scholarly journals The Efficiency of Resource Allocation Mechanisms for Budget-Constrained Users

2020 ◽  
Author(s):  
Ioannis Caragiannis ◽  
Alexandros A. Voudouris
Keyword(s):  
Resource Allocation ◽  
Differential Equations ◽  
Social Welfare ◽  
Price Of Anarchy ◽  
Budget Constraint ◽  
Budget Constraints ◽  
Tight Bound ◽  
Worst Case ◽  
Seminal Work ◽  
The Social

We study the efficiency of mechanisms for allocating a divisible resource. Given scalar signals submitted by all users, such a mechanism decides the fraction of the resource that each user will receive and a payment that will be collected from her. Users are self-interested and aim to maximize their utility (defined as their value for the resource fraction they receive minus their payment). Starting with the seminal work of Johari and Tsitsiklis, a long list of papers studied the price of anarchy (in terms of the social welfare—the total users’ value) of resource allocation mechanisms for a variety of allocation and payment rules. Here, we further assume that each user has a budget constraint that invalidates strategies that yield a payment that is higher than the user’s budget. This subtle assumption, which is arguably more realistic, constitutes the traditional price of anarchy analysis meaningless as the set of equilibria may change drastically and their social welfare can be arbitrarily far from optimal. Instead, we study the price of anarchy using the liquid welfare benchmark that measures efficiency taking budget constraints into account. We show a tight bound of 2 on the liquid price of anarchy of the well-known Kelly mechanism and prove that this result is essentially best possible among all multiuser resource allocation mechanisms. This comes in sharp contrast to the no-budget setting where there are mechanisms that considerably outperform Kelly in terms of social welfare and even achieve full efficiency. In our proofs, we exploit the particular structure of worst-case games and equilibria, which also allows us to design (nearly) optimal two-player mechanisms by solving simple differential equations.

scholarly journals The Impact of Selfishness in Hypergraph Hedonic Games

2020 ◽  
Vol 34 (02) ◽  
pp. 1766-1773
Author(s):  
Alessandro Aloisio ◽  
Michele Flammini ◽  
Cosimo Vinci
Keyword(s):  
Social Welfare ◽  
Price Of Anarchy ◽  
Maximum Size ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
The Social ◽  
Worst Case Ratio ◽  
Distinct Node ◽  
Hedonic Games ◽  
The Impact

We consider a class of coalition formation games that can be succinctly represented by means of hypergraphs and properly generalizes symmetric additively separable hedonic games. More precisely, an instance of hypegraph hedonic game consists of a weighted hypergraph, in which each agent is associated to a distinct node and her utility for being in a given coalition is equal to the sum of the weights of all the hyperedges included in the coalition. We study the performance of stable outcomes in such games, investigating the degradation of their social welfare under two different metrics, the k-Nash price of anarchy and k-core price of anarchy, where k is the maximum size of a deviating coalition. Such prices are defined as the worst-case ratio between the optimal social welfare and the social welfare obtained when the agents reach an outcome satisfying the respective stability criteria. We provide asymptotically tight upper and lower bounds on the values of these metrics for several classes of hypergraph hedonic games, parametrized according to the integer k, the hypergraph arity r and the number of agents n. Furthermore, we show that the problem of computing the exact value of such prices for a given instance is computationally hard, even in case of non-negative hyperedge weights.

scholarly journals Representative Committees of Peers

2021 ◽  
Vol 71 ◽  
pp. 401-429
Author(s):  
Reshef Meir ◽  
Fedor Sandomirskiy ◽  
Moshe Tennenholtz
Keyword(s):  
Social Welfare ◽  
Social Cost ◽  
Majority Vote ◽  
Preference Profile ◽  
Final Decision ◽  
Worst Case ◽  
Optimal Rule ◽  
The Social ◽  
Small Committee ◽  
Elected Representatives

A population of voters must elect representatives among themselves to decide on a sequence of possibly unforeseen binary issues. Voters care only about the final decision, not the elected representatives. The disutility of a voter is proportional to the fraction of issues, where his preferences disagree with the decision. While an issue-by-issue vote by all voters would maximize social welfare, we are interested in how well the preferences of the population can be approximated by a small committee. We show that a k-sortition (a random committee of k voters with the majority vote within the committee) leads to an outcome within the factor 1+O(1/√ k) of the optimal social cost for any number of voters n, any number of issues m, and any preference profile. For a small number of issues m, the social cost can be made even closer to optimal by delegation procedures that weigh committee members according to their number of followers. However, for large m, we demonstrate that the k-sortition is the worst-case optimal rule within a broad family of committee-based rules that take into account metric information about the preference profile of the whole population.

scholarly journals Selfishness Level of Strategic Games

2014 ◽  
Vol 49 ◽  
pp. 207-240 ◽  
Author(s):  
K. R. Apt ◽  
G. Schaefer
Keyword(s):  
Nash Equilibrium ◽  
Social Welfare ◽  
Price Of Anarchy ◽  
Congestion Games ◽  
Price Of Stability ◽  
Social Optimum ◽  
Potential Game ◽  
Strategic Games ◽  
The Social ◽  
The Impact

We introduce a new measure of the discrepancy in strategic games between the social welfare in a Nash equilibrium and in a social optimum, that we call selfishness level. It is the smallest fraction of the social welfare that needs to be offered to each player to achieve that a social optimum is realized in a pure Nash equilibrium. The selfishness level is unrelated to the price of stability and the price of anarchy and is invariant under positive linear transformations of the payoff functions. Also, it naturally applies to other solution concepts and other forms of games. We study the selfishness level of several well-known strategic games. This allows us to quantify the implicit tension within a game between players' individual interests and the impact of their decisions on the society as a whole. Our analyses reveal that the selfishness level often provides a deeper understanding of the characteristics of the underlying game that influence the players' willingness to cooperate. In particular, the selfishness level of finite ordinal potential games is finite, while that of weakly acyclic games can be infinite. We derive explicit bounds on the selfishness level of fair cost sharing games and linear congestion games, which depend on specific parameters of the underlying game but are independent of the number of players. Further, we show that the selfishness level of the $n$-players Prisoner's Dilemma is c/(b(n-1)-c), where b and c are the benefit and cost for cooperation, respectively, that of the n-players public goods game is (1-c/n)/(c-1), where c is the public good multiplier, and that of the Traveler's Dilemma game is (b-1)/2, where b is the bonus. Finally, the selfishness level of Cournot competition (an example of an infinite ordinal potential game), Tragedy of the Commons, and Bertrand competition is infinite.

Payment Tracking System

2019 ◽  
Vol 1 (2) ◽  
pp. 43-50
Author(s):  
Sakthi Sree T ◽  
Rajagopal T.K.P. ◽  
Ananthi Priya S ◽  
Ganesh M ◽  
Venkatesh V ◽  
...  
Keyword(s):  
Social Welfare ◽  
Tracking System ◽  
Single Point ◽  
Optimal Solution ◽  
Constant Factor ◽  
Worst Case ◽  
Web Based ◽  
The Social ◽  
The Right ◽  
Management Capabilities

Payment Tracking System is a web-based application for tracking and managing the payments for various vendors. It provides a single point of contact that consolidates payment requests from the accounts department to the top management to deliver the supplier payments on time, using integrated best practices to manage operations and services. It offers integrated Transaction Management capabilities like Ledger view and Hold/Release Payments. It ensures visibility, insight, isolation and faster resolution of Payment related issues for any type of organization by providing the right information at the right time as required by the user. For both models, we design incentive resource allocation mechanisms to maximize the social welfare. Theoretically analysis shows that the proposed mechanisms are truthful for general monotonic pro?t functions and the worst-case performance on the social welfare are well-bounded within a constant factor of the optimal solution for linear pro?t functions. Simulation results also demonstrate that the performances of the proposed mechanisms are very close to the optimal solution, in terms of maximizing the social welfare.

An Analytical Exposition of the Social Welfare Role of Wealth in Islam

2015 ◽  
Author(s):  
Ahmad Bello Dogarawa ◽  
Suleiman Muhammad Hussain
Keyword(s):  
Social Welfare ◽  
The Social
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