scholarly journals Nash Social Welfare Approximation for Strategic Agents

2021 ◽  
Author(s):  
Simina Brânzei ◽  
Vasilis Gkatzelis ◽  
Ruta Mehta
Keyword(s):  
Nash Equilibrium ◽  
Social Welfare ◽  
Geometric Mean ◽  
Market Game ◽  
Virtual Currency ◽  
Strategic Agents ◽  
Individual Needs

We study the problem of allocating divisible resources to agents with different preferences. We analyze a market game known as Trading Post, first considered by Shapley and Shubik, where each agent gets a budget of virtual currency to bid on goods: after bids are placed, goods are allocated to players in proportion to their bids. In this setting, the agents choose their bids strategically, aiming to maximize their utility, and this gives rise to a game. We study the equilibrium allocations of this game, measuring the quality of an allocation via the Nash social welfare, the geometric mean of utilities (a measure of aggregate welfare that respects individual needs). We show that any Nash equilibrium of Trading Post approximates the optimal Nash welfare within a factor of two for all concave valuations, and the mechanism is essentially optimal for Leontief valuations.

Manufacturing service order allocation in the context of social manufacturing based on Stackelberg game

2018 ◽  
Vol 233 (8) ◽  
pp. 1890-1901
Author(s):  
Wei Guo ◽  
Pingyu Jiang
Keyword(s):  
Quality Of Service ◽  
Nash Equilibrium ◽  
Manufacturing Industry ◽  
Stackelberg Game ◽  
Game Model ◽  
Service Cost ◽  
Order Allocation ◽  
Multi Objective ◽  
Bird Swarm Algorithm

For adapting the socialization, individuation and servitization in manufacturing industry, a new manufacturing paradigm called social manufacturing has received a lot of attention. Social manufacturing can be seen as a network that enterprises with socialized resources self-organized into communities that provide personalized machining and service capabilities to customers. Since a community of social manufacturing has multiple enterprises and emphasizes on the importance of service, manufacturing service order allocation must be studied from the new perspective considering objectives on service cost and quality of service. The manufacturing service order allocation can be seen as a one-to-many game model with multi-objective. In this article, a Stackelberg game model is proposed to tackle the manufacturing service order allocation problem with considering the payoffs on cost and quality of service. Since this Stackelberg game can be mapped to a multi-objective bi-level programming, a modified multi-objective hierarchical Bird Swarm Algorithm is used to find the Nash equilibrium of the game. Finally, a case from a professional printing firm is analyzed to validate the proposed methodology and model. The objective of this research is to find the Nash equilibrium on the manufacturing service order allocation and provide strategies guidance for customer and small- and medium-sized enterprises with optimal service cost and lead time. According to the game process and Nash equilibrium, some rules are revealed, and they are useful for guiding practical production.

scholarly journals The quantity and quality of anti-PRP induced by the new Indonesian DTwP-HB-Hib vaccine compared to the Hib vaccine given with the DTwP-HB vaccine

2018 ◽  
Vol 57 (5) ◽  
pp. 262
Author(s):  
Novilia Sjafri Bachtiar ◽  
Kusnandi Rusmil ◽  
Sunarjati Sudigdoadi ◽  
Hadyana Sukandar ◽  
Rini Mulia Sari ◽  
...  
Keyword(s):  
Phase Ii ◽  
Geometric Mean ◽  
Antibody Concentration ◽  
Open Label ◽  
Bactericidal Capacity ◽  
Monovalent Vaccine ◽  
Open Label Phase ◽  
Hb Vaccine ◽  
Blood Specimens

Background A phase II study of DTwP-HB-Hib vaccine compared to Hib (monovalent) vaccine given simultaneously with DTwP-HB vaccine has been done following the success of phase I study in infants, where the new DTwP-HB-Hib has excellent safety profiles and antibody responses in infants.Objective To evaluate the titer (quantity), avidity, and bactericidal capacity (quality of anti-polyribosylribitol phosphate/anti-PRP), of a new combined Bio Farma DTwP-HB-Hib (pentavalent) vaccine, compared to the Hib monovalent vaccine given simultaneously with the DTwP-HB vaccine (DTwP-HB+Hib).Methods The study was a prospective, randomized, open label, phase II trial. Subjects aged 6-11 weeks were allocated according to the randomization list. The pentavalent group received the DTwP-HB-Hib vaccine, while the monovalent group received the Hib monovalent and DTwP-HB vaccines separately. Immunizations were given in three doses with 28-day intervals. Blood specimens were taken before the first dose and 28 days after the last dose. We evaluated anti-PRP titers quantity (geometric mean antibody concentration/GMC) and seroprotection), followed by avidity and bactericidal (quality) testing. Titer and avidity of anti-PRP were tested using a modified version of the improved Phipps ELISA. Bactericidal capacity was evaluated using a Hib killing assay. Immune responses against other antigens in the vaccine were reported separately.Results One hundred five subjects in the pentavalent group and 106 subjects in the Hib monovalent group were tested for anti-PRP titers. Only 102 specimens for each group were available for bactericidal testing, due to insufficient volume for testing. Both vaccines induced similar anti-PRP titers, for GMC and seroprotection. Avidity increases were 82.9% and 76.4% in the pentavalent and Hib monovalent groups, respectively. Bactericidal activities were 94.1% and 89.2%, respectively. Both avidity and bactericidal activity were not significantly different between groups.Conclusion DTwP-HB-Hib vaccine induced anti-PRP quantity and quality comparable to those of the Hib monovalent vaccine given simultaneously with the DTwP-HB vaccine.

scholarly journals PERANAN PIMPINAN TERHADAP TINGKAT KINERJA APARATUR PEMERINTAH KABUPATEN BONE BOLANGO

2018 ◽  
Author(s):  
Muh Firyal Akbar
Keyword(s):  
Social Welfare ◽  
Qualitative Data ◽  
Leadership Role ◽  
Public Welfare ◽  
The Public ◽  
The Social ◽  
Data Source ◽  
District Government

This research is motivated by the leadership role of the aperture on the performance of the District Social Welfare Section of Bone Bolango, and addressing what led to the apparaturs can not improve its performance. Location / object of research in the Social Welfare Section of Bone Bolango District Secretariat, the research method used is descriptive qualitative data sources from the observation, interviews, and documentation. Informants were interviewed 6 (six) in the form of Deputy. Section, and staff,. Data analysis was done by analysis that includes observation, identification of the problem, determine the focus of the problem, collect the data source, making the analysis of data, and making conclusions. Results of the study found the following: 1. a leader as an innovator has yet to make staff / subordinates capable of reviewing what to expect, 2. Leadership as a motivator, in this case has not been fully motivate / encourage the morale of staff, 3. Leadership as a facilitator in accordance interviews some say has not been able to realize the needs of the staff and the organization, 4. Chief said as a mobilizer, there are leaders who have not been able to steer and drive the duties and functions, so the quality of the resulting performance apparatus has not been able to realize the needs of the organization. As for the hope of Bone Bolango District Government, is where all the apparatus that is required to dedicate itself to the development of more specialized areas within the public welfare.

scholarly journals Semidefinite Programming and Nash Equilibria in Bimatrix Games

2020 ◽  
Author(s):  
Amir Ali Ahmadi ◽  
Jeffrey Zhang
Keyword(s):  
Nash Equilibrium ◽  
Semidefinite Programming ◽  
Nash Equilibria ◽  
Valid Inequalities ◽  
Bimatrix Games ◽  
Competitive Game ◽  
Approximate Nash Equilibria ◽  
Hard Problems ◽  
Rank 2

We explore the power of semidefinite programming (SDP) for finding additive ɛ-approximate Nash equilibria in bimatrix games. We introduce an SDP relaxation for a quadratic programming formulation of the Nash equilibrium problem and provide a number of valid inequalities to improve the quality of the relaxation. If a rank-1 solution to this SDP is found, then an exact Nash equilibrium can be recovered. We show that, for a strictly competitive game, our SDP is guaranteed to return a rank-1 solution. We propose two algorithms based on the iterative linearization of smooth nonconvex objective functions whose global minima by design coincide with rank-1 solutions. Empirically, we demonstrate that these algorithms often recover solutions of rank at most 2 and ɛ close to zero. Furthermore, we prove that if a rank-2 solution to our SDP is found, then a [Formula: see text]-Nash equilibrium can be recovered for any game, or a [Formula: see text]-Nash equilibrium for a symmetric game. We then show how our SDP approach can address two (NP-hard) problems of economic interest: finding the maximum welfare achievable under any Nash equilibrium, and testing whether there exists a Nash equilibrium where a particular set of strategies is not played. Finally, we show the connection between our SDP and the first level of the Lasserre/sum of squares hierarchy.

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.

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