Bidding and sequential coalition formation with externalities

We study coalition formation games with externalities where each agent’s payoff depends on the entire partition. As in Bloch (Games Econ Behav 14:90–123, 1996) and Ray and Vohra (Games Econ Behav 26:268–336, 1999), we assume that coalitions form sequentially and agreements are irreversible. Instead of a fixed order protocol, we use a “bidding mechanism” (see Pérez-Castrillo and Wettstein in Am Econ Rev 92(5):1577–1587, 2002) to determine proposals and transfers among the agents. We show that such a mechanism facilitates the attainment of efficiency; in particular, our game admits a Markov perfect equilibrium with the property of full dynamic efficiency. In addition, the aggregate equilibrium payoffs of our game exhibit monotonicity in time. Nevertheless, inefficient equilibria can also emerge.     

An N-dimensional version of Scarf's example

This paper presents a unification of the contributions of Scarf [Some examples of global instability of competitive equilibrium, Int. Econ. Rev. 1 (1960) 157–172] and Gale [A note on global instability of competitive equilibrium, Nav. Res. Logist. Q. 10 (1963) 81–87] by means of a single class of utility functions. The unification extends Scarf's three-commodity, three-consumer economy to an n-commodity, n-consumer economy. We find that the stability of the extended economy depends on whether the law of demand for exchange economies, i.e., downward sloping excess demand, holds or not. Moreover, it is seen that there is a transition from instability to stability as substitution effect increases or as the desire of each consumer for his own commodity decreases.     

Comments on purification in continuum games

It is pointed out that Corollary 1 in a recent paper by Khan et al. (Int J Game Theory 34:91–104, 2006), presented there as an extension of the Dvoretzky–Wald–Wolfowitz theorem, is a special case of Lyapunov’s theorem for Young measures (Balder in Rend Instit Mat Univ Trieste 31 Suppl. 1:1–69) It is also pointed out that Theorems 1–4 in Khan et al. (Int J Game Theory 34:91–104, 2006) follow from a single strong purification per se result that is already contained, as an implementation of that Lyapunov theorem for Young measures, in the proof of Theorem 2.2.1 in Balder (J Econ Theory 102:437–470, 2002).     

Dynamic realization games in newsvendor inventory centralization

Consider a set N of n (> 1) stores with single-item and single-period nondeterministic demands like in a classic newsvendor setting with holding and penalty costs only. Assume a risk-pooling single-warehouse centralized inventory ordering option. Allocation of costs in the centralized inventory ordering corresponds to modelling it as a cooperative cost game whose players are the stores. It has been shown that when holding and penalty costs are identical for all subsets of stores, the game based on optimal expected costs has a non empty core (Hartman et al. 2000, Games Econ Behav 31:26–49; Muller et al. 2002, Games Econ Behav 38:118–126). In this paper we examine a related inventory centralization game based on demand realizations that has, in general, an empty core even with identical penalty and holding costs (Hartman and Dror 2005, IIE Trans Scheduling Logistics 37:93–107). We propose a repeated cost allocation scheme for dynamic realization games based on allocation processes introduced by Lehrer (2002a, Int J Game Theor 31:341–351). We prove that the cost subsequences of the dynamic realization game process, based on Lehrer’s rules, converge almost surely to either a least square value or the core of the expected game. We extend the above results to more general dynamic cost games and relax the independence hypothesis of the sequence of players’ demands at different stages.     

Efficiency and equilibria in games of optimal derivative design

In this paper, optimal derivative design when multiple firms compete for heterogenous customers is studied. Ties in the agents’ best responses generate discontinuous payoffs. Efficient tie-breaking rules are considered: In a first step, the model presented by Carlier et al. (Math Financ Econ 1:57–80, 2007) is extended, and results of Page and Monteiro (J Math Econ 39:63–109, 2003, J Econ Theory 134:566–575, 2007, Econ Theory 34:503–524, 2008) are used to prove the existence of (mixed-strategies) Nash equilibria. In a second step, the case of risk minimizing firms is studied. Socially efficient allocations are introduced, and their existence is proved. In particular, the entropic risk measure is considered.     

Note on universal conditional consistency

This note clarifies the implication of universal conditional consistency (UCC) in Fudenberg and Levine (Games Econ Behav 29:104–130, 1999) from the viewpoint of the no-regret test. We first show that the UCC property implies (universally) passing any countable set of no-regret tests. Furthermore, we show that the UCC implies universally passing uncountable (particular) no-regret tests so that the UCC theorem and the wide-range no-regret (WRNR) theorem in Lehrer (Games Econ Behav 42:101–115, 2003) may differ, as opposed to the thought that the UCC property is a special case of the WRNR property. Y. Noguchi is very grateful to Drew Fudenberg for his encouragement and helpful comments. He also thank an anonymous referee and Tatsuro Ichiishi for their helpful comments.     

Hedonic price function estimation in economics and marketing: revisiting Lancaster’s issue of “noncombinable” goods

Following Lancaster’s (J. Political Econ. 74(1):132–157, 1966; Variety, equity and efficiency, 1979) interpretation of his characteristics approach to consumer theory, this contribution focuses on theoretical and empirical arguments questioning the smoothness of traditional hedonic price estimation techniques. Lancaster argued strongly against “combinability”, i.e., that any efficient combination of characteristics is feasible and sensible. We therefore explicitly test the impact of convexity using a set of recent non-parametric estimators. The test is carried out on a sample of 114 digital cameras whose price evolution is followed over 6 months. The hypothesis of convexity is rejected using the Li (Econ. Rev. 15(3):261–274, 1996) test. The conclusions point out implications for economics and marketing.     

Resource location games

In this paper, we introduce and analyze resource location games. We show core non-emptiness by providing a set of intuitive core allocations, called Resource-Profit allocations. In addition, we present a sufficient condition for which the core and the set of Resource-Profit allocations coincide. Finally, we provide an example showing that when the sufficient condition is not satisfied, the coincidence is not guaranteed.     

Fuzzy identification problem for continuous extremal fuzzy dynamic system

This work deals with the problems of the Continuous Extremal Fuzzy Dynamic System (CEFDS) optimization and briefly discusses the results developed by Sirbiladze (Int J Gen Syst 34(2):107–138, 2005a; 34(2):139–167, 2005b; 34(2):169–198, 2005c; 35(4):435–459, 2006a; 35(5):529–554, 2006b; 36(1): 19–58, 2007; New Math Nat Comput 4(1):41–60, 2008a; Mat Zametki, 83(3):439–460, 2008b). The basic properties of extended extremal fuzzy measures and Sugeno’s type integrals are considered and several variants of their representation are given. Values of extended extremal conditional fuzzy measures are defined as a levels of expert knowledge reflections of CEFDS states in the fuzzy time intervals. The notions of extremal fuzzy time moments and intervals are introduced and their monotone algebraic structures that form the most important part of the fuzzy instrument of modeling extremal fuzzy dynamic systems are discussed. A new approach in modeling of CEFDS is developed. Applying the results of Sirbiladze (Int J Gen Syst 34(2) 107–138, 2005a; 34(2):139–167, 2005b), fuzzy processes with possibilistic uncertainty, the source of which are expert knowledge reflections on the states on CEFDS in extremal fuzzy time intervals, are constructed (Sirbiladze in Int J Gen Syst 34(2):169–198, 2005c). The dynamics of CEFDS’s is described. Questions of the ergodicity of CEFDS are considered. A fuzzy-integral representation of a continuous extremal fuzzy process is given. Based on the fuzzy-integral model, a method and an algorithm are developed for identifying the transition operator of CEFDS. The CEFDS transition operator is restored by means of expert data with possibilistic uncertainty, the source of which is expert knowledge reflections on the states of CEFDS in the extremal fuzzy time intervals. The regularization condition for obtaining quasi-optimal estimator of the transition operator is represented by the theorems. The corresponding calculating algorithm is provided. The results obtained are illustrated by an example in the case of a finite set of CEFDS states.     

Dynamic Walrasian price equilibrium problem: evolutionary variational approach with sensitivity analysis

Many authors have been devoted to the study of the static general economic equilibrium problem regulated to Walras’ law (see e.g. Arrow and Debreu in Econometrica 22:265–290, 1954; Arrow and Hahn in General competitive analysis, 1991; Arrow et al. in Econometrica 27:82–109, 1959; Border in Fixed point theorems with application to economics and game theory, Cambridge University Press, Cambridge, 1985; Dafermos in Math Programm 46:391–402, 1990; Dafermos and Zhao in Oper Res Lett 10:396–376, 1991; Donato et al. in J Glob Optim, 2007; Hahn in Stability, North Holland, Amsterdam, 1982; Jofré et al. in Math Oper Res, 2007; Nagurney in Network economics—a variational inequality approach, Kluwer, Dordrecht, 1999; Nagurney and Zhao in Network formalism for pure exchange economic equilibria, World Scientific Press, Singapore, 1993; Walker in J Polit Econ 94(4), 1987; Walras in Elements d’Economique Politique Pure, Corbaz, Lausanne, Switzerland, 1874; Zhao in Variational inequalities in general equilibrium: analysis and computation, PhD thesis, Brown University, 1988; and their bibliography). The aim of this paper is to provide a first approach to a particular dynamic general economic equilibrium problem: a Walrasian price equilibrium problem when the data are time-dependent. The equilibrium conditions that describe this pure exchange economic model are expressed in terms of an evolutionary variational inequality, for which existence and sensitivity results are given. Moreover, our problem can be expressed in a common way to many other equilibrium problems.     

The unit-level-core for multi-choice games: the replicated core for TU games

This note extends the solution concept of the core for traditional transferable-utility (TU) games to multi-choice TU games, which we name the unit-level-core. It turns out that the unit-level-core of a multi-choice TU game is a “replicated subset” of the core of a corresponding “replicated” TU game. We propose an extension of the theorem of Bondareva (Probl Kybern 10:119–139, 1963) and Shapley (Nav Res Logist Q 14:453–460, 1967) to multi-choice games. Also, we introduce the reduced games for multi-choice TU games and provide an axiomatization of the unit-level-core on multi-choice TU games by means of consistency and its converse.     

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.     

The multi-core,balancedness and axiomatizations for multi-choice games

This note extends the solution concept of the core for cooperative games to multi-choice games. We propose an extension of the theorem of Bondareva (Problemy Kybernetiki 10:119–139, 1963) and Shapley (Nav Res Logist Q 14:453–460, 1967) to multi-choice games. Also, we introduce a notion of reduced games for multi-choice games and provide an axiomatization of the core on multi-choice games by means of corresponding notion of consistency and its converse.     

On the relevance of alternatives in bargaining: generalized average pay-off solutions

We generalize the average pay-off solution proposed by Anbarci (Can J Econ 28:675–682, 1995), which depends on all the alternatives, and show that the Nash and Kalai–Smorodinsky solutions are limits of generalized average pay-off solutions. We formalize the notion of relevant alternatives and compare solutions in terms of the relevance of alternatives. I am much indebted to Roberto Serrano for his guidance and many discussions, and William Thomson for his numerous detailed suggestions for improvements. I thank Youngsub Chun, Michael Maschler, Yeneng Sun, Rajiv Vohra, Oscar Volij, Myrna Wooders, an associate editor, anonymous referees, and seminar participants at Brown University, the National University of Singapore, and the 2003 North American Summer Meetings of the Econometric Society for valuable comments. I gratefully acknowledge research support from Brown University through an Eccleston Fellowship award.     

An elementary non-constructive proof of the non-emptiness of the core of the Housing Market of Shapley and Scarf

Shapley and Scarf, by using the theory of balanced games, prove, in a well-known paper of 1974 (Journal of Mathematical Economics, 1, 23–28), the non-emptiness of the core of the Housing Market. The present paper provides a non-constructive, simple and short proof that gives some intuition about how blocking can be done by players who have not traded.     

Characterizing Useless-free Financial Structures

The boundedness of the set of admissible allocations is a basic property in economic models that proved to be of fundamental use to show the existence of equilibria (Debreu 1959; Hurwicz and Reiter, Int. Econ. Rev. 14(3), 580–586, 1973). In the study of financial markets without portfolio constraints, this boundedness property is standardly derived from the absence of redundant assets, an assumption that can be made without loss of generality since redundant assets can be eliminated at no cost. However, there are no a priori grounds to do so when agents do face portfolio constraints, and the elimination of redundant assets should be replaced by the elimination of useless portfolios as shown by Aouani and Cornet (2014). The purpose of this paper is thus to characterize financial structures that are useless-free (i.e., without useless portfolios) when agents face portfolio constraints, and show that the absence of useless portfolios adequately extends the absence of redundant assets in the constrained case. Our main result will then show the equivalence between the absence of useless portfolios, a dual non-redundancy property, and the boundedness property of different sets of admissible portfolio allocations.     

The pseudo-average rule: bankruptcy,cost allocation and bargaining

A division rule for claims problems, also known as bankruptcy or rationing problems, based on the pseudo-average solution is studied (for 2-person problems). This solution was introduced in Moulin (Jpn Econ Rev 46:303–332, 1995) for discrete cost allocation problems. Using the asymptotic approach, we obtain a division rule for claims problems. We characterize the division rule axiomatically and show that it coincides with the rule associated to the equal area bargaining solution (this is not true for n = 3). Moreover, following Moulin and Shenker (J Econ Theor 64:178–201, 1994), we show that its associated solution for continuous homogeneous goods is precisely the continuous pseudo-average solution.     

Equivalence theorem,consistency and axiomatizations of a multi-choice value

This paper is devoted to the study of solutions for multi-choice games which admit a potential, such as the potential associated with the extended Shapley value proposed by Hsiao and Raghavan (Int J Game Theory 21:301–302, 1992; Games Econ Behav 5:240–256, 1993). Several axiomatizations of the family of all solutions that admit a potential are offered and, as a main result, it is shown that each of these solutions can be obtained by applying the extended Shapley value to an appropriately modified game. In the framework of multi-choice games, we also provide an extension of the reduced game introduced by Hart and Mas-Colell (Econometrica 57:589–614, 1989). Different from the works of Hsiao and Raghavan (1992, 1993), we provide two types of axiomatizations, one is the analogue of Myerson’s (Int J Game Theory 9:169–182, 1980) axiomatization of the Shapley value based on the property of balanced contributions. The other axiomatization is obtained by means of the property of consistency.     

A simple model of corporate international investment under incomplete information and taxes

This paper extends the theory of corporate international investment in Choi (J. Int. Bus. Stud. 20: 145–155, 1989) in an environment where the segmentation of international capital markets for investors or the presence of agency costs provide some independence to corporate decisions. The model shows that the real exchange risk, the competition between firms in different markets and diversification gains affect corporate international investment. By accounting for the role of information as defined in the models of Merton (J. Finance 42: 483–510, 1987), Bellalah (Int. J. Finance Econ. 6: 59–67, 2001a) and Bellalah and Wu (Int. J. Theor. Appl. Finance 5(5): 479–495, 2002), the model embodies different existing explanations based on economic and behavioral variables. We show in a “two-country” firm model that real exchange risk, diversification motives and information costs are important elements in the determination of corporate international investment decisions. The dynamic portfolio model reflects the main results in several theories of foreign direct investment. Our model accounts for the role of information in explaining foreign investments. It provides simple explanations which are useful in explaining the home bias puzzle in international finance. Using the dynamical programming principle method, we provide the general solution for the proportion of firm’s total capital budget. We also use a new method to get explicit solutions in some special cases. This new method can be applied to solve other financial control problems. The simulating results are given to show our conclusion and the influence of some parameters to the optimal solution. The economic results can be seen as a generalization of the model in Solnik (J. Econ. Theory 8: 500–524, 1974).