scholarly journals The Pareto Frontier of Inefficiency in Mechanism Design

2021 ◽  
Author(s):  
Aris Filos-Ratsikas ◽  
Yiannis Giannakopoulos ◽  
Philip Lazos
Keyword(s):  
Mechanism Design ◽  
Price Of Anarchy ◽  
Pareto Frontier ◽  
Price Of Stability ◽  
Scheduling Problem ◽  
Natural Class ◽  
Trade Off ◽  
Definitive Answer ◽  
Price Formula ◽  
Scheduling Mechanisms

We study the trade-off between the price of anarchy (PoA) and the price of stability (PoS) in mechanism design in the prototypical problem of unrelated machine scheduling. We give bounds on the space of feasible mechanisms with respect to these metrics and observe that two fundamental mechanisms, namely the first price (FP) and the second price (SP), lie on the two opposite extrema of this boundary. Furthermore, for the natural class of anonymous task-independent mechanisms, we completely characterize the PoA/PoS Pareto frontier; we design a class of optimal mechanisms [Formula: see text] that lie exactly on this frontier. In particular, these mechanisms range smoothly with respect to parameter [Formula: see text] across the frontier, between the first price ([Formula: see text]) and second price ([Formula: see text]) mechanisms. En route to these results, we also provide a definitive answer to an important question related to the scheduling problem, namely whether nontruthful mechanisms can provide better makespan guarantees in the equilibrium compared with truthful ones. We answer this question in the negative by proving that the price of anarchy of all scheduling mechanisms is at least n, where n is the number of machines.

From Monetary to Nonmonetary Mechanism Design via Artificial Currencies

2021 ◽  
Author(s):  
Artur Gorokh ◽  
Siddhartha Banerjee ◽  
Krishnamurthy Iyer
Keyword(s):  
Decision Making ◽  
Mechanism Design ◽  
Real World ◽  
Price Of Anarchy ◽  
Black Box ◽  
Trade Off ◽  
Two Agents ◽  
Over Time ◽  
Artificial Currency

Nonmonetary mechanisms for repeated allocation and decision making are gaining widespread use in many real-world settings. Our aim in this work is to study the performance and incentive properties of simple mechanisms based on artificial currencies in such settings. To this end, we make the following contributions: For a general allocation setting, we provide two black-box approaches to convert any one-shot monetary mechanism to a dynamic nonmonetary mechanism using an artificial currency that simultaneously guarantees vanishing gains from nontruthful reporting over time and vanishing losses in performance. The two mechanisms trade off between their applicability and their computational and informational requirements. Furthermore, for settings with two agents, we show that a particular artificial currency mechanism also results in a vanishing price of anarchy.

Terminal Ranking Games

2021 ◽  
Author(s):  
Erhan Bayraktar ◽  
Yuchong Zhang
Keyword(s):  
Mechanism Design ◽  
Price Of Anarchy ◽  
Mean Field ◽  
Design Problems ◽  
Mean Field Game ◽  
Reward Functions

We analyze a mean field tournament: a mean field game in which the agents receive rewards according to the ranking of the terminal value of their projects and are subject to cost of effort. Using Schrödinger bridges we are able to explicitly calculate the equilibrium. This allows us to identify the reward functions which would yield a desired equilibrium and solve several related mechanism design problems. We are also able to identify the effect of reward inequality on the players’ welfare as well as calculate the price of anarchy.

THE PRICE OF NASH EQUILIBRIA IN MULTICAST TRANSMISSION GAMES

2010 ◽  
Vol 11 (03n04) ◽  
pp. 97-120 ◽  
Author(s):  
VITTORIO BILÒ
Keyword(s):  
Nash Equilibrium ◽  
Cost Sharing ◽  
Price Of Anarchy ◽  
Optimal Solution ◽  
Minimum Cost ◽  
Price Of Stability ◽  
Common Source ◽  
Cost Share ◽  
Worst Case ◽  
The Cost

We consider the problem of sharing the cost of multicast transmissions in non-cooperative undirected networks where a set of receivers R wants to be connected to a common source s. The set of choices available to each receiver r ∈ R is represented by the set of all (s, r)-paths in the network. Given the choices performed by all the receivers, a public known cost sharing method determines the cost share to be charged to each of them. Receivers are selfish agents aiming to obtain the transmission at the minimum cost share and their interactions create a non-cooperative game. Devising cost sharing methods yielding games whose price of anarchy (price of stability), defined as the worst-case (best-case) ratio between the cost of a Nash equilibrium and that of an optimal solution, is not too high is thus of fundamental importance in non-cooperative network design. Moreover, since cost sharing games naturally arise in socio-economical contests, it is convenient for a cost sharing method to meet some constraining properties. In this paper, we first define several such properties and analyze their impact on the prices of anarchy and stability. We also reconsider all the methods known so far by classifying them according to which properties they satisfy and giving the first non-trivial lower bounds on their price of stability. Finally, we propose a new method, namely the free-riders method, which admits a polynomial time algorithm for computing a pure Nash equilibrium whose cost is at most twice the optimal one. Some of the ideas characterizing our approach have been independently proposed in Ref. 10.

scholarly journals Flow-Based Network Creation Games

2020 ◽  
Author(s):  
Hagen Echzell ◽  
Tobias Friedrich ◽  
Pascal Lenzner ◽  
Anna Melnichenko
Keyword(s):  
Communication Networks ◽  
Network Flow ◽  
Price Of Anarchy ◽  
Simple Algorithm ◽  
Past Research ◽  
Price Of Stability ◽  
Central Position ◽  
Network Nodes ◽  
Strategic Agents ◽  
Network Creation Games

Network Creation Games(NCGs) model the creation of decentralized communication networks like the Internet. In such games strategic agents corresponding to network nodes selfishly decide with whom to connect to optimize some objective function. Past research intensively analyzed models where the agents strive for a central position in the network. This models agents optimizing the network for low-latency applications like VoIP. However, with today's abundance of streaming services it is important to ensure that the created network can satisfy the increased bandwidth demand. To the best of our knowledge, this natural problem of the decentralized strategic creation of networks with sufficient bandwidth has not yet been studied. We introduce Flow-Based NCGs where the selfish agents focus on bandwidth instead of latency. In essence, budget-constrained agents create network links to maximize their minimum or average network flow value to all other network nodes. Equivalently, this can also be understood as agents who create links to increase their connectivity and thus also the robustness of the network. For this novel type of NCG we prove that pure Nash equilibria exist, we give a simple algorithm for computing optimal networks, we show that the Price of Stability is 1 and we prove an (almost) tight bound of 2 on the Price of Anarchy. Last but not least, we show that our models do not admit a potential function.

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