/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Online mechanisms extend the methods of mechanism design to dynamic environments with multiple agents and private information. Decisions must be made as information about types is revealed online and without knowledge of the future in the sense of online algorithms. We first consider single-valued preference domains and characterize the space of decision policies that can be truthfully implemented in a dominant strategy equilibrium. Working in a model-free environment we present truthful auctions for domains with expiring items and limited-supply items. Turning to a more general preference domain, and assuming the existence of a probabilistic model for agent types, we define a dynamic Vickrey-Clarke-Groves mechanism that is efficient and Bayes-Nash incentive compatible. We close with some thoughts about future research directions in this area.

Algorithmic Game Theory: Quantifying the Inefficiency of Equilibria

Economics has much to do with incentives--not least, incentives to work hard, to produce quality products, to study, to invest, and to save. Although Adam Smith amply confirmed this more than two hundred years ago in his analysis of sharecropping contracts, only in recent decades has a theory begun to emerge to place the topic at the heart of economic thinking. In this book, Jean-Jacques Laffont and David Martimort present the most thorough yet accessible introduction to incentives theory to date. Central to this theory is a simple question as pivotal to modern-day management as it is to economics research: What makes people act in a particular way in an economic or business situation? In seeking an answer, the authors provide the methodological tools to design institutions that can ensure good incentives for economic agents. This book focuses on the principal-agent model, the "simple" situation where a principal, or company, delegates a task to a single agent through a contract--the essence of management and contract theory. How does the owner or manager of a firm align the objectives of its various members to maximize profits? Following a brief historical overview showing how the problem of incentives has come to the fore in the past two centuries, the authors devote the bulk of their work to exploring principal-agent models and various extensions thereof in light of three types of information problems: adverse selection, moral hazard, and non-verifiability. Offering an unprecedented look at a subject vital to industrial organization, labor economics, and behavioral economics, this book is set to become the definitive resource for students, researchers, and others who might find themselves pondering what contracts, and the incentives they embody, are really all about.

/pdf/the-theory-of-incentives-the-principal-agent-model-5dmc8btucq.pdf

The Theory of Incentives: The Principal-Agent Model

A new era of theoretical computer science addresses fundamental problems about auctions, networks, and human behavior.

http://www.maths.lse.ac.uk/Personal/stengel/TEXTE/agt-stengel.pdf

Algorithmic Game Theory

Spectral graph theory is the study of the eigenvalues and eigenvectors of matrices associated with graphs. In this tutorial, we will try to provide some intuition as to why these eigenvectors and eigenvalues have combinatorial significance, and will sitn'ey some of their applications.

/pdf/spectral-graph-theory-and-its-applications-3r848wnqmh.pdf

Spectral Graph Theory and its Applications

Strategy-proof Social Choice Correspondences

This paper identifies a class of mechanisms, called elementary mechanisms, which are (in a precisely defined sense) the “simplest” mechanisms that can implement efficient outcomes in economic environments. The class of social choice correspondences that can be implemented by elementary mechanisms is completely characterized in a variety of different economic contexts.

Nash implementation through elementary mechanisms in economic environments

We study strategic voting after weakening the notion of strategy-proofness to Ordinal Bayesian Incentive Compatibility (OBIC). Under OBIC, truth-telling is required to maximize the expected utility of every voter, expected utility being computed with respect to the voter's prior beliefs and under the assumption that everybody else is also telling the truth. We show that for a special type of priors, i.e., the uniform priors, there exists a large class of social choice functions that are OBIC. However, for priors that are generic in the set of independent beliefs, a social choice function is OBIC only if it is dictatorial. This result underlines the robustness of the Gibbard-Satterthwaite Theorem.

Ordinally Bayesian incentive compatible voting rules

In this paper we consider the standard voting model with a finite set of alternatives A and n voters and address the following question: what are the characteristics of domains $${\mathcal D}$$
 that induce the property that every strategy-proof social choice function $${f: {\mathcal D}^n \rightarrow A}$$
 satisfying unanimity, has the tops-only property? We first impose a minimal richness condition which ensures that for every alternative a, there exists an admissible ordering where a is maximal. We identify conditions on $${\mathcal D}$$
 that are sufficient for strategy-proofness and unanimity to imply tops onlyness in the general case of n voters and in the special case, n = 2. We provide an algorithm for constructing tops-only domains from connected graphs with elements of A as nodes. We provide several applications of our results. Finally, we relax the minimal richness assumption and partially extend our results.

https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=1402&context=soe_research

Tops-Only Domains

http://econdse.org/wp-content/uploads/2012/02/arunavags.pdf

Another direct proof of the Gibbard–Satterthwaite Theorem

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