuation seller and the sellers are sufficiently heterogeneous; however, significant delay in reaching agreements may arise when they are not. In case the buyer bargains with the higher-valuation seller first, an inefficient outcome is shown to exist even when players are extremely impatient.     

On the non-emptiness of the one-core and the bargaining set of committee games

We study the committee decision making process using game theory. Shenoy  [15] introduced two solution concepts: the one-core and the bargaining set, and showed that the one-core of a simple committee game is nonempty if there are at most four players. We extend this result by proving that whether the committee is simple or not, as far as there are less than five players, the one-core is nonempty. This result also holds for the bargaining set.     

Timing and eco(nomic) efficiency of climate-friendly investments in supply chains

Emission trading schemes such as the European Union Emissions Trading System (EUETS) attempt to reconcile economic efficiency with ecological efficiency by creating financial incentives for companies to invest in climate-friendly innovations. Using real options methodology, we demonstrate that under uncertainty, economic and ecological efficiency continue to be mutually exclusive. This problem is even worse if a climate-friendly project depends on investing in of a whole supply chain. We model a sequential bargaining game in a supply chain where the parties negotiate over implementation of a carbon dioxide (CO₂) saving investment project. We show that the outcome of their bargaining is not economically efficient and even less ecologically efficient. Furthermore, we show that a supply chain becomes less economically efficient and less ecologically efficient with every additional chain link. Finally, we make recommendations for how managers or politicians can improve the situation and thereby increase economic as well as ecological efficiency and thus also the eco-efficiency of supply chains.     

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.     

Aubin cores and bargaining sets for convex cooperative fuzzy games

In this paper, we deal with Aubin cores and bargaining sets in convex cooperative fuzzy games. We first give a simple and direct proof to the well-known result (proved by Branzei et al. (Fuzzy Sets Syst 139:267–281, 2003)) that for a convex cooperative fuzzy game v, its Aubin core C(v) coincides with its crisp core C ^cr (v). We then introduce the concept of bargaining sets for cooperative fuzzy games and prove that for a continuous convex cooperative fuzzy game v, its bargaining set coincides with its Aubin core, which extends a well-known result by Maschler et al. for classical cooperative games to cooperative fuzzy games. We also show that some results proved by Shapley (Int J Game Theory 1:11–26, 1971) for classical decomposable convex cooperative games can be extended to convex cooperative fuzzy games.     

Share the gain,share the pain? Almost transferable utility,changes in production possibilities,and bargaining solutions

We consider an n-person economy in which efficiency is independent of distribution but the cardinal properties of the agents’ utility functions may preclude transferable utility (a property we call “Almost TU”). Holding the disagreement point fixed, we show that Almost TU is a necessary and sufficient condition for all agents to either benefit jointly or suffer jointly with any change in production possibilities under well-behaved generalized utilitarian bargaining solutions (of which the Nash bargaining and the utilitarian solutions are special cases). We apply the result to policy analysis and to incentive compatibility.     

Game theoretic analysis of the bargaining process over a long-term replenishment contract

This paper presents supplier–buyer models to describe the bargaining process between a supplier and a buyer over a long-term replenishment contract. Two different models are developed: one for the situation where the supplier has superior bargaining power over the buyer, and the other for the reverse situation. For each model, a method is derived that employs game theory-based analysis to determine the best strategy for each agent. A computational experiment is conducted to estimate the efficiency of the methods and to determine the economic implications of the results. The result indicates that each algorithm is very efficient compared to other strategies. We also verify that the solutions derived from each model are Nash equilibrium. Significantly improved outcomes are obtained for both agents by agreeing to the terms generated by the algorithms over the terms selected in the usual manner.     

Sequential share bargaining

This paper presents a new extension of the Rubinstein-St?hl bargaining model to the case with n players, called sequential share bargaining. The bargaining protocol is natural and has as its main feature that the players’ shares in the surplus are determined sequentially rather than simultaneously. The protocol also assumes orderly voting, a restriction on the order in which players respond to a proposal. The bargaining protocol requires unanimous agreement for proposals to be implemented. Unlike all existing bargaining protocols with unanimous agreement, the resulting game has unique subgame perfect equilibrium utilities for any value of the discount factor. The result builds on the analysis of so-called one-dimensional bargaining problems. We show that also one-dimensional bargaining problems have unique subgame perfect equilibrium utilities for any value of the discount factor.     

基于合作博弈纳什议价的几种网络定价结构模型比较

本文基于目前的网络资费模式,提炼出三种网络定价结构模型,研究本地网络服务提供商(ISP)及用户之间的利润分配.首先,利用一个简化的网络业务质量(Qos)保证模型构造目标函数,说明合作博弈得到的解比非合作博弈情形下更优,合作博弈时得到纳什议价解与双方的相对议价权力有关.然后,从社会结构理论角度,说明议价权力取决于网络结构类型以及局中人在结构中所处的位置.相对议价权力大,获益较多;相对议价权力小,获益较少.最后,通过实例分析得到三种网络定价结构模型下的纳什议价解.结果表明,本地网络服务提供商的合并、收购、互联有利于提高其相对议价权力,从而获益增加.     

三方相互体谅讨价还价模型

对于较重要的三方合作利益分配博弈问题,将相互体谅作为基本遵循并基于适应性预期模型,建立三方相互体谅讨价还价模型.运用这个模型,可以把三方相互体谅讨价还价达成均衡,归结为单调有界数列收敛与常系数非齐次线性差分方程组求解的结合运用.三方相互体谅讨价还价属于不完全信息动态合作博弈.对模型求解,一般地揭示三方相互体谅讨价还价达成均衡的过程与结果,阐明讨价还价有满足初始条件的唯一解和充要条件,以及充要条件的经济含义和数学意义.三方相互体谅讨价还价模型是对于两方相互体谅讨价还价模型的拓展,可以为建立更多方相互体谅讨价还价模型提供借鉴.     

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.     

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.     

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.     

Equilibrium selection in a bargaining problem with transaction costs

It is the purpose of the paper to analyse a bargeining situation with the help of the equilibrium selection theory of John C. Harsanyi and Reinhard Selten. This theory selects one equilibrium point in every finite non-cooperative game. The bargaining problem is the following one: the two bargainers — player 1 and player 2 — simultaneously and independently propose a payoffx of player 1 in the interval 〈0, 1〉. If agreement is reached player 2's payoffs is 1?x. Otherwise both receive zero. Each playeri has a further alternativeW _i , namely not to bargain at all (i=1, 2). Thereby he avoids transaction costsc andd of bargaining which arise whether an agreement is reached or not. One may think of an illegal deal where bargaining involves a risk of being punished — independently whether the deal is made or not. The model has the form of a (K+1)×(K+1)-bimatrix game. It is assumed that there is an indivisable smallest money unit. The game hasK+1 pure strategy equilibrium points.K of them correspond to an agreement and the last one is the strategy pair where both players refuse to bargain. Each of theK+1 equilibrium points can be the solution of the game. The aim of the Harsanyi-Selten-theory is to select in a unique way one of these equilibrium points by an iterative process of elimination (by payoff dominance and risk dominance relationships) and substitution. For each parameter combination (c, d) a sequence of candidate sets arises which becomes smaller and smaller until finally a candidate set with exactly one equilibrium point — the solution of the game — is found. For the sake of shortness the paper will report results without detailed proofs, which can be found elsewhere [Leopold-Wildburger].     

A bargaining game model for measuring performance of two-stage network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs), where the internal structures of DMUs are treated as a black-box. Recently DEA has been extended to examine the efficiency of DMUs that have two-stage network structures or processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The current paper develops a Nash bargaining game model to measure the performance of DMUs that have a two-stage structure. Under Nash bargaining theory, the two stages are viewed as players and the DEA efficiency model is a cooperative game model. It is shown that when only one intermediate measure exists between the two stages, our newly developed Nash bargaining game approach yields the same results as applying the standard DEA approach to each stage separately. Two real world data sets are used to demonstrate our bargaining game model.     

Share the gain, share the pain? Almost transferable utility, changes in production possibilities, and bargaining solutions

We consider an n-person economy in which efficiency is independent of distribution but the cardinal properties of the agents’ utility functions may preclude transferable utility (a property we call “Almost TU”). Holding the disagreement point fixed, we show that Almost TU is a necessary and sufficient condition for all agents to either benefit jointly or suffer jointly with any change in production possibilities under well-behaved generalized utilitarian bargaining solutions (of which the Nash bargaining and the utilitarian solutions are special cases). We apply the result to policy analysis and to incentive compatibility.     

Nash equilibria in optimal reinsurance bargaining

We introduce a strategic behavior in reinsurance bilateral transactions, where agents choose the risk preferences they will appear to have in the transaction. Within a wide class of risk measures, we identify agents’ strategic choices to a range of risk aversion coefficients. It is shown that at the strictly beneficial Nash equilibria, agents appear homogeneous with respect to their risk preferences. While the game does not cause any loss of total welfare gain, its allocation between agents is heavily affected by the agents’ strategic behavior. This allocation is reflected in the reinsurance premium, while the insurance indemnity remains the same in all strictly beneficial Nash equilibria. Furthermore, the effect of agents’ bargaining power vanishes through the game procedure and the agent who gets more welfare gain is the one who has an advantage in choosing the common risk aversion at the equilibrium.     

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.