Designing Economic Mechanisms
A mechanism is a mathematical structure that models institutions through which economic activity is guided and coordinated. There are many such institutions; markets are the most familiar ones. Lawmakers, administrators and officers of private companies create institutions in order to achieve desired goals. They seek to do so in ways that economize on the resources needed to operate the institutions, and that provide incentives that induce the required behaviors. This book presents systematic procedures for designing mechanisms that achieve specified performance, and economize on the resources required to operate the mechanism. The systematic design procedures are algorithms for designing informationally efficient mechanisms. Most of the book deals with these procedures of design. When there are finitely many environments to be dealt with, and there is a Nash-implementing mechanism, our algorithms can be used to make that mechanism into an informationally efficient one. Informationally efficient dominant strategy implementation is also studied.
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A-set agent algorithm assume Chapter coarsening columns compute condensation construction contour set covering correspondence covering CV decentralized mechanism deﬁned deﬁnition denote differentiable manifolds dimension Edgeworth box encoded revelation mechanism environment equation system equilibrium message equivalence relation equivalent Euclidean space F-cc Figure ﬁnite ﬁrst follows Forester function F game form given goal function Hence informational efﬁciency informationally efﬁcient inner product Jacobian L-dot left-RM Lemma level sets matrix maximally coarse mechanism design mechanism that realizes message correspondence message space minimal Nash equilibrium neighborhood notation outcome function p-functions parameter point parameter space parameter transfer Pareto optimality partition procedure proof quotient quotient object rank realize a given realizes F realizes the goal rectangles method rectangular covering rRM covering satisﬁes Section self-belonging correspondence speciﬁed subset Suppose Theorem transversal variables vector veriﬁcation Walrasian example