Conditional on the considered equilibrium, the probability of a bank run in the demand-deposit contract models of Bryant (1980) and of Diamond and Dybvig (1983) is either one or zero. In contrast, we establish the existence of an interval - being a strict subset of the unit-interval - of possible bank run probabilities for a two-player demand-deposit contract model where players receive independent signals about their liquidity desire from a continuous type space. As our main result we demonstrate that this interval reduces to a unique probability of a panic-based bank strictly smaller than one if and only if there exist types for which not running on the bank is a dominant action. In addition to existing models of bank runs such as, e.g., Goldstein and Pauzner (2005), our approach also provides some assessment of the likelihood of a bank run if there are no types for which not running on the bank is a dominant action. As a consequence, we can investigate the comparative statics of the likelihood of bank runs with respect to a larger range of payoff parameters than considered in previous models. Furthermore, we derive a technical result by which the findings of Morris and Shin (2005) on the dominance-solvability of binary action games with strategic complements also apply to nice games in the sense of Moulin (1984) if players' best response functions are increasing.
{"title":"Assessing the Likelihood of Panic-Based Bank Runs","authors":"A. Zimper","doi":"10.2202/1534-5971.1323","DOIUrl":"https://doi.org/10.2202/1534-5971.1323","url":null,"abstract":"Conditional on the considered equilibrium, the probability of a bank run in the demand-deposit contract models of Bryant (1980) and of Diamond and Dybvig (1983) is either one or zero. In contrast, we establish the existence of an interval - being a strict subset of the unit-interval - of possible bank run probabilities for a two-player demand-deposit contract model where players receive independent signals about their liquidity desire from a continuous type space. As our main result we demonstrate that this interval reduces to a unique probability of a panic-based bank strictly smaller than one if and only if there exist types for which not running on the bank is a dominant action. In addition to existing models of bank runs such as, e.g., Goldstein and Pauzner (2005), our approach also provides some assessment of the likelihood of a bank run if there are no types for which not running on the bank is a dominant action. As a consequence, we can investigate the comparative statics of the likelihood of bank runs with respect to a larger range of payoff parameters than considered in previous models. Furthermore, we derive a technical result by which the findings of Morris and Shin (2005) on the dominance-solvability of binary action games with strategic complements also apply to nice games in the sense of Moulin (1984) if players' best response functions are increasing.","PeriodicalId":282221,"journal":{"name":"Contributions in Theoretical Economics","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121151760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper analyses conditions on agents' preferences for a unique stable matching in models of two-sided matching with non-transferable utility. The No Crossing Condition (NCC) is sufficient for uniqueness; it is based on the notion that a person's characteristics, for example their personal qualities or their productive capabilities, not only form the basis of their own attraction to the opposite sex but also determine their own preferences. The paper also shows that a weaker condition, alpha-reducibility, is both necessary and sufficient for a population and any of its subpopulations to have a unique stable matching. If preferences are based on utility functions with agents' characteristics as arguments, then the NCC may be easy to verify. The paper explores conditions on utility functions which imply that the NCC is satisfied whatever the distribution of characteristics. The usefulness of this approach is illustrated by two simple models of household formation.
{"title":"The Uniqueness of Stable Matchings","authors":"Simon J Clark","doi":"10.2202/1534-5971.1283","DOIUrl":"https://doi.org/10.2202/1534-5971.1283","url":null,"abstract":"This paper analyses conditions on agents' preferences for a unique stable matching in models of two-sided matching with non-transferable utility. The No Crossing Condition (NCC) is sufficient for uniqueness; it is based on the notion that a person's characteristics, for example their personal qualities or their productive capabilities, not only form the basis of their own attraction to the opposite sex but also determine their own preferences. The paper also shows that a weaker condition, alpha-reducibility, is both necessary and sufficient for a population and any of its subpopulations to have a unique stable matching. If preferences are based on utility functions with agents' characteristics as arguments, then the NCC may be easy to verify. The paper explores conditions on utility functions which imply that the NCC is satisfied whatever the distribution of characteristics. The usefulness of this approach is illustrated by two simple models of household formation.","PeriodicalId":282221,"journal":{"name":"Contributions in Theoretical Economics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134624015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper extends the Downsian-Hotelling model of electoral competition to allow for unobserved qualitative differences between candidates. I show that these underlying qualitative differences generate pure strategy Nash equilibria, even if policies are defined in a multidimensional space, and explain platform divergence from the median. Moreover, the extension gives content to a second (well-known) role elections play apart from bridging conflict: to reveal information about candidates.
{"title":"A Spatial Election with Common Values","authors":"Carlos Maravall-Rodriguez","doi":"10.2202/1534-5971.1269","DOIUrl":"https://doi.org/10.2202/1534-5971.1269","url":null,"abstract":"This paper extends the Downsian-Hotelling model of electoral competition to allow for unobserved qualitative differences between candidates. I show that these underlying qualitative differences generate pure strategy Nash equilibria, even if policies are defined in a multidimensional space, and explain platform divergence from the median. Moreover, the extension gives content to a second (well-known) role elections play apart from bridging conflict: to reveal information about candidates.","PeriodicalId":282221,"journal":{"name":"Contributions in Theoretical Economics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131051897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A bilateral trading model with investment is considered. In a cooperative investment version of the model, the seller's investment stochastically determines the buyer's valuation of the good. The value and cost of the good are realized only after the investment is made, and the investment level and the realization of the good's value and cost are private information. I show that, under these assumptions, no contract made before the investment can simultaneously induce efficient investment and efficient ex post trade when the buyer's type is continuously distributed. This inefficiency result contrasts sharply with the efficiency result under the standard selfish investment model, where the seller's investment stochastically determines the seller's cost.
{"title":"Inefficiency in a Bilateral Trading Problem with Cooperative Investment","authors":"Kazumi Hori","doi":"10.2202/1534-5971.1248","DOIUrl":"https://doi.org/10.2202/1534-5971.1248","url":null,"abstract":"A bilateral trading model with investment is considered. In a cooperative investment version of the model, the seller's investment stochastically determines the buyer's valuation of the good. The value and cost of the good are realized only after the investment is made, and the investment level and the realization of the good's value and cost are private information. I show that, under these assumptions, no contract made before the investment can simultaneously induce efficient investment and efficient ex post trade when the buyer's type is continuously distributed. This inefficiency result contrasts sharply with the efficiency result under the standard selfish investment model, where the seller's investment stochastically determines the seller's cost.","PeriodicalId":282221,"journal":{"name":"Contributions in Theoretical Economics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131865323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A distributed system model is studied, where individual agents play repeatedly against each other and change their strategies based upon previous play. It is shown how to model this environment in terms of continuous population densities of agent types. A complication arises because the population densities of different strategies depend upon each other not only through game payoffs, but also through the strategy distributions themselves. In spite of this, it is shown that when an agent imitates the strategy of his previous opponent at a sufficiently high rate, the system of equations which governs the dynamical evolution of agent populations can be reduced to one equation for the total population. In a sense, the dynamics 'collapse' to the dynamics of the entire system taken as a whole, which describes the behavior of all types of agents. We explore the implications of this model, and present both analytical and simulation results.
{"title":"Finite Memory Distributed Systems","authors":"Victor Dorofeenko, J. Shorish","doi":"10.2202/1534-5971.1315","DOIUrl":"https://doi.org/10.2202/1534-5971.1315","url":null,"abstract":"A distributed system model is studied, where individual agents play repeatedly against each other and change their strategies based upon previous play. It is shown how to model this environment in terms of continuous population densities of agent types. A complication arises because the population densities of different strategies depend upon each other not only through game payoffs, but also through the strategy distributions themselves. In spite of this, it is shown that when an agent imitates the strategy of his previous opponent at a sufficiently high rate, the system of equations which governs the dynamical evolution of agent populations can be reduced to one equation for the total population. In a sense, the dynamics 'collapse' to the dynamics of the entire system taken as a whole, which describes the behavior of all types of agents. We explore the implications of this model, and present both analytical and simulation results.","PeriodicalId":282221,"journal":{"name":"Contributions in Theoretical Economics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133882014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper characterizes the optimal provision of quality by a monopolist facing a population of consumers with private valuation for quality. Unlike previous models by Mussa and Rosen (1978) and others, this paper assumes there is a mass of consumers who prefer the highest quality goods. I liken these consumers to snobs who demand the highest valued goods. I show that the quality supplied jumps discontinuously as the highest valued consumers are encountered and the variety of products is reduced as the population of snobs increases. I also show that only snobs may be supplied once their population grows to a critical size.
{"title":"Snobs and Quality Gaps","authors":"S. Basov","doi":"10.2202/1534-5971.1254","DOIUrl":"https://doi.org/10.2202/1534-5971.1254","url":null,"abstract":"The paper characterizes the optimal provision of quality by a monopolist facing a population of consumers with private valuation for quality. Unlike previous models by Mussa and Rosen (1978) and others, this paper assumes there is a mass of consumers who prefer the highest quality goods. I liken these consumers to snobs who demand the highest valued goods. I show that the quality supplied jumps discontinuously as the highest valued consumers are encountered and the variety of products is reduced as the population of snobs increases. I also show that only snobs may be supplied once their population grows to a critical size.","PeriodicalId":282221,"journal":{"name":"Contributions in Theoretical Economics","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133635782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Within a costly state verification setting, we derive the optimal financial contract between an entrepreneur, a (potentially financing) supervisor and a pure investor when there is non-verifiable and non-contractible monitoring and limited liability. We show that diversion of cash flows to the entrepreneur arises as optimal behaviour and that to get the best reporting and monitoring incentives it is crucial to separate the financing from the monitoring role. In particular, higher efficiency can be achieved by ensuring that the entrepreneur and the supervisor do not collect any cash flows in low states. These should be paid to a third party instead, the pure investor, who in exchange provides funding. However, whether the pure investor entirely finances the project (and the supervisor purely acts as a monitor) or only provides partial finance (with the supervisor cofinancing) is immaterial, as the optimal financing of the project can justify a range of alternative financial structures.
{"title":"Liars and Inspectors: Optimal Financial Contracts When Monitoring is Non-Observable","authors":"A. Menichini, P. Simmons","doi":"10.2202/1534-5971.1216","DOIUrl":"https://doi.org/10.2202/1534-5971.1216","url":null,"abstract":"Within a costly state verification setting, we derive the optimal financial contract between an entrepreneur, a (potentially financing) supervisor and a pure investor when there is non-verifiable and non-contractible monitoring and limited liability. We show that diversion of cash flows to the entrepreneur arises as optimal behaviour and that to get the best reporting and monitoring incentives it is crucial to separate the financing from the monitoring role. In particular, higher efficiency can be achieved by ensuring that the entrepreneur and the supervisor do not collect any cash flows in low states. These should be paid to a third party instead, the pure investor, who in exchange provides funding. However, whether the pure investor entirely finances the project (and the supervisor purely acts as a monitor) or only provides partial finance (with the supervisor cofinancing) is immaterial, as the optimal financing of the project can justify a range of alternative financial structures.","PeriodicalId":282221,"journal":{"name":"Contributions in Theoretical Economics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129751026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Several studies have recently adopted the segmented markets model as a framework for monetary analysis. The characteristic assumption is that some households never participate in financial markets. This paper proves the existence of an equilibrium for segmented markets models where monetary policy is defined in terms of the short-term nominal interest rate. The model allows us to consider the important cases where monetary policy affects output, and responds to any sources of uncertainty, including output itself. The assumptions required for existence constrain the maximum value and the variability of the nominal interest rate. The period utility function is logarithmic. The proof is constructive, and shows how the model can be solved numerically. A similar proof can be used in the case that monetary policy is defined in terms of the bond supply.
{"title":"Existence of Equilibrium for Segmented Markets Models with Interest Rate Monetary Policies","authors":"Filippo Occhino","doi":"10.2202/1534-5971.1288","DOIUrl":"https://doi.org/10.2202/1534-5971.1288","url":null,"abstract":"Several studies have recently adopted the segmented markets model as a framework for monetary analysis. The characteristic assumption is that some households never participate in financial markets. This paper proves the existence of an equilibrium for segmented markets models where monetary policy is defined in terms of the short-term nominal interest rate. The model allows us to consider the important cases where monetary policy affects output, and responds to any sources of uncertainty, including output itself. The assumptions required for existence constrain the maximum value and the variability of the nominal interest rate. The period utility function is logarithmic. The proof is constructive, and shows how the model can be solved numerically. A similar proof can be used in the case that monetary policy is defined in terms of the bond supply.","PeriodicalId":282221,"journal":{"name":"Contributions in Theoretical Economics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115143208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study a model with product differentiation by manufacturers and spatial differentiation by supermarkets where the customers visit only one shop and the supermarkets carry both goods. Under fixed fee pricing by the manufacturers the intensity of interbrand competition increases with the degree of differentiation between the supermarkets. When the supermarkets are more and more spatially differentiated the struggle between manufacturers and supermarkets dominates the competition between the manufacturers and results in lower wholesale prices and manufacturers profits.
{"title":"Are Manufacturers Competing through or with Supermarkets? A Theoretical Investigation","authors":"D. Laussel","doi":"10.2202/1534-5971.1317","DOIUrl":"https://doi.org/10.2202/1534-5971.1317","url":null,"abstract":"We study a model with product differentiation by manufacturers and spatial differentiation by supermarkets where the customers visit only one shop and the supermarkets carry both goods. Under fixed fee pricing by the manufacturers the intensity of interbrand competition increases with the degree of differentiation between the supermarkets. When the supermarkets are more and more spatially differentiated the struggle between manufacturers and supermarkets dominates the competition between the manufacturers and results in lower wholesale prices and manufacturers profits.","PeriodicalId":282221,"journal":{"name":"Contributions in Theoretical Economics","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124674691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper provides a general framework for pricing of real options for wide classes of payoff streams that are functions of Levy processes. As applications, we calculate the values of sequences of embedded options, (which we call Russian dolls), and study two models of expansion of a monopoly. In the first model, the monopoly increases capital stock each time the stochastic demand crosses the boundary of the inaction region. Assuming that above a certain level, the stochastic demand factor increases slower than in the standard geometric Levy models, we demonstrate that the investment threshold is lower than in the standard models. Moreover, in the intermediate range between the regimes of the fast and slow growth, the monopoly may find it optimal to simultaneously increase the capital stock and decrease the output price. In a two-factor model of technology adoption, we show that diffusion and jump uncertainty can produce opposite effects.
{"title":"General Option Exercise Rules, with Applications to Embedded Options and Monopolistic Expansion","authors":"S. Boyarchenko, S. Levendorskii","doi":"10.2202/1534-5971.1292","DOIUrl":"https://doi.org/10.2202/1534-5971.1292","url":null,"abstract":"This paper provides a general framework for pricing of real options for wide classes of payoff streams that are functions of Levy processes. As applications, we calculate the values of sequences of embedded options, (which we call Russian dolls), and study two models of expansion of a monopoly. In the first model, the monopoly increases capital stock each time the stochastic demand crosses the boundary of the inaction region. Assuming that above a certain level, the stochastic demand factor increases slower than in the standard geometric Levy models, we demonstrate that the investment threshold is lower than in the standard models. Moreover, in the intermediate range between the regimes of the fast and slow growth, the monopoly may find it optimal to simultaneously increase the capital stock and decrease the output price. In a two-factor model of technology adoption, we show that diffusion and jump uncertainty can produce opposite effects.","PeriodicalId":282221,"journal":{"name":"Contributions in Theoretical Economics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131814312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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