Farsightedness and Cautiousness in Coalition Formation Games with Positive Spillovers

We adopt the largest consistent set defined by Chwe (1994; J. Econ. Theory 63: 299–325) to predict which coalition structures are possibly stable when players are farsighted. We also introduce a refinement, the largest cautious consistent set, based on the assumption that players are cautious. For games with positive spillovers, many coalition structures may belong to the largest consistent set. The grand coalition, which is the efficient coalition structure, always belongs to the largest consistent set and is the unique one to belong to the largest cautious consistent set.     

A Banzhaf share function for cooperative games in coalition structure

A cooperative game with transferable utility–or simply a TU-game– describes a situation in which players can obtain certain payoffs by cooperation. A value function for these games assigns to every TU-game a distribution of payoffs over the players. Well-known solutions for TU-games are the Shapley and the Banzhaf value. An alternative type of solution is the concept of share function, which assigns to every player in a TU-game its share in the worth of the grand coalition. In this paper we consider TU-games in which the players are organized into a coalition structure being a finite partition of the set of players. The Shapley value has been generalized by Owen to TU-games in coalition structure. We redefine this value function as a share function and show that this solution satisfies the multiplication property that the share of a player in some coalition is equal to the product of the Shapley share of the coalition in a game between the coalitions and the Shapley share of the player in a game between the players within the coalition. Analogously we introduce a Banzhaf coalition structure share function. Application of these share functions to simple majority games show some appealing properties.     

Game-theoretic analyses of coalition behavior

Coalitions are frequently more visible than payoffs. The theory of n-person games seeks primarily to identify stable allocations of valued resources; consequently, it gives inadequate attention to predicting which coalitions form. This paper explores a way of correcting this deficiency of game-theoretic reasoning by extending the theory of two-person cooperative games to predict both coalitions and payoffs in a three-person game of status in which each player seeks to maximize the rank of his total score. To accomplish this, we analyze the negotiations within each potential two-person coalition from the perspective of Nash's procedure for arbitrating two-person bargaining games, then assume that players expect to achieve the arbitrated outcome selected by this procedure and use these expectations to predict achieved ranks and to identify players' preferences between alternative coalition partners in order to predict the probability that each coalition forms. We test these payoff and coalition predictions with data from three laboratory studies, and compare the results with those attained in the same data by von Neumann and Morgenstern's solution of two-person cooperative games, Aumann and Maschler's bargaining set solution for cooperative n-person games, and an alternative model of coalition behavior in three-person sequential games of status.

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Population monotonic path schemes for simple games

A path scheme for a game is composed of a path, i.e., a sequence of coalitions that is formed during the coalition formation process and a scheme, i.e., a payoff vector for each coalition in the path. A path scheme is called population monotonic if a player’s payoff does not decrease as the path coalition grows. In this study, we focus on Shapley path schemes of simple games in which for every path coalition the Shapley value of the associated subgame provides the allocation at hand. Obviously, each Shapley path scheme of a game is population monotonic if and only if the Shapley allocation scheme of the game is population monotonic in the sense of Sprumont (Games Econ Behav 2:378–394, 1990). We prove that a simple game allows for population monotonic Shapley path schemes if and only if the game is balanced. Moreover, the Shapley path scheme of a specific path is population monotonic if and only if the first winning coalition that is formed along the path contains every minimal winning coalition. We also show that each Shapley path scheme of a simple game is population monotonic if and only if the set of veto players of the game is a winning coalition. Extensions of these results to other efficient probabilistic values are discussed.     

The role of risk preferences in bargaining when acceptance of a proposal requires less than unanimous approval

The role of risk preferences in determining the outcome to bargaining is examined for the case in which acceptance of a proposal requires less than unanimous approval. Using an n-agent extension of the Ståhl-Rubinstein alternating offer model, we find that risk preferences play a fundamentally different role when bargaining is settled using a nonunanimity voting rule. Risk preferences determine not only an agent's reservation price but also the likelihood that he is made part of the winning coalition. An implication of this analysis is that when the preferences of the agents are not too diverse, it is advantageous for an agent to be relatively risk-averse.The helpful comments and suggestions of Rich McLean and an anonymous referee are gratefully acknowledged. This article was presented as a paper at the 1988 Winter Econometric Society Meetings.     

知识产权的优化配置(英文)

产权明晰可以通过自由交易实现资源优化配置,因其权威性,科斯定理的这一思想在知识产权领域的应用很少受到人们的置疑。本文拟从知识产权特性出发,分析科斯定理产权黑箱思想对知识产权生产的适用性、科斯定理隐含的福利原则和知识传播的公平性的影响,揭示完全遵从科斯定理建立、执行知识产权制度的弊端,为优化知识产权配置寻找新的理论基础。     

Stable coalition structures in symmetric majority games: a coincidence between myopia and farsightedness

The objective of this paper is to study stable coalition structures in symmetric majority games. We assume that players deviate from a coalition structure to another to maximize their power given by the Owen power index. We introduce three myopic core concepts and one farsighted stability concept, the farsighted vNM stable set. Our main result is that the pessimistic core, the largest myopic core, coincides with some farsighted vNM stable set for any number of players. Moreover, we show that a coalition structure belongs to the pessimistic core and the farsighted vNM stable set if and only if it contains an exact majority coalition.     

Socially Structured Games

We generalize the concept of a cooperative non-transferable utility game by introducing a socially structured game. In a socially structured game every coalition of players can organize themselves according to one or more internal organizations to generate payoffs. Each admissible internal organization on a coalition yields a set of payoffs attainable by the members of this coalition. The strengths of the players within an internal organization depend on the structure of the internal organization and are represented by an exogenously given power vector. More powerful players have the power to take away payoffs of the less powerful players as long as those latter players are not able to guarantee their payoffs by forming a different internal organization within some coalition in which they have more power. We introduce the socially stable core as a solution concept that contains those payoffs that are both stable in an economic sense, i.e., belong to the core of the underlying cooperative game, and stable in a social sense, i.e., payoffs are sustained by a collection of internal organizations of coalitions for which power is distributed over all players in a balanced way. The socially stable core is a subset and therefore a refinement of the core. We show by means of examples that in many cases the socially stable core is a very small subset of the core. We will state conditions for which the socially stable core is non-empty. In order to derive this result, we formulate a new intersection theorem that generalizes the KKMS intersection theorem. We also discuss the relationship between social stability and the wellknown concept of balancedness for NTU-games, a sufficient condition for non-emptiness of the core. In particular we give an example of a socially structured game that satisfies social stability and therefore has a non-empty core, but whose induced NTU-game does not satisfy balancedness in the general sense of Billera.      

An Alternative Model of the Formation of Political Coalitions

Most models of the formation of political coalitions use either Euclidean spaces or rely purely on game theory. This limits their applicability. In this article, a single model is presented which is more broadly applicable. In principle any kind of set can be used as a policy space. The model is also able to incorporate different kinds of party motivations: both rent-seeking and idealism. The model uses party preferences and power to identify stable coalitions and predict government policy as well as to indicate which member of the opposition will be able to break up the governing coalition if no stable coalition exists. In the latter case it will also indicate on which issue the government is likely to split. Parties may have preferences over issues such as the composition of cabinet and/or the governing coalition as well as the more traditional issues of government formation. The model also provides a rationale for log-rolling.     

BARGAINING AND DELAY: THE ROLE OF EXTERNAL INFORMATION

This paper examines the notion that delay in reaching agreement in bargaining may be caused by learning that is independent of the bargaining procedure. In particular, learning is not due to inference from the observed offers and responses of the opponent, but derives from observation of an exogenous, costly signal – we call this 'investigation'. First we observe that even if learning is costless and perfectly informative, investigation may not occur in equilibrium. Under more general conditions, however, uninformed agents typically have an incentive to try to manipulate their prior beliefs through investigation. The main result is that investigation by an uninformed agent may result in significant delay occurring before agreement is reached. We show that this delay may be sustained in the limit as the length of time period vanishes, and that this result depends crucially on the properties of the information production technology underlying investigation. Also, the delay we observe is shown to be robust to changes in the bargaining procedure.     

Bargaining Solutions as Social Compromises

A bargaining solution is a social compromise if it is metrically rationalizable, i.e., if it has an optimum (depending on the situation, smallest or largest) distance from some reference point. We explore the workability and the limits of metric rationalization in bargaining theory where compromising is a core issue. We demonstrate that many well-known bargaining solutions are social compromises with respect to reasonable metrics. In the metric approach, bargaining solutions can be grounded in axioms on how society measures differences between utility allocations. Using this approach, we provide an axiomatic characterization for the class of social compromises that are based on p-norms and for the attending bargaining solutions. We further show that bargaining solutions which satisfy Pareto Optimality and Individual Rationality can always be metrically rationalized.     

从技科学视角看哥本哈根世界气候大会

技科学（technoscience）是指科学并非独立于社会、政治与经济之外,它是一种建构性的实践活动,并处在一张由人类因素和非人类因素等异质性力量构成的动态无缝之网中,其中,政治、科学、技术、社会、自然等各因素相互缠绕在一起,无法分开。哥本哈根世界气候大会的目标是各种谈判力量在所谓科学“证据”的基础上相互博弈,建立起某种行动者网络或联盟,即达成一份新协议。但由于各方的科学“证据”分歧太大,这种联盟无法建立,会议也几近失败。因此,虽然发达国家与发展中国家之间有学术交流的公平原则,但他们在气候研究方面的不对称性同样导致了极不公平的政治与经济后果。中国要改变这种不对称地位,就应加强相对自主的气候科研,争取更多的气候科学话语权。     

On arguments from self-interest for the Nash solution and the Kalai egalitarian solution to the bargaining problem

I argue in this paper that there are two considerations which govern the dynamics of a two-person bargaining game, viz. relative proportionate utility loss from conceding to one's opponent's proposal and relative non-proportionate utility loss from not conceding to one's opponent's proposal, if she were not to concede as well. The first consideration can adequately be captured by the information contained in vNM utilities. The second requires measures of utility which allow for an interpersonal comparison of utility differences. These considerations respectively provide for a justification of the Nash solution and the Kalai egalitarian solution. However, none of these solutions taken by themselves can provide for a full story of bargaining, since, if within a context of bargaining one such consideration is overriding, the solution which does not match this consideration will yield unreasonable results. I systematically present arguments to the effect that each justification from self-interest for respectively the Nash and the Kalai egalitarian solution is vulnerable to this kind of objection. I suggest that the search for an integrative model may be a promising line of research.I am grateful to Jon Elster, A. Hylland, F. Spinnewijn, J. Verhoeven and the members of the research group for theoretical sociology in the K.U.L. for their comments on an earlier version of this paper. I also thank the Ministry for Foreign Affairs (Norway) for its financial support and the members of the department of sociology in the University of Oslo for their hospitality and interest in my work.     

Unanimity and Resource Monotonicity

In the context of indivisible public objects problems (e.g., candidate selection or qualification) with “separable” preferences, unanimity rule accepts each object if and only if the object is in everyone’s top set. We establish two axiomatizations of unanimity rule. The main axiom is resource monotonicity, saying that resource increase should affect all agents in the same direction. This axiom is considered in combination with simple Pareto (there is no Pareto improvement by addition or subtraction of a single object), independence of irrelevant alternatives, and either path independence or strategy-proofness.     

On the emptiness of the stability set of order d

We know from Li's theorem (1993) that the stability set of order d may be empty for some preference profiles. However, one may wonder whether such situations are just rare oddities or not. In this paper, we partially answer this question by considering the restrictive case where the number of alternatives is the smallest compatible with an empty stability set. More precisely, we provide an upper bound on the probability for having an empty stability set of order d for the majority game under the Impartial Weak Ordering Culture assumption. This upper bound is already extremely low for small population and tends to zero as the number of individuals goes to infinity.     

Bargaining strength in three-person characteristic-function games with v(i)> 0 a reanalysis of Kahan and Rapoport (1977)

Kahan and Rapoport (1977) investigated the effects of guaranteed payoffs on bargaining in three-person cooperative games by systematically varying different sources of power: the power arising from the 1-person values, the power emerging from the pair coalitions as reflected by the quotas of the non-normalized game, and the grand coalition value. In the present paper it is suggested that one additionally take into account the assumption of strategic equivalence and that one analyze games with v(i)>0 in terms of the quotas of the zero-normalized game. Ostmann's (1984) rather sophisticated game theoretic framework, permitting the standardization of all three-person games, is introduced. A reanalysis of Kahan and Rapoport's data employing this perspective yields results which can be interpreted more easily than those of the original study. Moreover, they are consistent with the findings of almost all studies on 3-person characteristic-function games. It is argued that one could use the introduced analytical framework to investigate the range of empirical validity of the mathematical assumption of invariance under strategic equivalence.     

Nullified equal loss property and equal division values

We provide characterizations of the equal division values and their convex mixtures, using a new axiom on a fixed player set based on player nullification which requires that if a player becomes null, then any two other players are equally affected. Two economic applications are also introduced concerning bargaining under risk and common-pool resource appropriation.     

Mixed risk aversion and preference for risk disaggregation: a story of moments

In a recent article entitled “Putting Risk in its Proper Place,” Eeckhoudt and Schlesinger (2006) established a theorem linking the sign of the n-th derivative of an agent’s utility function to her preferences among pairs of simple lotteries. We characterize these lotteries and show that, in a given pair, they only differ by their moments of order greater than or equal to n. When the n-th derivative of the utility function is positive (negative) and n is odd (even), the agent prefers a lottery with higher (lower) n + 2p-th moments for p belonging to the set of positive integers. This result links the preference for disaggregation of risks across states of nature to the complete structure of moments preferred by mixed risk averse agents. It can be viewed as a generalization of a proposition appearing in Ekern (1980) which focused only on the differences in the n-th moments.     

Distributive justice of bargaining and risk sensitivity

In this paper we will point out some possibilities and limitations of the discussion of distributive justice by bargaining in the classical bargaining models.We start by considering a kind of bargaining situation where two persons with different risk aversions have to distribute a given quantity of a certain good. Then we define a model in which two bargaining situations are compared. In both situations two persons divide a quantity of a certain good; in the second situation one of the persons, say person 2, is replaced by a more risk averse person. From a well-known theorem of Kihlstrom, Roth and Schmeidler it follows that in the Nash solution, the Kalai-Smorodinsky solution and the Maschler-Perles solution person 1 prefers the situation with the more risk averse opponent.In both classes of problems the judgement of distributive justice is impossible because of an informational poverty of the classical bargaining model. We propose to integrate changes in the economic situation of the persons into the model.Therefore, in a third step, we compare two distributive situations, where differences in the situations are implied by changes in the initial endowments of the persons. Under the assumption that each person has a decreasing local risk aversion, we show that every reallocation of the initial endowments is enlarged or at least preserved by risk sensitive bargaining solutions. This fact has some significance for the discussion of distributive justice in social decision making by bargaining.