We study pillage games (Jordan in J Econ Theory 131(1):26–44, 2006), which model unstructured pow... more We study pillage games (Jordan in J Econ Theory 131(1):26–44, 2006), which model unstructured power contests. To enable empirical tests of pillage game theory, we relax a symmetry assumption that agents’ intrinsic contributions to a coalition’s power is identical. We characterise the core for all n. In the three-agent game: (i) only eight configurations are possible for the core, which contains at most six allocations; (ii) for each core configuration, the stable set is either unique or fails to exist; (iii) the linear power function creates a tension between a stable set’s existence and the interiority of its allocations, so that only special cases contain strictly interior allocations. Our analysis suggests that non-linear power functions may offer better empirical tests of pillage game theory.
The purpose of this paper is to examine the critical arguments made by Burmeister, Samuelson, and... more The purpose of this paper is to examine the critical arguments made by Burmeister, Samuelson, and others, with respect to Sraffa (1960). In his arguments about the standard commodity, Sraffa assumed that a change in income distribution has no effect on the output level and choice of techniques, while those critics argue that interdependence among changes in income distribution, output level, and choice of techniques should be taken into consideration in the arguments on the invariable measure of value and the linearity of income distribution. Given this debate, the paper considers general economies with non-increasing returns to scale, where such interdependence is a universal feature, in which a generalisation of the standard commodity is defined. Moreover, it is shown that the generalised standard commodity can serve as an invariable measure of value even in those general economies. Finally, the paper also characterises the necessary and sufficient condition under which the linear...
As in Roemer (1982, chapter 1), this paper considers a simple international trade model and exami... more As in Roemer (1982, chapter 1), this paper considers a simple international trade model and examines the existence and characterization of free trade equilibria involving the unequal exchange of labor (UE). The paper provides an almost complete characterization of the domain of economies in which free trade equilibria with incomplete specialization exist. Moreover, the necessary and sufficient conditions for free trade equilibrium to involve UE is identified. It suggests that the emergence of free trade equilibria with UE cannot be entailed by the competitive mechanism of markets and unequal distribution of wealth alone, but might be understood as an outcome of equilibrium selection on the basis of Nash bargaining between rich and
This paper examines the validity of the factor price equalisation theorem (FPET) in relation to c... more This paper examines the validity of the factor price equalisation theorem (FPET) in relation to capital theory. First, it presents a survey of the literature on Heckscher—Ohlin—Samuelson (HOS) models that treat capital as a primary factor, beginning with Samuelson (1953). In addition, by consulting the Cambridge capital controversies, this paper observes that the validity of the FPET relies crucially on this setting. It does no longer hold whenever capital is assumed to be a bundle of reproducible commodities. This paper also refers to the recent literature on the dynamic HOS trade theory and argues that such studies ignore the difficulties posed by the capital controversies. It thereby concludes that the FPET holds even when capital is modelled as a reproducible factor. In conclusion, the paper suggests the necessity of reconstructing basic theories of international trade without relying on the FPET.
This paper studies pillage games (Jordan in J Econ Theory 131.1:26-44, 2006, “Pillage and propert... more This paper studies pillage games (Jordan in J Econ Theory 131.1:26-44, 2006, “Pillage and property”), which are well suited to modelling unstructured power contests. To enable empirical test of pillage games’ predictions, it relaxes a symmetry assumption that agents’ intrinsic contributions to a coalition’s power is identical. In the three-agent game studied: (i) only eight configurations are possible for the core, which contains at most six allocations; (ii) for each core configuration, the stable set is either unique or fails to exist; (iii) the linear power function creates a tension between a stable set’s existence and the interiority of its allocations, so that only special cases contain strictly interior allocations. Our analysis suggests that non-linear power functions may offer better empirical tests of pillage game theory.
The purpose of this paper is to examine the critical arguments made by Burmeister, Samuelson, and... more The purpose of this paper is to examine the critical arguments made by Burmeister, Samuelson, and others, with respect to Sraffa (1960). In his arguments about the standard commodity, Sraffa assumed that a change in income distribution has no effect on the output level and choice of techniques, while those critics argue that interdependence among changes in income distribution, output level, and choice of techniques should be taken into consideration in the arguments on the invariable measure of value and the linearity of income distribution. Given this debate, the paper considers general economies with non-increasing returns to scale, where such interdependence is a universal feature, in which a generalisation of the standard commodity is defined. Moreover, it is shown that the generalised standard commodity can serve as an invariable measure of value even in those general economies. Finally, the paper also characterises the necessary and sufficient condition under which the linear...
Given the framework introduced by Dutta and Sen (2012), this paper offers a comprehensive analysi... more Given the framework introduced by Dutta and Sen (2012), this paper offers a comprehensive analysis of (Nash) implementation with partially honest agents when there are three or more participants. First, it establishes a condition which is necessary and suffi cient for implementation. Second, it provides simple tests for checking whether or not a social choice correspondence can be implemented. Their usefulness is shown by examining implementation in a wide variety of environments. JEL classification: C72; D71. Key-words: Implementation, Nash equilibrium, social choice correspondences, partial honesty, Condition μ∗. Acknowledgement: We are grateful to Hitoshi Matsushima, Hervé Moulin, Hans Peters, Tastuyoshi Saijo, Arunava Sen, Koichi Tadenuma, William Thomson, and audiences at Hitotsubashi G-COE Conference, Equality and Welfare 2013, for useful comments and suggestions. The usual caveat applies. ∗Adam Smith Business School, University of Glasgow, Glasgow, G12 8QQ, United Kingdom, e-...
Following the viewpoint of pure procedural justice, we analyze a social decision procedure for ch... more Following the viewpoint of pure procedural justice, we analyze a social decision procedure for choosing fair allocation rules in production economies, which is formulated as an extended Arrovian constitution that aggregates each profile of individual social welfare functions into a social so-cial welfare function. The identified allocation rule is characterized by three axioms with Rawlsian flavor. The difference principle is formulated, not in terms of the Rawlsian primary social goods, but in terms of the common ca-pability in the Sen space of functionings. In this sense, our theory synthesizes the Rawlsian theory of justice as fairness and the Sen theory of capability.
April 2004 Bibliography: p. 11-12 We reconsider the three well-known solutions: the Nash, the ega... more April 2004 Bibliography: p. 11-12 We reconsider the three well-known solutions: the Nash, the egalitarian and the Kalai-Smorodinsky solutions, to the classical domains of convex bargaining problems. A new proof for the Nash solution that highlights the crucial role the axiom Contraction Independence plays is provided. We also give new axiomatic characterizations for both the egalitarian and the Kalai-Smorodinsky solutions. Our results focus on both contraction and expansion independence properties of bargaining problems and, as a consequence, some new insights on the three solutions from the perspective of rational choice may be derived.
Conditions α and β are two well-known rationality conditions in the theory of rational choice. Th... more Conditions α and β are two well-known rationality conditions in the theory of rational choice. This paper examines the implication of weaker versions of these two rationality conditions in the context of solutions to non-convex bargaining problems. It is shown that, together with the standard axioms of efficiency, anonymity and scale invariance, they characterize the Nash solution. This result makes a further connection between solutions to non-convex bargaining problems and rationalizability of choice functions in the theory of rational choice.
March 2004 Bibliography: p. 12-13 This paper studies compact and comprehensive bargaining problem... more March 2004 Bibliography: p. 12-13 This paper studies compact and comprehensive bargaining problems for n players and axiomatically characterize the extensions of the three classical bargaining solutions to nonconvex bargaining problems: the Nash solution, the egalitarian solution and the Kalai-Smorodinsky solution. Our characterizing axioms are various extensions of Nash's original axioms.
In this paper, we reexamine the mathematical analysis of Marxian exploitation theory. First, we r... more In this paper, we reexamine the mathematical analysis of Marxian exploitation theory. First, we reexamine the validity of the two types of Marxian labor exploitation, Morishima's (1974) type and Roemer's type (1982), in the argument of Fundamental Marxian Theorem (FMT). We show that the FMT does not hold true if we adopt the Roemer exploitation, and equilibrium notions are the
In this paper, we consider political competition games of two parties in multi-dimensional policy... more In this paper, we consider political competition games of two parties in multi-dimensional policy spaces, where the two parties have two factions, opportunists and militants, that intra-party bargain with each other. In such a game, we adopt the party-unanimity Nash equilibrium (PUNE) [Roemer (1998; 1999; 2001)] as an appropriate solution concept, and examine the general existence problem of this. In
We study pillage games (Jordan in J Econ Theory 131(1):26–44, 2006), which model unstructured pow... more We study pillage games (Jordan in J Econ Theory 131(1):26–44, 2006), which model unstructured power contests. To enable empirical tests of pillage game theory, we relax a symmetry assumption that agents’ intrinsic contributions to a coalition’s power is identical. We characterise the core for all n. In the three-agent game: (i) only eight configurations are possible for the core, which contains at most six allocations; (ii) for each core configuration, the stable set is either unique or fails to exist; (iii) the linear power function creates a tension between a stable set’s existence and the interiority of its allocations, so that only special cases contain strictly interior allocations. Our analysis suggests that non-linear power functions may offer better empirical tests of pillage game theory.
The purpose of this paper is to examine the critical arguments made by Burmeister, Samuelson, and... more The purpose of this paper is to examine the critical arguments made by Burmeister, Samuelson, and others, with respect to Sraffa (1960). In his arguments about the standard commodity, Sraffa assumed that a change in income distribution has no effect on the output level and choice of techniques, while those critics argue that interdependence among changes in income distribution, output level, and choice of techniques should be taken into consideration in the arguments on the invariable measure of value and the linearity of income distribution. Given this debate, the paper considers general economies with non-increasing returns to scale, where such interdependence is a universal feature, in which a generalisation of the standard commodity is defined. Moreover, it is shown that the generalised standard commodity can serve as an invariable measure of value even in those general economies. Finally, the paper also characterises the necessary and sufficient condition under which the linear...
As in Roemer (1982, chapter 1), this paper considers a simple international trade model and exami... more As in Roemer (1982, chapter 1), this paper considers a simple international trade model and examines the existence and characterization of free trade equilibria involving the unequal exchange of labor (UE). The paper provides an almost complete characterization of the domain of economies in which free trade equilibria with incomplete specialization exist. Moreover, the necessary and sufficient conditions for free trade equilibrium to involve UE is identified. It suggests that the emergence of free trade equilibria with UE cannot be entailed by the competitive mechanism of markets and unequal distribution of wealth alone, but might be understood as an outcome of equilibrium selection on the basis of Nash bargaining between rich and
This paper examines the validity of the factor price equalisation theorem (FPET) in relation to c... more This paper examines the validity of the factor price equalisation theorem (FPET) in relation to capital theory. First, it presents a survey of the literature on Heckscher—Ohlin—Samuelson (HOS) models that treat capital as a primary factor, beginning with Samuelson (1953). In addition, by consulting the Cambridge capital controversies, this paper observes that the validity of the FPET relies crucially on this setting. It does no longer hold whenever capital is assumed to be a bundle of reproducible commodities. This paper also refers to the recent literature on the dynamic HOS trade theory and argues that such studies ignore the difficulties posed by the capital controversies. It thereby concludes that the FPET holds even when capital is modelled as a reproducible factor. In conclusion, the paper suggests the necessity of reconstructing basic theories of international trade without relying on the FPET.
This paper studies pillage games (Jordan in J Econ Theory 131.1:26-44, 2006, “Pillage and propert... more This paper studies pillage games (Jordan in J Econ Theory 131.1:26-44, 2006, “Pillage and property”), which are well suited to modelling unstructured power contests. To enable empirical test of pillage games’ predictions, it relaxes a symmetry assumption that agents’ intrinsic contributions to a coalition’s power is identical. In the three-agent game studied: (i) only eight configurations are possible for the core, which contains at most six allocations; (ii) for each core configuration, the stable set is either unique or fails to exist; (iii) the linear power function creates a tension between a stable set’s existence and the interiority of its allocations, so that only special cases contain strictly interior allocations. Our analysis suggests that non-linear power functions may offer better empirical tests of pillage game theory.
The purpose of this paper is to examine the critical arguments made by Burmeister, Samuelson, and... more The purpose of this paper is to examine the critical arguments made by Burmeister, Samuelson, and others, with respect to Sraffa (1960). In his arguments about the standard commodity, Sraffa assumed that a change in income distribution has no effect on the output level and choice of techniques, while those critics argue that interdependence among changes in income distribution, output level, and choice of techniques should be taken into consideration in the arguments on the invariable measure of value and the linearity of income distribution. Given this debate, the paper considers general economies with non-increasing returns to scale, where such interdependence is a universal feature, in which a generalisation of the standard commodity is defined. Moreover, it is shown that the generalised standard commodity can serve as an invariable measure of value even in those general economies. Finally, the paper also characterises the necessary and sufficient condition under which the linear...
Given the framework introduced by Dutta and Sen (2012), this paper offers a comprehensive analysi... more Given the framework introduced by Dutta and Sen (2012), this paper offers a comprehensive analysis of (Nash) implementation with partially honest agents when there are three or more participants. First, it establishes a condition which is necessary and suffi cient for implementation. Second, it provides simple tests for checking whether or not a social choice correspondence can be implemented. Their usefulness is shown by examining implementation in a wide variety of environments. JEL classification: C72; D71. Key-words: Implementation, Nash equilibrium, social choice correspondences, partial honesty, Condition μ∗. Acknowledgement: We are grateful to Hitoshi Matsushima, Hervé Moulin, Hans Peters, Tastuyoshi Saijo, Arunava Sen, Koichi Tadenuma, William Thomson, and audiences at Hitotsubashi G-COE Conference, Equality and Welfare 2013, for useful comments and suggestions. The usual caveat applies. ∗Adam Smith Business School, University of Glasgow, Glasgow, G12 8QQ, United Kingdom, e-...
Following the viewpoint of pure procedural justice, we analyze a social decision procedure for ch... more Following the viewpoint of pure procedural justice, we analyze a social decision procedure for choosing fair allocation rules in production economies, which is formulated as an extended Arrovian constitution that aggregates each profile of individual social welfare functions into a social so-cial welfare function. The identified allocation rule is characterized by three axioms with Rawlsian flavor. The difference principle is formulated, not in terms of the Rawlsian primary social goods, but in terms of the common ca-pability in the Sen space of functionings. In this sense, our theory synthesizes the Rawlsian theory of justice as fairness and the Sen theory of capability.
April 2004 Bibliography: p. 11-12 We reconsider the three well-known solutions: the Nash, the ega... more April 2004 Bibliography: p. 11-12 We reconsider the three well-known solutions: the Nash, the egalitarian and the Kalai-Smorodinsky solutions, to the classical domains of convex bargaining problems. A new proof for the Nash solution that highlights the crucial role the axiom Contraction Independence plays is provided. We also give new axiomatic characterizations for both the egalitarian and the Kalai-Smorodinsky solutions. Our results focus on both contraction and expansion independence properties of bargaining problems and, as a consequence, some new insights on the three solutions from the perspective of rational choice may be derived.
Conditions α and β are two well-known rationality conditions in the theory of rational choice. Th... more Conditions α and β are two well-known rationality conditions in the theory of rational choice. This paper examines the implication of weaker versions of these two rationality conditions in the context of solutions to non-convex bargaining problems. It is shown that, together with the standard axioms of efficiency, anonymity and scale invariance, they characterize the Nash solution. This result makes a further connection between solutions to non-convex bargaining problems and rationalizability of choice functions in the theory of rational choice.
March 2004 Bibliography: p. 12-13 This paper studies compact and comprehensive bargaining problem... more March 2004 Bibliography: p. 12-13 This paper studies compact and comprehensive bargaining problems for n players and axiomatically characterize the extensions of the three classical bargaining solutions to nonconvex bargaining problems: the Nash solution, the egalitarian solution and the Kalai-Smorodinsky solution. Our characterizing axioms are various extensions of Nash's original axioms.
In this paper, we reexamine the mathematical analysis of Marxian exploitation theory. First, we r... more In this paper, we reexamine the mathematical analysis of Marxian exploitation theory. First, we reexamine the validity of the two types of Marxian labor exploitation, Morishima's (1974) type and Roemer's type (1982), in the argument of Fundamental Marxian Theorem (FMT). We show that the FMT does not hold true if we adopt the Roemer exploitation, and equilibrium notions are the
In this paper, we consider political competition games of two parties in multi-dimensional policy... more In this paper, we consider political competition games of two parties in multi-dimensional policy spaces, where the two parties have two factions, opportunists and militants, that intra-party bargain with each other. In such a game, we adopt the party-unanimity Nash equilibrium (PUNE) [Roemer (1998; 1999; 2001)] as an appropriate solution concept, and examine the general existence problem of this. In
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