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14
A SparsityBased Model of Bounded Rationality ∗
, 2011
"... This paper proposes a model in which the decision maker builds an optimally simplified representation of the world which is “sparse,”i.e., uses few parameters that are nonzero. Sparsity is formulated so as to lead to wellbehaved, convex maximization problems. The agent’s choice of a representation ..."
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Cited by 17 (1 self)
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This paper proposes a model in which the decision maker builds an optimally simplified representation of the world which is “sparse,”i.e., uses few parameters that are nonzero. Sparsity is formulated so as to lead to wellbehaved, convex maximization problems. The agent’s choice of a representation of the world features a quadratic proxy for the benefits of thinking and a linear formulation for the costs of thinking. The agent then picks the optimal action given his representation of the world. This model yields a tractable procedure, which embeds the traditional rational agent as a particular case, and can be used for analyzing classic economic questions under bounded rationality. For instance, the paper studies how boundedly rational agents select a consumption bundle while paying imperfect attention to prices, and how frictionless firms set prices optimally in response. This leads to a novel mechanism for price rigidity. The model is also used to examine boundedly rational intertemporal consumption problems and portfolio choice with imperfect understanding of returns.
Efficiently learning from revealed preference
 In Internet and Network Economics
, 2012
"... ar ..."
The Empirical Implications of Rank in Bimatrix Games
, 2013
"... We study the structural complexity of bimatrix games, formalized via rank, from an empirical perspective. We consider a setting where we have data on player behavior in diverse strategic situations, but where we do not observe the relevant payoff functions. We prove that high complexity (high rank) ..."
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Cited by 2 (2 self)
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We study the structural complexity of bimatrix games, formalized via rank, from an empirical perspective. We consider a setting where we have data on player behavior in diverse strategic situations, but where we do not observe the relevant payoff functions. We prove that high complexity (high rank) has empirical consequences when arbitrary data is considered. Additionally, we prove that, in more restrictive classes of data (termed laminar), any observation is rationalizable using a lowrank game: specifically a zerosum game. Hence complexity as a structural property of a game is not always testable. Finally, we prove a general result connecting the structure of the feasible data sets with the highest rank that may be needed to rationalize a set of observations.
X Tatonnement in Ongoing Markets of Complementary Goods
"... This paper continues the study, initiated by Cole and Fleischer in [Cole and Fleischer 2008], of the behavior of a tatonnement price update rule in Ongoing Fisher Markets. The prior work showed fast convergence toward an equilibrium when the goods satisfied the weak gross substitutes property and ha ..."
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Cited by 2 (1 self)
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This paper continues the study, initiated by Cole and Fleischer in [Cole and Fleischer 2008], of the behavior of a tatonnement price update rule in Ongoing Fisher Markets. The prior work showed fast convergence toward an equilibrium when the goods satisfied the weak gross substitutes property and had bounded demand and income elasticities. The current work shows that fast convergence also occurs for the following types of markets: — All pairs of goods are complements to each other, and — the demand and income elasticities are suitably bounded. In particular, these conditions hold when all buyers in the market are equipped with CES utilities, where all the parameters ρ, one per buyer, satisfy −1 < ρ ≤ 0. In addition, we extend the above result to markets in which a mixture of complements and substitutes occur. This includes characterizing a class of nested CES utilities for which fast convergence holds. An interesting technical contribution, which may be of independent interest, is an amortized analysis for handling asynchronous events in settings in which there are a mix of continuous changes and discrete events.
A SparsityBased Model of Bounded Rationality, Applied to Basic Consumer and Equilibrium Theory ∗ Xavier Gabaix
, 2013
"... This paper defines and analyzes a “sparse max ” operator, which generalizes the traditional max operator used everywhere in economics. The agent builds (as economists do) a simplified model of the world which is sparse, considering only the variables of firstorder importance. His stylized model and ..."
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This paper defines and analyzes a “sparse max ” operator, which generalizes the traditional max operator used everywhere in economics. The agent builds (as economists do) a simplified model of the world which is sparse, considering only the variables of firstorder importance. His stylized model and his resulting choices both derive from constrained optimization. Still, the sparse max remains tractable to compute. Moreover, the induced outcomes reflect basic psychological forces governing limited attention. Withthesparsemax,wecanexplorehowavarietyofeconomicmodelschangewhen agents are less than fully rational. Here we give a behavioral version of two basic chapters of economics: basic theory of consumer demand and competitive equilibrium. We obtain a behavioral version of Marshallian and Hicksian demand, the Slutsky matrix, the Edgeworth box, Roy’s identity etc., and competitive equilibrium. The Slutsky matrix is no longer symmetric — nonsalient prices are associated with anomalously small demand elasticities. In the Edgeworth box, the offer curve is “extradimensional”: it is a twodimensional surface rather than a onedimensional curve. As a result, different aggregate price levels correspond to materially distinct competitive equilibria, in a similar spirit to a Phillips curve. This framework provides a way to assess which parts of basic microeconomics are robust, and which are not, to the assumption of perfect maximization.
Finding a Walrasian equilibrium is easy for a fixed number of agents
, 2012
"... In this work, we study the complexity of finding a Walrasian equilibrium. Our main result gives an algorithm which can compute an approximate Walrasian equilibrium in an exchange economy with general, but wellbehaved, utility functions in time that is polynomial in the number of goods when the numbe ..."
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In this work, we study the complexity of finding a Walrasian equilibrium. Our main result gives an algorithm which can compute an approximate Walrasian equilibrium in an exchange economy with general, but wellbehaved, utility functions in time that is polynomial in the number of goods when the number of agents is held constant. This result has applications to macroeconomics and finance, where applications of Walrasian equilibrium theory tend to deal with many goods but a fixed number of agents.
Complexity and economics: . . .
, 2010
"... Recent results in complexity theory suggest that various economic theories require agents to solve intractable problems. However, such results assume the agents are optimizing explicit utility functions, whereas the economic theories merely assume the agents are rational, where rational behavior is ..."
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Recent results in complexity theory suggest that various economic theories require agents to solve intractable problems. However, such results assume the agents are optimizing explicit utility functions, whereas the economic theories merely assume the agents are rational, where rational behavior is defined via some optimization problem. Might making rational choices be easier than solving the corresponding optimization problem? For at least one major economic theory, the theory of the consumer, we find this is indeed the case.
Tatonnement in Ongoing Markets of Complementary Goods
, 2013
"... This paper continues the study, initiated by Cole and Fleischer in [6], of the behavior of a tatonnement price update rule in Ongoing Fisher Markets. The prior work showed fast convergence toward an equilibrium when the goods satisfied the weak gross substitutes property and had bounded demand and i ..."
Abstract
 Add to MetaCart
This paper continues the study, initiated by Cole and Fleischer in [6], of the behavior of a tatonnement price update rule in Ongoing Fisher Markets. The prior work showed fast convergence toward an equilibrium when the goods satisfied the weak gross substitutes property and had bounded demand and income elasticities. The current work shows that fast convergence also occurs for the following types of markets: • All pairs of goods are complements to each other, and • the demand and income elasticities are suitably bounded. In particular, these conditions hold when all buyers in the market are equipped with CES utilities, where all the parameters ρ, one per buyer, satisfy −1 < ρ ≤ 0. In addition, we extend the above result to markets in which a mixture of complements and substitutes occur. This includes characterizing a class of nested CES utilities for which fast convergence holds. An interesting technical contribution, which may be of independent interest, is an amortized analysis for handling asynchronous events in settings in which there are a mix of continuous changes and discrete events. 1