Browsing by Subject "Bounded rationality"

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Bounded Rationalities and Computable Economies
    (Center for Economic Research, Department of Economics, University of Minnesota, 1996-12) Richter, Marcel K.; Wong, Kam-Chau
    This paper studies economic equilibrium theory with a "uniformity principle" constraining the magnitudes (prices, quantities, etc.) and the operations (to perceive, evaluate, choose, communicate, etc.) that agents can use. For the special case of computability constraints, all prices, quantities, preference relations, utility functions, demand functions, etc. are required to be computable by finite algorithms. Then we obtain sharper versions of several traditional assertions on utility representation, existence of consumer demand functions, the fundamental welfare theorems, characterizations of market excess demands, and others. These positive results hold despite the fact that commodity and price spaces are no longer topologically complete. On the other hand, we give "computable counterexamples" to several traditional assertions, including the existence of a competitive equilibrium. The results can be interpreted as possibility and impossibility results in both computability-bounded rationality and in computational economics.
  • Thumbnail Image
    Item
    Bounded Rationalities and Definable Economies
    (Center for Economic Research, Department of Economics, University of Minnesota, 1996-12) Richter, Marcel K.; Wong, Kam-Chau
    Classical economic agents perform arbitrarily complex operations on arbitrarily complex magnitudes (real numbers). By contrast, real world agents have bounds on their abilities to perceive, think about, calculate with, and communicate magnitudes. There are many ways to model agents with bounded abilities, and here we mention two - one through bounds on computational abilities, and one through bounds on descriptive or definitional abilities. In both cases, we propose a "uniformity principle" constraining in a parallel fashion both the magnitudes (prices, quantities, etc.) and the operations (to perceive, evaluate, choose, communicate, etc.) that agents can use. We focus on the definitional bounds, deferring computational bounds to other papers (1996a,b). The languages allowed are those of ordered rings, and certain expansions; the structures are those of real closed ordered fields, and corresponding expansions. It is not obvious that a theory of definable economies is possible, since there may not be any definable structures that are reasonably close to the classical one. And even if such structures existed, it is not obvious that the classical theorems of economics would hold in them. Our two main conclusions are positive: In many interesting cases mathematical structures do exist with definability-bounded agents. Furthermore, many classical theorems of economic theory survive in a definable context: existence of demand and utility functions, existence of competitive equilibria, First and Second Welfare Theorems, characterization of aggregate excess demand, etc. Our proofs rely on theorems of mathematical logic (completeness (Tarski), model completeness (A. Robinson, Wilkie), o-minimality (van den Dries, Pillay and Steinhorn, Wilkie)) that allow us to establish existence of definable models and to transfer classical theorems to a definable framework. Although superficially different, the concepts underlying (Blume and Zame, 1992) are fundamentally close to the ones we use here.
  • Thumbnail Image
    Item
    Boundedly rational user equilibrium: models and applications
    (2014-08) Di, Xuan
    Efficient transportation management requires good understanding of people's travel behavior. Most transportation planning models assume travelers are perfectly rational in decision-making. However, much of the empirical evidence from psychology, economics, and transportation has shown that perfect rationality is not realistic in modeling travelers' decision-making process. Thus existing transportation planning models may provide inaccurate predictions to transportation planners. Motivated by travelers' route choice changes in response to the reopening of the I-35W Bridge in Minneapolis, this dissertation shows that travelers are boundedly rational (BR) in making route choices. Though the BR travel behavioral model was proposed in the 1980's, empirical validation of such behavioral principle using real-world data along with a theoretical framework was non-existent. This study is dedicated to bridging these gaps from both empirical and theoretical perspectives.The first contribution of this dissertation is the empirical verification and estimation of boundedly rational route choice behavior. By analyzing recorded GPS trajectories from 143 commuters before and after the reopening of the I-35W Bridge in Minneapolis, we employ a probit model to estimate the bounded rationality parameters in Twin Cities. Despite the behavioral appeal of bounded rationality, a rigorous study of boundedly rational user equilibria (BRUE) solution has been lacking, partly due to its mathematical complexity. This research offers a systematic approach of deriving the BRUE solutions analytically on networks with fixed travel demands. Based on the definition of ε-BRUE, where ε is the indifference band for perceived travel times, we formulate the ε-BRUE problem as a nonlinear complementarity problem (NCP). With the increase of the indifference band, the path set that contains equilibrium flows will be augmented and the critical values of the indifference band to augment the path set can be identified by solving a sequence of mathematical programs with equilibrium constraints (MPEC). A novel solution method is provided to obtain the BRUE solution set and numerical examples are given to illustrate this finding. To provide guidelines to policy-makers for congestion mitigation, this research also explores an important phenomenon which should be avoided in transportation network design, i.e., Braess paradox. The classical Braess paradox was built upon the perfectly rational behavioral assumption. Under the framework of bounded rationality, each equilibrium flow pattern leads to a different total system travel time, resulting in non-unique network performance measures. Because of the non-uniqueness of BRUE solutions, which particular equilibrium pattern should be used to compare network performances before and after new roads are built remains a question. This dissertation aims to study the analytical properties of Braess paradox under bounded rationality by exploring the relationships between the occurrence of Braess paradox and the indifference band as well as the demand level. The unveiled relationships offer a guideline for transportation planners to prevent the occurrence of Braess paradox and pave the way for strategic transportation management under the bounded rationality assumption.
  • Thumbnail Image
    Item
    Computability of Preference, Utility, and Demand
    (Center for Economic Research, Department of Economics, University of Minnesota, 1996-12) Richter, Marcel K.; Wong, Kam-Chau
    This paper studies consumer theory from the bounded rationality approach proposed in Richter and Wong (1996a), with a "uniformity principle" constraining the magnitudes (prices, quantities, etc.) and the operations (to perceive, evaluate, choose, communicate, etc.) that agents can use. In particular, we operate in a computability framework, where commodity quantities, prices, consumer preferences, utility functions, and demand functions are computable by finite algorithms (Richter and Wong (1996a)). We obtain a computable utility representation theorem. We prove an existence theorem for computable maximizers of quasiconcave computable utility functions (preferences), and prove the computability of the demand functions generated by such functions (preferences). We also provide a revealed preference characterization of computable rationality for the finite case. Beyond consumer theory, the results have applications in general equilibrium theory (Richter and Wong (1996a)).