Sidartha Gordon - Academia.edu (original) (raw)
Papers by Sidartha Gordon
Journal of Mathematical Economics, Dec 1, 2013
We consider collective decision problems given by a pro…le of single-peaked preferences de…ned ov... more We consider collective decision problems given by a pro…le of single-peaked preferences de…ned over the real line and a set of pure public facilities to be located on the line. In this context, Bochet and Gordon (2012) provide a large class of priority rules based on e¢ ciency, object-population monotonicity and sovereignty. Each such rule is described by a …xed priority ordering among interest groups. We show that any priority rule which treats agents symmetrically-anonymity-, respects some form of coherence across collective decision problems-reinforcement-and only depends on peak informationpeak-only-, is a weighted majoritarian rule. Each such rule de…nes priorities based on the relative size of the interest groups and speci…c weights attached to locations. We give an explicit account of the richness of this class of rules.
Games and Economic Behavior, Mar 1, 2016
We examine project selection decisions of …rms constrained in the number of projects they can han... more We examine project selection decisions of …rms constrained in the number of projects they can handle at once. Taking on a project requires a commitment of uncertain duration, restricting the …rm from selecting another project in subsequent periods. Due to the capacity constraints and need for commitment, some positive return projects are rejected. In a sequential move dynamic game, we …nd that the …rst mover strategically rejects some projects that are then selected by the second mover, even when both …rms are symmetric and equally informed. We study the e¤ects of competition on project selection, and compare the jointly optimal selection decision to the behavior of strategic non-cooperative …rms.
American Economic Journal: Microeconomics, Aug 1, 2014
We study mechanisms for selecting up to m out of n projects. Project managers' private informatio... more We study mechanisms for selecting up to m out of n projects. Project managers' private information on quality is elicited through transfers. Under limited liability, the optimal mechanism selects projects that maximize some function of the project's observable and reported characteristics. When all reported qualities exceed their own project-specific thresholds, the selected set only depends on observable characteristics, not reported qualities. Each threshold is related to (i) the outside option level at which the cost and benefit of eliciting information on the project cancel out and (ii) the optimal value of selecting one among infinitely many ex ante identical projects.
Games and Economic Behavior, 2012
A collective decision problem is described by a set of agents, a profile of single-peaked prefere... more A collective decision problem is described by a set of agents, a profile of single-peaked preferences over the real line and a number k of public facilities to be located. We consider public facilities that do not suffer from congestion and are non-excludable. We provide a characterization of the class of rules satisfying Pareto-efficiency, object-population monotonicity and sovereignty. Each rule in the class is a priority rule that selects locations according to a predetermined priority ordering among "interest groups". We characterize each of the subclasses of priority rules that respectively satisfy anonymity, hiding-proofness and strategy-proofness. In particular, we prove that a priority rule is strategy-proof if and only if it partitions the set of agents into a fixed hierarchy. Alternatively, any such rule can be viewed as a collection of fixed-populations generalized peakselection median rules (Moulin, 1980), that are linked across populations, in a way that we describe.
Social Science Research Network, 2010
Conflicts are likely less violent if individuals entertain the possibility that the opponent may ... more Conflicts are likely less violent if individuals entertain the possibility that the opponent may be right. Why is it so di cult to observe this attitude? In this paper, we consider a game of conflict where two opponents fight in order to impose their preferred policy. Before entering the conflict, one opponent (the agent) trusts the information received by his principal. The principal wants to a↵ect the agent's e↵ort, but he also cares that the agent selects the correct policy and that he has the right incentives to acquire information. We find conditions under which the principal induces hawkish attitudes in the agent. As a result, the agent has no doubts about the optimality of his preferred policy, conflicts are violent and bad decisions are sometimes made. Under some other conditions, the agent adopts dovish attitudes of systematic doubt and conflicts are less violent.
We propose a new selection criterion from the set of Bayesian-Nash equilibria in cheap talk signa... more We propose a new selection criterion from the set of Bayesian-Nash equilibria in cheap talk signalling games à la Crawford and Sobel (1982). A candidate strategy pro…le is stable if the in…nite iteration of the composed best-response mapping from any neighboring perturbation of the candidate pro…le converges back to this same pro…le. Under some conditions, any game in which the maximal number of actions taken in equilibrium is some maximal integer max ; has a unique stable equilibrium. If the sender's bias is either "upward bias at the top" or "downward at the bottom," the selected equilibrium induces max actions and it is maximal for some partial order over interval partitions, with respect to which the composed best-response is increasing. If the sender's bias is "inward," the selected equilibrium may induce either max or max 1 actions. In particular, if the game is symmetric with respect to the central type, the selected equilibrium induces max 1 actions. We compare our concept to Chen, Kartik and Sobel's (2008) NITS criterion.
Abstract: We introduce a new fixed point method to analyze cheap talk games, in the tradition of ... more Abstract: We introduce a new fixed point method to analyze cheap talk games, in the tradition of Crawford and Sobel (1982). We illustrate it in a class of one-dimensional games, where the sender’s bias may depend on the state of the world, and which contains Crawford and Sobel’s model as a special case. The method yields new results on the structure of the equilibrium set. For games in which the sender has an outward bias, i.e. the sender is more extreme than the receiver whenever the state of the world is extreme, we prove that for any positive integer k, there is an equilibrium with exactly k pools, and at least one equilibrium with an infinite number of pools. We discuss the extent to which the fixed point method can be used to analyze other cheap talk signalling problems.
We study a two-step R&D race between two rms, each with private information on its own position.... more We study a two-step R&D race between two rms, each with private information on its own position. Each rms can publish,that is, announce its own progress in a veri able manner. Publications do not directly a¤ect the position of the rival, but only provide information on the position of the announcer and may be used strategically to induce the rival to cut the intensity of its own R&D investment. Within a certain parameter set of interest, we characterize the class of symmetric, perfect Bayesian equilibria in pure strategies satisfying a weak Markovian property of invention-date-independence. There are either one or two such equilibria. In one equilibrium, only the rst rm which completes the intermediate step publishes and does so immediately. In the other equilibrium, no rm ever publishes any progress at all. Incentives and disincentives to publish are analyzed in terms of three distinct strategic e¤ects. For parameters with two equilibria, we show that the rmsjoint expected...
We study the implications of population-monotonicity (Thomson, 1983) and replacement-domination (... more We study the implications of population-monotonicity (Thomson, 1983) and replacement-domination (Moulin, 1987) in the class of attributebased preference domains (Nehring and Puppe 2002 a,b). Both conditions require that when some parameters of the economy change, the agents whose parameters are kept xed, should either all weakly lose or all weakly win. Population-monotonicity applies to the arrival and departure of agents, while replacement-domination applies to changes in preferences. Using results by Nehring and Puppe (2002b) on strategyproof and onto choice functions, we characterize on attribute-based preference domains the unanimity rules as the class of choice functions that satisfy either condition of solidarity and are in addition strategyproof and onto. We also characterize the attribute-based domains on which these properties are compatible. Next, we characterize the class of tree-structured domains as the ones where population-monotonicity and Pareto-e¢ ciency are compat...
We introduce a new fixed point method to analyze cheap talk games, in the tradition of Crawford a... more We introduce a new fixed point method to analyze cheap talk games, in the tradition of Crawford and Sobel (1982). We illustrate it in a class of onedimensional games, where the sender's bias may depend on the state of the world, and which contains Crawford and Sobel's model as a special case. The method yields new results on the structure of the equilibrium set. For games in which the sender has an outward bias, i.e. the sender is more extreme than the receiver whenever the state of the world is extreme, we prove that for any positive integer k, there is an equilibrium with exactly k pools, and at least one equilibrium with an infinite number of pools. We discuss the extent to which the fixed point method can be used to analyze other cheap talk signalling problems.
A collective decision problem is described by a set of agents, a profile of single-peaked prefere... more A collective decision problem is described by a set of agents, a profile of single-peaked preferences over the real line and a number of public facilities to be located. We consider public facilities that do not suffer from congestion and are non-excludable. We characterize the class of rules satisfying Pareto-efficiency, object-population monotonicity and sovereignty. Each rule in the class is a priority rule that selects locations according to a predetermined priority ordering among “interest groups”. We characterize the subclasses of priority rules that respectively satisfy anonymity, avoid the no-show paradox, strategy-proofness and population-monotonicity. In particular, we prove that a priority rule is strategy-proof if and only if it partitions the set of agents into a fixed hierarchy. Any such rule can also be viewed as a collection of generalized peak-selection median rules, that are linked across populations, in a way that we describe.
This paper studies the problem of providing two public goods for agents with single-peaked prefer... more This paper studies the problem of providing two public goods for agents with single-peaked preferences. A decision rule selects two points on the segment [0,1] for the public goods for every profile of reported preferences. Agents compare public good pairs by the lexmax ordering over pairs induced by their singlepeaked preference over single locations. We derive implications of strategyproofness in this setting and compare them with those in the model with one public good and in the model with two public goods under the max extension. We characterize the class of decision rules satisfying strategy-proofness, anonymity and continuity with respect to preferences .W e also characterize subclasses of rules that satisfy additional properties.
Games and Economic Behavior
In this paper, we study the implications of two solidarity conditions on the efficient location o... more In this paper, we study the implications of two solidarity conditions on the efficient location of a public good on a cycle, when agents have single-peaked, symmetric preferences. Solidarity requirements say that when the economy changes, the agents who are not causing the change should all be affected in the same direction: either they all gain or they all loose. The first requirement we study, population-monotonicity, applies to arrival or departure of one agent. The second requirement, replacement-domination, applies to changes in the preferences of one agent. We first restrict agents' preferred points to be located at the vertices of a regular polygon inscribed in the circle. Solutions satisfying the requirements for polygons with three, four or five vertices are characterized. When the number of vertices of the polygon is greater than five, we show that no solution satisfy the requirements. This incompatibility extends to the unconstrained problem where agents' preferred points can be located anywhere on the circle.
SSRN Electronic Journal, 2000
This paper studies a game of con ‡ict where two individuals …ght in order to choose a policy. Int... more This paper studies a game of con ‡ict where two individuals …ght in order to choose a policy. Intuitively, con ‡icts will be less violent if individuals entertain the possibility that their opponent may be right. Why is it so di¢ cult to observe this attitude? To answer this question, this paper considers a model of indoctrination where altruistic advisors (such as, preachers or parents), after receiving signals from Nature, send messages to the participants in the con ‡ict. In some cases, as a result of indoctrination, both individuals never doubt about the possibility of being wrong, although all available information suggests otherwise. In other cases, one of the two individuals is excessively reasonable: he believes that the opponent may be right even when all the evidence indicates beyond any doubt that the policy preferred by the opponent is suboptimal. The common feature in both cases is that information is distorted, although in di¤ erent directions. The model has a rich set of predictions concerning the incidence and intensity of con ‡ict, and the evolution of indoctrination strategies over time.
Journal of Mathematical Economics, Dec 1, 2013
We consider collective decision problems given by a pro…le of single-peaked preferences de…ned ov... more We consider collective decision problems given by a pro…le of single-peaked preferences de…ned over the real line and a set of pure public facilities to be located on the line. In this context, Bochet and Gordon (2012) provide a large class of priority rules based on e¢ ciency, object-population monotonicity and sovereignty. Each such rule is described by a …xed priority ordering among interest groups. We show that any priority rule which treats agents symmetrically-anonymity-, respects some form of coherence across collective decision problems-reinforcement-and only depends on peak informationpeak-only-, is a weighted majoritarian rule. Each such rule de…nes priorities based on the relative size of the interest groups and speci…c weights attached to locations. We give an explicit account of the richness of this class of rules.
Games and Economic Behavior, Mar 1, 2016
We examine project selection decisions of …rms constrained in the number of projects they can han... more We examine project selection decisions of …rms constrained in the number of projects they can handle at once. Taking on a project requires a commitment of uncertain duration, restricting the …rm from selecting another project in subsequent periods. Due to the capacity constraints and need for commitment, some positive return projects are rejected. In a sequential move dynamic game, we …nd that the …rst mover strategically rejects some projects that are then selected by the second mover, even when both …rms are symmetric and equally informed. We study the e¤ects of competition on project selection, and compare the jointly optimal selection decision to the behavior of strategic non-cooperative …rms.
American Economic Journal: Microeconomics, Aug 1, 2014
We study mechanisms for selecting up to m out of n projects. Project managers' private informatio... more We study mechanisms for selecting up to m out of n projects. Project managers' private information on quality is elicited through transfers. Under limited liability, the optimal mechanism selects projects that maximize some function of the project's observable and reported characteristics. When all reported qualities exceed their own project-specific thresholds, the selected set only depends on observable characteristics, not reported qualities. Each threshold is related to (i) the outside option level at which the cost and benefit of eliciting information on the project cancel out and (ii) the optimal value of selecting one among infinitely many ex ante identical projects.
Games and Economic Behavior, 2012
A collective decision problem is described by a set of agents, a profile of single-peaked prefere... more A collective decision problem is described by a set of agents, a profile of single-peaked preferences over the real line and a number k of public facilities to be located. We consider public facilities that do not suffer from congestion and are non-excludable. We provide a characterization of the class of rules satisfying Pareto-efficiency, object-population monotonicity and sovereignty. Each rule in the class is a priority rule that selects locations according to a predetermined priority ordering among "interest groups". We characterize each of the subclasses of priority rules that respectively satisfy anonymity, hiding-proofness and strategy-proofness. In particular, we prove that a priority rule is strategy-proof if and only if it partitions the set of agents into a fixed hierarchy. Alternatively, any such rule can be viewed as a collection of fixed-populations generalized peakselection median rules (Moulin, 1980), that are linked across populations, in a way that we describe.
Social Science Research Network, 2010
Conflicts are likely less violent if individuals entertain the possibility that the opponent may ... more Conflicts are likely less violent if individuals entertain the possibility that the opponent may be right. Why is it so di cult to observe this attitude? In this paper, we consider a game of conflict where two opponents fight in order to impose their preferred policy. Before entering the conflict, one opponent (the agent) trusts the information received by his principal. The principal wants to a↵ect the agent's e↵ort, but he also cares that the agent selects the correct policy and that he has the right incentives to acquire information. We find conditions under which the principal induces hawkish attitudes in the agent. As a result, the agent has no doubts about the optimality of his preferred policy, conflicts are violent and bad decisions are sometimes made. Under some other conditions, the agent adopts dovish attitudes of systematic doubt and conflicts are less violent.
We propose a new selection criterion from the set of Bayesian-Nash equilibria in cheap talk signa... more We propose a new selection criterion from the set of Bayesian-Nash equilibria in cheap talk signalling games à la Crawford and Sobel (1982). A candidate strategy pro…le is stable if the in…nite iteration of the composed best-response mapping from any neighboring perturbation of the candidate pro…le converges back to this same pro…le. Under some conditions, any game in which the maximal number of actions taken in equilibrium is some maximal integer max ; has a unique stable equilibrium. If the sender's bias is either "upward bias at the top" or "downward at the bottom," the selected equilibrium induces max actions and it is maximal for some partial order over interval partitions, with respect to which the composed best-response is increasing. If the sender's bias is "inward," the selected equilibrium may induce either max or max 1 actions. In particular, if the game is symmetric with respect to the central type, the selected equilibrium induces max 1 actions. We compare our concept to Chen, Kartik and Sobel's (2008) NITS criterion.
Abstract: We introduce a new fixed point method to analyze cheap talk games, in the tradition of ... more Abstract: We introduce a new fixed point method to analyze cheap talk games, in the tradition of Crawford and Sobel (1982). We illustrate it in a class of one-dimensional games, where the sender’s bias may depend on the state of the world, and which contains Crawford and Sobel’s model as a special case. The method yields new results on the structure of the equilibrium set. For games in which the sender has an outward bias, i.e. the sender is more extreme than the receiver whenever the state of the world is extreme, we prove that for any positive integer k, there is an equilibrium with exactly k pools, and at least one equilibrium with an infinite number of pools. We discuss the extent to which the fixed point method can be used to analyze other cheap talk signalling problems.
We study a two-step R&D race between two rms, each with private information on its own position.... more We study a two-step R&D race between two rms, each with private information on its own position. Each rms can publish,that is, announce its own progress in a veri able manner. Publications do not directly a¤ect the position of the rival, but only provide information on the position of the announcer and may be used strategically to induce the rival to cut the intensity of its own R&D investment. Within a certain parameter set of interest, we characterize the class of symmetric, perfect Bayesian equilibria in pure strategies satisfying a weak Markovian property of invention-date-independence. There are either one or two such equilibria. In one equilibrium, only the rst rm which completes the intermediate step publishes and does so immediately. In the other equilibrium, no rm ever publishes any progress at all. Incentives and disincentives to publish are analyzed in terms of three distinct strategic e¤ects. For parameters with two equilibria, we show that the rmsjoint expected...
We study the implications of population-monotonicity (Thomson, 1983) and replacement-domination (... more We study the implications of population-monotonicity (Thomson, 1983) and replacement-domination (Moulin, 1987) in the class of attributebased preference domains (Nehring and Puppe 2002 a,b). Both conditions require that when some parameters of the economy change, the agents whose parameters are kept xed, should either all weakly lose or all weakly win. Population-monotonicity applies to the arrival and departure of agents, while replacement-domination applies to changes in preferences. Using results by Nehring and Puppe (2002b) on strategyproof and onto choice functions, we characterize on attribute-based preference domains the unanimity rules as the class of choice functions that satisfy either condition of solidarity and are in addition strategyproof and onto. We also characterize the attribute-based domains on which these properties are compatible. Next, we characterize the class of tree-structured domains as the ones where population-monotonicity and Pareto-e¢ ciency are compat...
We introduce a new fixed point method to analyze cheap talk games, in the tradition of Crawford a... more We introduce a new fixed point method to analyze cheap talk games, in the tradition of Crawford and Sobel (1982). We illustrate it in a class of onedimensional games, where the sender's bias may depend on the state of the world, and which contains Crawford and Sobel's model as a special case. The method yields new results on the structure of the equilibrium set. For games in which the sender has an outward bias, i.e. the sender is more extreme than the receiver whenever the state of the world is extreme, we prove that for any positive integer k, there is an equilibrium with exactly k pools, and at least one equilibrium with an infinite number of pools. We discuss the extent to which the fixed point method can be used to analyze other cheap talk signalling problems.
A collective decision problem is described by a set of agents, a profile of single-peaked prefere... more A collective decision problem is described by a set of agents, a profile of single-peaked preferences over the real line and a number of public facilities to be located. We consider public facilities that do not suffer from congestion and are non-excludable. We characterize the class of rules satisfying Pareto-efficiency, object-population monotonicity and sovereignty. Each rule in the class is a priority rule that selects locations according to a predetermined priority ordering among “interest groups”. We characterize the subclasses of priority rules that respectively satisfy anonymity, avoid the no-show paradox, strategy-proofness and population-monotonicity. In particular, we prove that a priority rule is strategy-proof if and only if it partitions the set of agents into a fixed hierarchy. Any such rule can also be viewed as a collection of generalized peak-selection median rules, that are linked across populations, in a way that we describe.
This paper studies the problem of providing two public goods for agents with single-peaked prefer... more This paper studies the problem of providing two public goods for agents with single-peaked preferences. A decision rule selects two points on the segment [0,1] for the public goods for every profile of reported preferences. Agents compare public good pairs by the lexmax ordering over pairs induced by their singlepeaked preference over single locations. We derive implications of strategyproofness in this setting and compare them with those in the model with one public good and in the model with two public goods under the max extension. We characterize the class of decision rules satisfying strategy-proofness, anonymity and continuity with respect to preferences .W e also characterize subclasses of rules that satisfy additional properties.
Games and Economic Behavior
In this paper, we study the implications of two solidarity conditions on the efficient location o... more In this paper, we study the implications of two solidarity conditions on the efficient location of a public good on a cycle, when agents have single-peaked, symmetric preferences. Solidarity requirements say that when the economy changes, the agents who are not causing the change should all be affected in the same direction: either they all gain or they all loose. The first requirement we study, population-monotonicity, applies to arrival or departure of one agent. The second requirement, replacement-domination, applies to changes in the preferences of one agent. We first restrict agents' preferred points to be located at the vertices of a regular polygon inscribed in the circle. Solutions satisfying the requirements for polygons with three, four or five vertices are characterized. When the number of vertices of the polygon is greater than five, we show that no solution satisfy the requirements. This incompatibility extends to the unconstrained problem where agents' preferred points can be located anywhere on the circle.
SSRN Electronic Journal, 2000
This paper studies a game of con ‡ict where two individuals …ght in order to choose a policy. Int... more This paper studies a game of con ‡ict where two individuals …ght in order to choose a policy. Intuitively, con ‡icts will be less violent if individuals entertain the possibility that their opponent may be right. Why is it so di¢ cult to observe this attitude? To answer this question, this paper considers a model of indoctrination where altruistic advisors (such as, preachers or parents), after receiving signals from Nature, send messages to the participants in the con ‡ict. In some cases, as a result of indoctrination, both individuals never doubt about the possibility of being wrong, although all available information suggests otherwise. In other cases, one of the two individuals is excessively reasonable: he believes that the opponent may be right even when all the evidence indicates beyond any doubt that the policy preferred by the opponent is suboptimal. The common feature in both cases is that information is distorted, although in di¤ erent directions. The model has a rich set of predictions concerning the incidence and intensity of con ‡ict, and the evolution of indoctrination strategies over time.