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 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 Matching IoT Devices to the Fog Service Providers: A Mechanism Design Perspective

Sensors ◽  
2020 ◽  
Vol 20 (23) ◽  
pp. 6761
Author(s):  
Anjan Bandyopadhyay ◽  
Vikash Kumar Singh ◽  
Sajal Mukhopadhyay ◽  
Ujjwal Rai ◽  
Fatos Xhafa ◽  
...  
Keyword(s):  
Internet Of Things ◽  
Mechanism Design ◽  
Service Providers ◽  
The Internet ◽  
Preference Ordering ◽  
Cloud Architecture ◽  
Game Theoretic ◽  
Design Perspective ◽  
Iot Devices ◽  
The Internet Of Things

In the Internet of Things (IoT) + Fog + Cloud architecture, with the unprecedented growth of IoT devices, one of the challenging issues that needs to be tackled is to allocate Fog service providers (FSPs) to IoT devices, especially in a game-theoretic environment. Here, the issue of allocation of FSPs to the IoT devices is sifted with game-theoretic idea so that utility maximizing agents may be benign. In this scenario, we have multiple IoT devices and multiple FSPs, and the IoT devices give preference ordering over the subset of FSPs. Given such a scenario, the goal is to allocate at most one FSP to each of the IoT devices. We propose mechanisms based on the theory of mechanism design without money to allocate FSPs to the IoT devices. The proposed mechanisms have been designed in a flexible manner to address the long and short duration access of the FSPs to the IoT devices. For analytical results, we have proved the economic robustness, and probabilistic analyses have been carried out for allocation of IoT devices to the FSPs. In simulation, mechanism efficiency is laid out under different scenarios with an implementation in Python.

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