scholarly journals Cake Cutting: Envy and Truth

2017 ◽  
Author(s):  
Xiaohui Bei ◽  
Ning Chen ◽  
Guangda Huzhang ◽  
Biaoshuai Tao ◽  
Jiajun Wu
Keyword(s):  
Nash Equilibrium ◽  
Private Information ◽  
General Setting ◽  
Impossibility Result ◽  
Market Model ◽  
Truth Telling ◽  
Piecewise Constant ◽  
Cake Cutting ◽  
Strategic Agents ◽  
To Receive

We study envy-free cake cutting with strategic agents, where each agent may manipulate his private information in order to receive a better allocation. We focus on piecewise constant utility functions and consider two scenarios: the general setting without any restriction on the allocations and the restricted setting where each agent has to receive a connected piece. We show that no deterministic truthful envy-free mechanism exists in the connected piece scenario, and the same impossibility result for the general setting with some additional mild assumptions on the allocations. Finally, we study a large market model where the economy is replicated and demonstrate that truth-telling converges to a Nash equilibrium.

scholarly journals Information Elicitation Mechanisms for Statistical Estimation

2020 ◽  
Vol 34 (02) ◽  
pp. 2095-2102 ◽  
Author(s):  
Yuqing Kong ◽  
Grant Schoenebeck ◽  
Biaoshuai Tao ◽  
Fang-Yi Yu
Keyword(s):  
Private Information ◽  
Impossibility Result ◽  
Statistical Properties ◽  
Truth Telling ◽  
Bayesian Nash Equilibrium ◽  
Discrete Signals ◽  
Private Signals ◽  
Large Populations ◽  
Strategic Agents ◽  
Information Elicitation

We study learning statistical properties from strategic agents with private information. In this problem, agents must be incentivized to truthfully reveal their information even when it cannot be directly verified. Moreover, the information reported by the agents must be aggregated into a statistical estimate. We study two fundamental statistical properties: estimating the mean of an unknown Gaussian, and linear regression with Gaussian error. The information of each agent is one point in a Euclidean space.Our main results are two mechanisms for each of these problems which optimally aggregate the information of agents in the truth-telling equilibrium:• A minimal (non-revelation) mechanism for large populations — agents only need to report one value, but that value need not be their point.• A mechanism for small populations that is non-minimal — agents need to answer more than one question.These mechanisms are “informed truthful” mechanisms where reporting unaltered data (truth-telling) 1) forms a strict Bayesian Nash equilibrium and 2) has strictly higher welfare than any oblivious equilibrium where agents' strategies are independent of their private signals. We also show a minimal revelation mechanism (each agent only reports her signal) for a restricted setting and use an impossibility result to prove the necessity of this restriction.We build upon the peer prediction literature in the single-question setting; however, most previous work in this area focuses on discrete signals, whereas our setting is inherently continuous, and we further simplify the agents' reports.

scholarly journals Deterministic, Strategyproof, and Fair Cake Cutting

2017 ◽  
Author(s):  
Vijay Menon ◽  
Kate Larson
Keyword(s):  
Mechanism Design ◽  
Impossibility Result ◽  
Restricted Class ◽  
Piecewise Constant ◽  
Incentive Compatible ◽  
Negative Results ◽  
Cake Cutting ◽  
Design Perspective ◽  
A Minor ◽  
Cutting Problem

We study the classic cake cutting problem from a mechanism design perspective, in particular focusing on deterministic mechanisms that are strategyproof and fair. We begin by looking at mechanisms that are non-wasteful and primarily show that for even the restricted class of piecewise constant valuations there exists no direct-revelation mechanism that is strategyproof and even approximately proportional. Subsequently, we remove the non-wasteful constraint and show another impossibility result stating that there is no strategyproof and approximately proportional direct-revelation mechanism that outputs contiguous allocations, again, for even the restricted class of piecewise constant valuations. In addition to the above results, we also present some negative results when considering an approximate notion of strategyproofness, show a connection between direct-revelation mechanisms and mechanisms in the Robertson-Webb model when agents have piecewise constant valuations, and finally also present a (minor) modification to the well-known Even-Paz algorithm that has better incentive-compatible properties for the cases when there are two or three agents.

scholarly journals Truthful fair division without free disposal

2020 ◽  
Vol 55 (3) ◽  
pp. 523-545 ◽  
Author(s):  
Xiaohui Bei ◽  
Guangda Huzhang ◽  
Warut Suksompong
Keyword(s):  
Fair Division ◽  
Multiple Agents ◽  
Two Agents ◽  
Free Disposal ◽  
Cake Cutting ◽  
Strategic Agents ◽  
Additional Constraints

Abstract We study the problem of fairly dividing a heterogeneous resource, commonly known as cake cutting and chore division, in the presence of strategic agents. While a number of results in this setting have been established in previous works, they rely crucially on the free disposal assumption, meaning that the mechanism is allowed to throw away part of the resource at no cost. In the present work, we remove this assumption and focus on mechanisms that always allocate the entire resource. We exhibit a truthful and envy-free mechanism for cake cutting and chore division for two agents with piecewise uniform valuations, and we complement our result by showing that such a mechanism does not exist when certain additional constraints are imposed on the mechanisms. Moreover, we provide bounds on the efficiency of mechanisms satisfying various properties, and give truthful mechanisms for multiple agents with restricted classes of valuations.

Applications to Economics

2016 ◽  
Author(s):  
Jacob K. Goeree ◽  
Charles A. Holt ◽  
Thomas R. Palfrey
Keyword(s):  
Nash Equilibrium ◽  
Private Information ◽  
Price Competition ◽  
Quantal Response ◽  
Unique Nash Equilibrium ◽  
Common Effort ◽  
The Cost ◽  
All Pay Auction ◽  
Individual Effort ◽  
Applications To Economics

This chapter explores whether the equilibrium effects of noisy behavior can cause large deviations from standard predictions in economically relevant situations. It considers a simple price-competition game, which is also partly motivated by the possibility of changing a payoff parameter that has no effect on the unique Nash equilibrium, but which may be expected to affect quantal response equilibrium. In the minimum-effort coordination game studied, any common effort in the range of feasible effort levels is a Nash equilibrium, but one would expect that an increase in the cost of individual effort or an increase in the number of players who are trying to coordinate would reduce the effort levels observed in an experiment. The chapter presents an analysis of the logit equilibrium and rent dissipation for a rent-seeking contest that is modeled as an “all-pay auction.” The final two applications in this chapter deal with auctions with private information.

A global game of diplomacy

2019 ◽  
Vol 31 (4) ◽  
pp. 480-506 ◽  
Author(s):  
Matt Malis ◽  
Alastair Smith
Keyword(s):  
Private Information ◽  
Learning Effect ◽  
Political Competition ◽  
Public Information ◽  
Selection Effect ◽  
Strengthening Effect ◽  
Global Game ◽  
The Public ◽  
Multiplier Effect ◽  
To Receive

Diplomacy always occurs in the shadow of domestic political competition. We develop a model of top-level diplomatic exchange between an incumbent and a foreign leader, embedded within a global game of regime change, and examine four mechanisms that induce a relationship between diplomatic visits and regime survival. First, the foreign leader chooses to visit incumbents who are ex ante more secure in office (a selection effect). Second, because the foreign leader’s decision is based partly on private information, the citizens update on the revelation of that information (a learning effect) and are discouraged from mounting a challenge. Third, the foreign leader can bolster the incumbent’s strength in office with a transfer of material support (a strengthening effect). The latter two effects are then amplified by the complementarities in the citizens’ strategies (a multiplier effect). Contrary to standard global games results, we show that increased precision in the public information transmitted strategically by the foreign power induces a unique equilibrium, as citizens coordinate on the foreign leader’s action. Our findings explain why leaders are so eager to receive state visits from major world powers.

scholarly journals Relational Contracts with Private Information on the Future Value of the Relationship: The Upside of Implicit Downsizing Costs

2019 ◽  
Vol 11 (4) ◽  
pp. 33-58
Author(s):  
Matthias Fahn ◽  
Nicolas Klein
Keyword(s):  
Private Information ◽  
Alternative Explanation ◽  
Relational Contracts ◽  
Truth Telling ◽  
Relational Contract ◽  
Bonus Payments ◽  
The Future ◽  
Short Run ◽  
Future Value ◽  
The Relationship

We analyze a relational-contracting problem, in which the principal has private information about the future value of the relationship. In order to reduce bonus payments, the principal is tempted to claim that the value of the future relationship is lower than it actually is. To induce truth-telling, the optimal relational contract may introduce distortions after a bad report. For some levels of the discount factor, output is reduced by more than would be sequentially optimal. This distortion is attenuated over time even if prospects remain bad. Our model thus provides an alternative explanation for indirect short-run costs of downsizing. (JEL D23, D82, D86)

scholarly journals Public Transfers and Domestic Violence: The Roles of Private Information and Spousal Control

2013 ◽  
Vol 5 (1) ◽  
pp. 179-205 ◽  
Author(s):  
Gustavo J Bobonis ◽  
Melissa González-Brenes ◽  
Roberto Castro
Keyword(s):  
Domestic Violence ◽  
Private Information ◽  
Spousal Abuse ◽  
Decision Makers ◽  
Transfer Programs ◽  
Female Partners ◽  
Public Transfers ◽  
Using Data ◽  
The Impact ◽  
To Receive

We study whether transfer programs in which funds are targeted to women decrease the incidence of spousal abuse. We examine the impact of the Mexican Oportunidades program on spousal abuse rates and threats of violence using data from a specialized survey. Beneficiary women are 40 percent less likely to be victims of physical abuse, but are more likely to receive violent threats with no associated abuse. This evidence is consistent with a model of decision-makers' interactions with asymmetric information in the male partner's gains to marriage, who can then use threats of violence to extract rents from their female partners. (JEL D82, J12, J16, K42, O15, O17)

Insider trading surrounding securities class action litigation and settlement announcements

2017 ◽  
Vol 43 (1) ◽  
pp. 124-140 ◽  
Author(s):  
Frederick Davis ◽  
Behzad Taghipour ◽  
Thomas J. Walker
Keyword(s):  
Insider Trading ◽  
Private Information ◽  
Stock Prices ◽  
Class Action ◽  
Market Model ◽  
Trading Activity ◽  
Content Type ◽  
Sarbanes Oxley ◽  
Abnormal Profits ◽  
The Impact

Purpose The purpose of this paper is to investigate the trading patterns of corporate insiders, both managing and non-managing, around the announcement dates of securities class action lawsuits and related legal settlements. Design/methodology/approach The authors use market model event study methodology to examine the impact of class action litigation and settlement announcements on the stock prices of sued firms. The authors then determine the extent of abnormal insider trading surrounding such announcements by comparing insider trading activity (volume and transaction counts) to prior insider trading in the same firm, and to a matched sample of firms not experiencing such litigation announcements. A multivariate framework is utilized to provide further insight into the determinants of such abnormal insider trading. Findings The authors establish that class action litigation and settlement announcements have a significant impact on the stock prices of sued firms, and that foreknowledge of these events appears to be used by insiders to earn abnormal profits. Moreover, results indicate that managing insiders exhibit higher opportunistic abnormal trading activity than non-managing insiders. Multivariate analysis shows that size, prior firm returns, and the implementation of the Sarbanes-Oxley Act are important determinants of such insider trading. Originality/value This appears to be the first paper to analyze insider trading surrounding class action settlement announcements, and raises concerns about the ethical conduct of certain insider groups while highlighting the importance of access to private information, even amongst insiders themselves.

scholarly journals Mechanism Design for Facility Location Problems: A Survey

2021 ◽  
Author(s):  
Hau Chan ◽  
Aris Filos-Ratsikas ◽  
Bo Li ◽  
Minming Li ◽  
Chenhao Wang
Keyword(s):  
Mechanism Design ◽  
Facility Location ◽  
Private Information ◽  
Practical Importance ◽  
Future Research ◽  
Facility Location Problems ◽  
Social Objective ◽  
Comprehensive Survey ◽  
Strategic Agents ◽  
High Level

The study of approximate mechanism design for facility location has been in the center of research at the intersection of artificial intelligence and economics for the last decade, largely due to its practical importance in various domains, such as social planning and clustering. At a high level, the goal is to select a number of locations on which to build a set of facilities, aiming to optimize some social objective based on the preferences of strategic agents, who might have incentives to misreport their private information. This paper presents a comprehensive survey of the significant progress that has been made since the introduction of the problem, highlighting all the different variants and methodologies, as well as the most interesting directions for future research.

scholarly journals Efficient Multi-Attribute Auctions Considering Supply Disruption

2019 ◽  
Vol 36 (03) ◽  
pp. 1950013
Author(s):  
Jie Xiang ◽  
Juliang Zhang ◽  
T. C. E. Cheng ◽  
Jose Maria Sallan ◽  
Guowei Hua
Keyword(s):  
Private Information ◽  
Dominant Strategy ◽  
Purchase Decisions ◽  
Reverse Auctions ◽  
Reverse Auction ◽  
Truth Telling ◽  
Supply Disruption ◽  
Bidding Strategies ◽  
Numerical Studies ◽  
The Cost

Although supply disruption is ubiquitous because of natural or man-made disasters, many firms still use the price-only reverse auction (only the cost is considered) to make purchase decisions. We first study the suppliers’ equilibrium bidding strategies and the buyer’s expected revenue under the first- and second-price price-only reverse auctions when the suppliers are unreliable and have private information on their costs and disruption probabilities. We show that the two auctions are equivalent and not efficient. Then we propose two easily implementable reverse auctions, namely the first-price and second-price format announced penalty reverse auction (APRA), and show that the “revenue equivalence principle” holds, i.e., the two auctions generate the same ex ante expected profit to the buyer. We further show that the two reverse auctions are efficient and “truth telling” is the suppliers’ dominant strategy in the second-price format APRA. We conduct numerical studies to assess the impacts of some parameters on the bidding strategies, the buyer’s profit and social profit.

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