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Essays on bounded rationality, complexity, and strategic interactions

Agostino Manduchi, 1999
Faculty Advisor: Duncan Foley
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Abstract

The present dissertation consists of three essays. The essays analyze situations in which the economic agents face plausible limitations and costs of decision-making and communication. Such limitations and costs play a substantial role in determining the results of the analysis developed in each essay.

The first essay analyzes the interactions among adaptive agents, producing idiosyncratic goods. Each agent cannot consume the own good, but can only consume the good produced by a neighbor, as defined by the spatial structure imposed on the economy. A protocol governing the exchanges, requiring the agents to put forth some marketing effort, is considered. Its performance-and the average reward to production-depends on the percentage of active producers. The interactions between the marketing and the production decisions can cause fluctuations in average output and utility.

The second essay analyzes an economy with a spatial structure in which neighboring agents play a repeated prisoner's dilemma, by means of two-state automata. The model can have multiple stationary Nash-equilibria. However, the equilibria-except those with pairs of neighboring cooperators, amidst regions of defectors, and possibly those with generalized cooperation-may not survive the introduction of “trembles”. If the players can condition their responses to acts of defection upon the defector's identity, additional “robust” ways to implement the configurations of cooperators and defectors may become available.

The third essay analyzes the evolutionary dynamics of a modified version of Rosenthal's “centipede”. The players' strategies are represented by finite-state automata, possibly featuring different complexity costs. With the unperturbed replicator dynamics, and low levels of the complexity costs, the asymptotic attractor of the fractions of the populations adopting different automata is a subset of that of the original game, and is such that all players' payoffs are zero. The model also has an unstable equilibrium at which some players achieve strictly positive payoffs. Higher levels of the complexity cost and-or perturbations of the replicator dynamics can change the qualitative dynamics of the system, and lead the players to obtain strictly positive payoffs, on average.

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