The expected externality mechanism in a level-\(k\) environment
type: Item
instance of: scholarly article
title: The expected externality mechanism in a level-\(k\) environment
zbMATH Open document ID: 1396.91249
author: Olga Gorelkina
published in: International Journal of Game Theory
publication date: 2018-04-11T00:00:00Z
review text: The author studies the expected externality (AVG) mechanism of \textit{C. d'Aspremont} and \textit{L.-A. Gerard-Varet} [Cah. Cent. Étud. Rech. Opér. 18, 167--172 (1976; Zbl 0324.90108)] in the level-\(k\) model, where agents maximize their payoffs against a non-equilibrium belief about other agents' strategies by performing at most \(k\) iterations of best reply. It is obtained that, if level-\(0\) agents truthfully reveal their preference types to the principal, then the AVG mechanism leads to efficient implementation, while, if level-\(0\) agents report distorted preferences, then the AVG mechanism does not induce truth-telling and produces a suboptimal allocation, and the deviation from the optimal strategy tends to zero as \(k\) tends to infinity. The author also shows that, by introducing a betting round -- where agents guess the reports of each other -- and an incentive transfer rewarding truth-telling, the AVG mechanism can be altered to produce close-to-efficient allocation even if level-\(0\) agents report distorted preferences and the principal does not know the deviation of reported preferences from the true preference distribution. The level-\(k\) model is a game of incomplete information where for each agent \(i \in I\), with type \(\theta_{i} \in \Theta\), the payoffs are given by \(u_{i}(s,\theta_{i})\) where \(s=(s_{1},s_{2},\dots,s_{n})\) is a strategy profile, i.e., \(s_{j}\) associates actions to types. The types of agents have a commonly known distribution \(F\). Agents engage in iterations of best reply to maximize their payoff. Their utility is of the form \(v_{i} (x,\theta_{i})+T_{i}\) where \(x\) is the allocation and \(T_{i}\) is the monetary transfer to agent \(i\). The functions \(v_{i}\) are assumed to satisfy the Spence-Mirrlees condition. The strategy \(s^{(k)}_{i}(\theta_{i})\) is recursively defined to maximize the expected payoff against opponents making exactly \(k-1\) iterations of best reply. Level-\(0\) agents are nonstrategic, m…
reviewed by: Tamás Mátrai
Mathematics Subject Classification ID: 91B26
Mathematics Subject Classification ID: 91A10
zbMATH DE Number: 6858289
zbMATH Keywords: expected externality mechanism
zbMATH Keywords: level-\(k\) model
zbMATH Keywords: bounded rationality
zbMATH Keywords: efficient allocation
Wikidata QID: Q59614609
MaRDI profile type: Publication
full work available at URL: s00182-017-0579-5
OpenAlex ID: W1923149708
cites work: An Efficient Dynamic Mechanism
cites work: Crowdsourced Bayesian auctions
cites work: Robust Mechanism Design
cites work: Subgame Perfect Implementation
cites work: Supermodular mechanism design
cites work: A Cognitive Hierarchy Model of Games
cites work: Efficient mechanisms for level-\(k\) bilateral trading
cites work: Level-k Auctions: Can a Nonequilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private-Value Auctions?
cites work: Efficient mechanisms for bilateral trading
cites work: Stochastic orders
cites work: Q3199166
DBLP publication ID: journals/ijgt/Gorelkina18
DOI: 10.1007/S00182-017-0579-5
description: scientific article; zbMATH DE number 6858289