Many local public goods are provided by coalitions and some of them have network e¤ects. Namely, ... more Many local public goods are provided by coalitions and some of them have network e¤ects. Namely, people prefer to consume a public good in a coalition with more members. This paper adopts the Drèze and Greenberg (1980) type utility function where players have preferences over goods as well as coalition members. In a game with anonymous and separable network e¤ect, the core is nonempty when coalition feasible sets are monotonic and players'preferences over public goods have connected support. All core allocations consist of connected coalitions and they are Tiebout equilibria as well. We also examine the no-exodus equilibrium for games whose feasible sets are not monotonic.
We study the formation of coalitions that provide public goods to members. Individuals are linked... more We study the formation of coalitions that provide public goods to members. Individuals are linked on a tree graph and those with similar preferences are connected on the tree. We present a solution that selects allocations belonging to the coalition structure core and that are also envy-free.
In a production economy, multiple public goods are produced by …rms in competitive markets, and p... more In a production economy, multiple public goods are produced by …rms in competitive markets, and provided by the government together with contributions from consumers. There are widespread externalities: all consumers' consumption and contributions and all …rms'production enter into utility functions. Public goods can be imperfectly substitutes or complements, and they can be coalition or club goods. Zero bounds that require consumers to make nonnegative contributions complicate the di¤erentiable approach. Applying parametric transversality theorem for smooth economies in a regular parameterization, we obtain the existence of a contribution equilibrium and generic regularity of equilibria.
International Journal of Economic Theory, Dec 18, 2019
Models of city systems based on market theories are unable to replicate their size distribution. ... more Models of city systems based on market theories are unable to replicate their size distribution. The stochastic process approach to size distribution, which asserts proportional growth, does not provide a strong economic foundation. Hence an apparent irreconcilability. We propose that since there is a continuum of equilibrium set in market models of cities, as pointed out by Berliant and Kung (2006), proportional growth can work as an equilibrium selection. We compute an urban configuration that has not been presented in the literature before. A small city locates inside a larger city's agricultural supply zone. This gives a larger variation in city size that may contain Zipf's distribution.
We study how individuals divide themselves into coalitions and choose a public alternative for ea... more We study how individuals divide themselves into coalitions and choose a public alternative for each coalition. When preferences have consecutive support and coalition feasible sets are positively population-responsive, the proposed consecutive benevolence solution generates allocations belonging to the coalition structure core and that are also Tiebout equilibria. However, when each coalition follows a single-valued collective decision rule, the coalition structure core may be empty. Our results show that if individual preferences are, in a sense, similar and if members can be as well o¤ when a coalition enlarges, then a stable formation of collective decision-making units can be guaranteed. A predetermined decision rule makes coalitions less stable.
A great deal of production and consumption behavior takes place in the context of social organiza... more A great deal of production and consumption behavior takes place in the context of social organizations that seem to fall outside of the traditional paradigm of profit/utility maximization. These organizations are voluntary in nature and rely on contributions from members to achieve their objectives. Examples include the Linux operating system and other FOSS projects, political movements, churches and religious groups, Habitat for Humanity, and similar charitable organizations. In this paper, we consider a world containing agents with heterogeneous abilities who may voluntarily choose to make effort contributions to one or more different public projects. Agents are motivated by a desire to be seen as significant contributors to important and valuable projects, the warm glow from the act of contributing, and a desire to directly enjoy the benefits of projects when complete. We find that contributions from others can be either strategic complements or substitutes. We show that Nash equilibria exist and study how agents' abilities and project quality affect the equilibrium levels of contributions.
It is well known that externalities cause fundamental non-convexity problems in the production se... more It is well known that externalities cause fundamental non-convexity problems in the production set. We demonstrate that the differentiable approach is a proper tool. Existence of equilibrium obtains without requiring aggregate convexity in consumption or production. Our model allows general externalities in consumption and production and also price dependency.
A great deal of production and consumption behavior takes place in the context of social organiza... more A great deal of production and consumption behavior takes place in the context of social organizations that seem to fall outside of the traditional paradigm of profit/utility maximization. These organizations are voluntary in nature and rely on contributions from members to achieve their objectives. Examples include the Linux operating system and other FOSS projects, political movements, churches and religious groups, Habitat for Humanity, and similar charitable organizations. In this paper, we consider a world containing agents with heterogeneous abilities who may voluntarily choose to make effort contributions to one or more different public projects. Agents are motivated by a desire to be seen as significant contributors to important and valuable projects, the warm glow from the act of contributing, and a desire to directly enjoy the benefits of projects when complete. We find that contributions from others can be either strategic complements or substitutes. We show that Nash equilibria exist and study how agents' abilities and project quality affect the equilibrium levels of contributions.
The tomahawk bifurcation is used by Fujita et al. (1999) in a model with two regions to explain t... more The tomahawk bifurcation is used by Fujita et al. (1999) in a model with two regions to explain the formation of a core-periphery urban pattern from an initial uniform distribution. Baldwin et al. (2003) show that the tomahawk bifurcation disappears when the two regions have an uneven population of immobile agricultural workers. Thus, the appearance of this type of bifurcation is the result of assumed exogenous model symmetry. We provide a general analysis in a regional model of the class of bifurcations that have crossing equilibrium loci, including the tomahawk bifurcation, by examining arbitrary smooth parameter paths in a higher dimensional parameter space. We …nd that, in a parameter space satisfying a mild rank condition, generically in all parameter The authors thank Yuri Mansury for helpful comments but retain responsibility for any errors herein.
ABSTRACT We extends the single-crossing property of preferences to tree graphs, and show that it ... more ABSTRACT We extends the single-crossing property of preferences to tree graphs, and show that it is equivalent to intermediate preferences and order restriction, also extended to tree graphs. Moreover, to facilitate the use of single-crossing in network games, we develop algorithms to answer the following questions. Given a preference profile, can we construct a tree graph that supports single-crossing, if it is? Given a set of alternatives, can we generate single-crossing preference profiles with associated tree graphs?
This paper analyzes the genericity of bifurcations of one-parameter families of smooth (C1) vecto... more This paper analyzes the genericity of bifurcations of one-parameter families of smooth (C1) vector fields that are embedded in an underlying multi-dimensional parameter space. Bifurcations with crossing equilibrium loci are called 'split bifurcations.' They include, for example, the pitchfork bifurcation and the transcritical bifurcation. In a regular parameter space where the system's Jacobian matrix with respect to endogenous variables and parameters has full rank at every equilibrium for all parameter values, there is a generic (open and dense) set of one-parameter C1 families of vector fields without split bifurcations. It is not difficult to obtain a regular parameter space when there are enough parameters. A regional migration model (a la Fujita, Krugman and Venables 1999) featuring the pitchfork bifurcation is presented as an example.
Oxford Research Encyclopedia of Economics and Finance, Apr 20, 2022
Economic and social activities in different locations interact through systematic connections, wh... more Economic and social activities in different locations interact through systematic connections, which can be modeled as network structures. For example, production processes combine various inputs, tasks, and intermediate products that are spread over space; laborers transmit knowledge and skills along networks of work relations; products are delivered through transportation networks; and local public goods have external effects that spill over into the network of neighborhoods. Such networks bring benefits to connected nodes in the form of externalities. Approaches adopted for modeling networks of locations or that are applicable to spatial economics can be placed into two major categories. First, networks can be formed endogenously when nodes choose links strategically. Thus, networks are outcomes that emerge from strategic equilibria. This approach anylyzes the patterns of networks that are in equilibrium and patterns that are efficient. Second, networks can be a background structure with fixed existing links. In this approach, centrality measures are designed to indicate the importance of a node in the network. In many contexts, these measures determine the equilibrium and efficient behavior of nodes. Networks can be applied to broad issues in urban, regional, and location economics, such as neighborhood interactions, transportation, local public goods, trade, industrial sites, business operations. The strategic connection approach models the network as a strategic game. Both cooperative and noncooperative equilibrium concepts have been adopted in the literature. A link may form cooperatively when both nodes are better off, or one node may force a link noncooperatively onto another. The structure of intracity and intercity networks can be investigated using this framework: In a city, neighborhoods are networks of blocks, which are connected by streets and sidewalks; external benefits spill over into connected blocks; locally integrated neighborhoods emerge in equilibrium; and cities are connected by intercity transportation networks. In such models, the core–periphery patterns of cities are found to emerge in the equilibrium. The structural approach treats network structures as exogenously fixed, and links are not subject to change. In such settings, centrality measures, which indicate how centrally connected the position of a node is in the network, determine the behaviors of nodes. For example, when there are widespread externalities so that payoffs of nodes are determined by efforts of all connected nodes, the equilibrium effort of a node is proportional to its Bonacich centrality measure. Centrality measures determine equilibrium and efficient outcomes in other network settings as well. Examples of such are how conformity in peer networks affects criminal behaviors, how nodes choose security investments against the spread of infection in the network, how intercity transportation networks determine the distribution of city size, and how community residents choose the number of visits to an urban center. Futher findings include, for example, in an economy-wide trade network of intermediate inputs, local economic shocks can cause aggregate production fluctuations; in a network of neighboring jurisdictions, voluntary contributions to local public goods are neutral to income transfers; in a geographical trade network, a firm that already exports to a location will have a higher probability of exporting to a second location if the two locations have a larger volume of trade; and firms spread adverse impacts from a local economic shock through their internal networks across regions.
We study the indeterminacy of equilibrium in the Fujita-Krugman (1995) model of city formation un... more We study the indeterminacy of equilibrium in the Fujita-Krugman (1995) model of city formation under monopolistic competition and increasing returns. Both the number and the locations of cities are endogenously determined. Assuming smooth transportation costs, we examine equilibria in city-economies where a …nite number of cities form endogenously. For any positive integer K, the set of equilibria with K distinct cities has a smooth manifold of dimension K 1 as its interior for almost all parameter values in a regular parameterization. The disjoint union of these sets over all positive integers K constitutes the entire equilibrium set.
Jacques Thisse, and Alison Watts. Needless to say, the usual disclaimer applies. The views expres... more Jacques Thisse, and Alison Watts. Needless to say, the usual disclaimer applies. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.
Oxford Research Encyclopedia of Economics and Finance
Economic and social activities in different locations interact through systematic connections, wh... more Economic and social activities in different locations interact through systematic connections, which can be modeled as network structures. For example, production processes combine various inputs, tasks, and intermediate products that are spread over space; laborers transmit knowledge and skills along networks of work relations; products are delivered through transportation networks; and local public goods have external effects that spill over into the network of neighborhoods. Such networks bring benefits to connected nodes in the form of externalities. Approaches adopted for modeling networks of locations or that are applicable to spatial economics can be placed into two major categories. First, networks can be formed endogenously when nodes choose links strategically. Thus, networks are outcomes that emerge from strategic equilibria. This approach anylyzes the patterns of networks that are in equilibrium and patterns that are efficient. Second, networks can be a background struct...
We develop a framework of group corruption via back-door negotiations between an outside initiato... more We develop a framework of group corruption via back-door negotiations between an outside initiator and an authority of decision-makers in a hierarchical organization. We examine the role played by the architecture of a multi-tier authority and determine under such a structure how bargaining proceeds, in what order, and when it breaks down. We verify that equilibrium bargaining sequence proceeds as a chain through decision-making agents, regardless of the hierarchy of the organization. We prove the existence of a compromised equilibrium, where the decision of the authority is compromised, and establish sufficient conditions under which the most natural bottom-up bargaining configuration arises in equilibrium where a proposer negotiates with an immediately higher ranked respondent, starting with the initiator bargaining with the lowest ranked decision-maker in the organization. We then show the circumstances under which a top-down or a non-monotonic equilibrium configuration may emerge, and those under which the deal may break down. This enables us to capture a rich array of group corruptive configurations as observed. We conclude by investigating the extension to multi-tier authorities with multiple agents of the same rank in each tier, such as in a tree hierarchy.
Many local public goods are provided by coalitions and some of them have network e¤ects. Namely, ... more Many local public goods are provided by coalitions and some of them have network e¤ects. Namely, people prefer to consume a public good in a coalition with more members. This paper adopts the Drèze and Greenberg (1980) type utility function where players have preferences over goods as well as coalition members. In a game with anonymous and separable network e¤ect, the core is nonempty when coalition feasible sets are monotonic and players'preferences over public goods have connected support. All core allocations consist of connected coalitions and they are Tiebout equilibria as well. We also examine the no-exodus equilibrium for games whose feasible sets are not monotonic.
We study the formation of coalitions that provide public goods to members. Individuals are linked... more We study the formation of coalitions that provide public goods to members. Individuals are linked on a tree graph and those with similar preferences are connected on the tree. We present a solution that selects allocations belonging to the coalition structure core and that are also envy-free.
In a production economy, multiple public goods are produced by …rms in competitive markets, and p... more In a production economy, multiple public goods are produced by …rms in competitive markets, and provided by the government together with contributions from consumers. There are widespread externalities: all consumers' consumption and contributions and all …rms'production enter into utility functions. Public goods can be imperfectly substitutes or complements, and they can be coalition or club goods. Zero bounds that require consumers to make nonnegative contributions complicate the di¤erentiable approach. Applying parametric transversality theorem for smooth economies in a regular parameterization, we obtain the existence of a contribution equilibrium and generic regularity of equilibria.
International Journal of Economic Theory, Dec 18, 2019
Models of city systems based on market theories are unable to replicate their size distribution. ... more Models of city systems based on market theories are unable to replicate their size distribution. The stochastic process approach to size distribution, which asserts proportional growth, does not provide a strong economic foundation. Hence an apparent irreconcilability. We propose that since there is a continuum of equilibrium set in market models of cities, as pointed out by Berliant and Kung (2006), proportional growth can work as an equilibrium selection. We compute an urban configuration that has not been presented in the literature before. A small city locates inside a larger city's agricultural supply zone. This gives a larger variation in city size that may contain Zipf's distribution.
We study how individuals divide themselves into coalitions and choose a public alternative for ea... more We study how individuals divide themselves into coalitions and choose a public alternative for each coalition. When preferences have consecutive support and coalition feasible sets are positively population-responsive, the proposed consecutive benevolence solution generates allocations belonging to the coalition structure core and that are also Tiebout equilibria. However, when each coalition follows a single-valued collective decision rule, the coalition structure core may be empty. Our results show that if individual preferences are, in a sense, similar and if members can be as well o¤ when a coalition enlarges, then a stable formation of collective decision-making units can be guaranteed. A predetermined decision rule makes coalitions less stable.
A great deal of production and consumption behavior takes place in the context of social organiza... more A great deal of production and consumption behavior takes place in the context of social organizations that seem to fall outside of the traditional paradigm of profit/utility maximization. These organizations are voluntary in nature and rely on contributions from members to achieve their objectives. Examples include the Linux operating system and other FOSS projects, political movements, churches and religious groups, Habitat for Humanity, and similar charitable organizations. In this paper, we consider a world containing agents with heterogeneous abilities who may voluntarily choose to make effort contributions to one or more different public projects. Agents are motivated by a desire to be seen as significant contributors to important and valuable projects, the warm glow from the act of contributing, and a desire to directly enjoy the benefits of projects when complete. We find that contributions from others can be either strategic complements or substitutes. We show that Nash equilibria exist and study how agents' abilities and project quality affect the equilibrium levels of contributions.
It is well known that externalities cause fundamental non-convexity problems in the production se... more It is well known that externalities cause fundamental non-convexity problems in the production set. We demonstrate that the differentiable approach is a proper tool. Existence of equilibrium obtains without requiring aggregate convexity in consumption or production. Our model allows general externalities in consumption and production and also price dependency.
A great deal of production and consumption behavior takes place in the context of social organiza... more A great deal of production and consumption behavior takes place in the context of social organizations that seem to fall outside of the traditional paradigm of profit/utility maximization. These organizations are voluntary in nature and rely on contributions from members to achieve their objectives. Examples include the Linux operating system and other FOSS projects, political movements, churches and religious groups, Habitat for Humanity, and similar charitable organizations. In this paper, we consider a world containing agents with heterogeneous abilities who may voluntarily choose to make effort contributions to one or more different public projects. Agents are motivated by a desire to be seen as significant contributors to important and valuable projects, the warm glow from the act of contributing, and a desire to directly enjoy the benefits of projects when complete. We find that contributions from others can be either strategic complements or substitutes. We show that Nash equilibria exist and study how agents' abilities and project quality affect the equilibrium levels of contributions.
The tomahawk bifurcation is used by Fujita et al. (1999) in a model with two regions to explain t... more The tomahawk bifurcation is used by Fujita et al. (1999) in a model with two regions to explain the formation of a core-periphery urban pattern from an initial uniform distribution. Baldwin et al. (2003) show that the tomahawk bifurcation disappears when the two regions have an uneven population of immobile agricultural workers. Thus, the appearance of this type of bifurcation is the result of assumed exogenous model symmetry. We provide a general analysis in a regional model of the class of bifurcations that have crossing equilibrium loci, including the tomahawk bifurcation, by examining arbitrary smooth parameter paths in a higher dimensional parameter space. We …nd that, in a parameter space satisfying a mild rank condition, generically in all parameter The authors thank Yuri Mansury for helpful comments but retain responsibility for any errors herein.
ABSTRACT We extends the single-crossing property of preferences to tree graphs, and show that it ... more ABSTRACT We extends the single-crossing property of preferences to tree graphs, and show that it is equivalent to intermediate preferences and order restriction, also extended to tree graphs. Moreover, to facilitate the use of single-crossing in network games, we develop algorithms to answer the following questions. Given a preference profile, can we construct a tree graph that supports single-crossing, if it is? Given a set of alternatives, can we generate single-crossing preference profiles with associated tree graphs?
This paper analyzes the genericity of bifurcations of one-parameter families of smooth (C1) vecto... more This paper analyzes the genericity of bifurcations of one-parameter families of smooth (C1) vector fields that are embedded in an underlying multi-dimensional parameter space. Bifurcations with crossing equilibrium loci are called 'split bifurcations.' They include, for example, the pitchfork bifurcation and the transcritical bifurcation. In a regular parameter space where the system's Jacobian matrix with respect to endogenous variables and parameters has full rank at every equilibrium for all parameter values, there is a generic (open and dense) set of one-parameter C1 families of vector fields without split bifurcations. It is not difficult to obtain a regular parameter space when there are enough parameters. A regional migration model (a la Fujita, Krugman and Venables 1999) featuring the pitchfork bifurcation is presented as an example.
Oxford Research Encyclopedia of Economics and Finance, Apr 20, 2022
Economic and social activities in different locations interact through systematic connections, wh... more Economic and social activities in different locations interact through systematic connections, which can be modeled as network structures. For example, production processes combine various inputs, tasks, and intermediate products that are spread over space; laborers transmit knowledge and skills along networks of work relations; products are delivered through transportation networks; and local public goods have external effects that spill over into the network of neighborhoods. Such networks bring benefits to connected nodes in the form of externalities. Approaches adopted for modeling networks of locations or that are applicable to spatial economics can be placed into two major categories. First, networks can be formed endogenously when nodes choose links strategically. Thus, networks are outcomes that emerge from strategic equilibria. This approach anylyzes the patterns of networks that are in equilibrium and patterns that are efficient. Second, networks can be a background structure with fixed existing links. In this approach, centrality measures are designed to indicate the importance of a node in the network. In many contexts, these measures determine the equilibrium and efficient behavior of nodes. Networks can be applied to broad issues in urban, regional, and location economics, such as neighborhood interactions, transportation, local public goods, trade, industrial sites, business operations. The strategic connection approach models the network as a strategic game. Both cooperative and noncooperative equilibrium concepts have been adopted in the literature. A link may form cooperatively when both nodes are better off, or one node may force a link noncooperatively onto another. The structure of intracity and intercity networks can be investigated using this framework: In a city, neighborhoods are networks of blocks, which are connected by streets and sidewalks; external benefits spill over into connected blocks; locally integrated neighborhoods emerge in equilibrium; and cities are connected by intercity transportation networks. In such models, the core–periphery patterns of cities are found to emerge in the equilibrium. The structural approach treats network structures as exogenously fixed, and links are not subject to change. In such settings, centrality measures, which indicate how centrally connected the position of a node is in the network, determine the behaviors of nodes. For example, when there are widespread externalities so that payoffs of nodes are determined by efforts of all connected nodes, the equilibrium effort of a node is proportional to its Bonacich centrality measure. Centrality measures determine equilibrium and efficient outcomes in other network settings as well. Examples of such are how conformity in peer networks affects criminal behaviors, how nodes choose security investments against the spread of infection in the network, how intercity transportation networks determine the distribution of city size, and how community residents choose the number of visits to an urban center. Futher findings include, for example, in an economy-wide trade network of intermediate inputs, local economic shocks can cause aggregate production fluctuations; in a network of neighboring jurisdictions, voluntary contributions to local public goods are neutral to income transfers; in a geographical trade network, a firm that already exports to a location will have a higher probability of exporting to a second location if the two locations have a larger volume of trade; and firms spread adverse impacts from a local economic shock through their internal networks across regions.
We study the indeterminacy of equilibrium in the Fujita-Krugman (1995) model of city formation un... more We study the indeterminacy of equilibrium in the Fujita-Krugman (1995) model of city formation under monopolistic competition and increasing returns. Both the number and the locations of cities are endogenously determined. Assuming smooth transportation costs, we examine equilibria in city-economies where a …nite number of cities form endogenously. For any positive integer K, the set of equilibria with K distinct cities has a smooth manifold of dimension K 1 as its interior for almost all parameter values in a regular parameterization. The disjoint union of these sets over all positive integers K constitutes the entire equilibrium set.
Jacques Thisse, and Alison Watts. Needless to say, the usual disclaimer applies. The views expres... more Jacques Thisse, and Alison Watts. Needless to say, the usual disclaimer applies. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.
Oxford Research Encyclopedia of Economics and Finance
Economic and social activities in different locations interact through systematic connections, wh... more Economic and social activities in different locations interact through systematic connections, which can be modeled as network structures. For example, production processes combine various inputs, tasks, and intermediate products that are spread over space; laborers transmit knowledge and skills along networks of work relations; products are delivered through transportation networks; and local public goods have external effects that spill over into the network of neighborhoods. Such networks bring benefits to connected nodes in the form of externalities. Approaches adopted for modeling networks of locations or that are applicable to spatial economics can be placed into two major categories. First, networks can be formed endogenously when nodes choose links strategically. Thus, networks are outcomes that emerge from strategic equilibria. This approach anylyzes the patterns of networks that are in equilibrium and patterns that are efficient. Second, networks can be a background struct...
We develop a framework of group corruption via back-door negotiations between an outside initiato... more We develop a framework of group corruption via back-door negotiations between an outside initiator and an authority of decision-makers in a hierarchical organization. We examine the role played by the architecture of a multi-tier authority and determine under such a structure how bargaining proceeds, in what order, and when it breaks down. We verify that equilibrium bargaining sequence proceeds as a chain through decision-making agents, regardless of the hierarchy of the organization. We prove the existence of a compromised equilibrium, where the decision of the authority is compromised, and establish sufficient conditions under which the most natural bottom-up bargaining configuration arises in equilibrium where a proposer negotiates with an immediately higher ranked respondent, starting with the initiator bargaining with the lowest ranked decision-maker in the organization. We then show the circumstances under which a top-down or a non-monotonic equilibrium configuration may emerge, and those under which the deal may break down. This enables us to capture a rich array of group corruptive configurations as observed. We conclude by investigating the extension to multi-tier authorities with multiple agents of the same rank in each tier, such as in a tree hierarchy.
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