Fixed Points of Choice-Improving Correspondences on the Space of Direct Mechanisms are Dictatorial

AUDAY, MARCELO; TOHMÉ, FERNANDO

Bahía Blanca

Congreso; XLII Reunión Anual de la Asociación Argentina de Economía Política; 2007

Asociación Argentina de Economía Política

The theory of Mechanism Design intends to find ways to implement social choice functions. That is, to characterize rules such that, for any profile of actual preferences, game solutions support the outcomes of those functions. Maskin, in his seminal 1977 paper showed that game formsgame forms provide a natural framework to analyze this problem. We focus here on game forms in which the strategies are declarations of preferences over the outcomes. These game forms are called direct mechanisms. On the space of this kind of game forms we postulate an operation, that given a direct mechanism provides other mechanisms (not necessarily a single one), by optimizing the preferences of the agents. A fixed point under this operation is shown to be not strategically manipulable by individual agents. We characterize this fixed point in terms of one of the main impossibility theorems in Social Choice theory, Gibbard- Satterthwaite’s, to show that it is dictatorial, i.e. it implements the most preferred outcomes of a single agent. operation, that given a direct mechanism provides other mechanisms (not necessarily a single one), by optimizing the preferences of the agents. A fixed point under this operation is shown to be not strategically manipulable by individual agents. We characterize this fixed point in terms of one of the main impossibility theorems in Social Choice theory, Gibbard- Satterthwaite’s, to show that it is dictatorial, i.e. it implements the most preferred outcomes of a single agent. operation, that given a direct mechanism provides other mechanisms (not necessarily a single one), by optimizing the preferences of the agents. A fixed point under this operation is shown to be not strategically manipulable by individual agents. We characterize this fixed point in terms of one of the main impossibility theorems in Social Choice theory, Gibbard- Satterthwaite’s, to show that it is dictatorial, i.e. it implements the most preferred outcomes of a single agent. mechanisms. On the space of this kind of game forms we postulate an operation, that given a direct mechanism provides other mechanisms (not necessarily a single one), by optimizing the preferences of the agents. A fixed point under this operation is shown to be not strategically manipulable by individual agents. We characterize this fixed point in terms of one of the main impossibility theorems in Social Choice theory, Gibbard- Satterthwaite’s, to show that it is dictatorial, i.e. it implements the most preferred outcomes of a single agent. operation, that given a direct mechanism provides other mechanisms (not necessarily a single one), by optimizing the preferences of the agents. A fixed point under this operation is shown to be not strategically manipulable by individual agents. We characterize this fixed point in terms of one of the main impossibility theorems in Social Choice theory, Gibbard- Satterthwaite’s, to show that it is dictatorial, i.e. it implements the most preferred outcomes of a single agent. operation, that given a direct mechanism provides other mechanisms (not necessarily a single one), by optimizing the preferences of the agents. A fixed point under this operation is shown to be not strategically manipulable by individual agents. We characterize this fixed point in terms of one of the main impossibility theorems in Social Choice theory, Gibbard- Satterthwaite’s, to show that it is dictatorial, i.e. it implements the most preferred outcomes of a single agent. mechanisms. On the space of this kind of game forms we postulate an operation, that given a direct mechanism provides other mechanisms (not necessarily a single one), by optimizing the preferences of the agents. A fixed point under this operation is shown to be not strategically manipulable by individual agents. We characterize this fixed point in terms of one of the main impossibility theorems in Social Choice theory, Gibbard- Satterthwaite’s, to show that it is dictatorial, i.e. it implements the most preferred outcomes of a single agent. operation, that given a direct mechanism provides other mechanisms (not necessarily a single one), by optimizing the preferences of the agents. A fixed point under this operation is shown to be not strategically manipulable by individual agents. We characterize this fixed point in terms of one of the main impossibility theorems in Social Choice theory, Gibbard- Satterthwaite’s, to show that it is dictatorial, i.e. it implements the most preferred outcomes of a single agent. operation, that given a direct mechanism provides other mechanisms (not necessarily a single one), by optimizing the preferences of the agents. A fixed point under this operation is shown to be not strategically manipulable by individual agents. We characterize this fixed point in terms of one of the main impossibility theorems in Social Choice theory, Gibbard- Satterthwaite’s, to show that it is dictatorial, i.e. it implements the most preferred outcomes of a single agent. direct mechanisms. On the space of this kind of game forms we postulate an operation, that given a direct mechanism provides other mechanisms (not necessarily a single one), by optimizing the preferences of the agents. A fixed point under this operation is shown to be not strategically manipulable by individual agents. We characterize this fixed point in terms of one of the main impossibility theorems in Social Choice theory, Gibbard- Satterthwaite’s, to show that it is dictatorial, i.e. it implements the most preferred outcomes of a single agent. operation, that given a direct mechanism provides other mechanisms (not necessarily a single one), by optimizing the preferences of the agents. A fixed point under this operation is shown to be not strategically manipulable by individual agents. We characterize this fixed point in terms of one of the main impossibility theorems in Social Choice theory, Gibbard- Satterthwaite’s, to show that it is dictatorial, i.e. it implements the most preferred outcomes of a single agent. operation, that given a direct mechanism provides other mechanisms (not necessarily a single one), by optimizing the preferences of the agents. A fixed point under this operation is shown to be not strategically manipulable by individual agents. We characterize this fixed point in terms of one of the main impossibility theorems in Social Choice theory, Gibbard- Satterthwaite’s, to show that it is dictatorial, i.e. it implements the most preferred outcomes of a single agent. . On the space of this kind of game forms we postulate an operation, that given a direct mechanism provides other mechanisms (not necessarily a single one), by optimizing the preferences of the agents. A fixed point under this operation is shown to be not strategically manipulable by individual agents. We characterize this fixed point in terms of one of the main impossibility theorems in Social Choice theory, Gibbard- Satterthwaite’s, to show that it is dictatorial, i.e. it implements the most preferred outcomes of a single agent.