Filters








204 Hits in 4.4 sec

Nash Social Welfare, Matrix Permanent, and Stable Polynomials [article]

Nima Anari, Shayan Oveis Gharan, Amin Saberi, Mohit Singh
2016 arXiv   pre-print
We study the problem of allocating m items to n agents subject to maximizing the Nash social welfare (NSW) objective.  ...  Our main technical contribution is an extension of Gurvits's lower bound on the coefficient of the square-free monomial of a degree m-homogeneous stable polynomial on m variables to all homogeneous polynomials  ...  Our Contributions Our main contribution is to show an intricate connection between the Nash welfare maximization problem, the theory of real stable polynomials, and the problem of approximating the permanent  ... 
arXiv:1609.07056v2 fatcat:gg5uimranzeytkdlni66qzjcfm

Nash Social Welfare, Matrix Permanent, and Stable Polynomials

Nima Anari, Shayan Oveis Gharan, Amin Saberi, Mohit Singh
unpublished
We study the problem of allocating m items to n agents subject to maximizing the Nash social welfare (NSW) objective.  ...  Our main technical contribution is an extension of Gurvits's lower bound on the coefficient of the square-free monomial of a degree m-homogeneous stable polynomial on m variables to all homogeneous polynomials  ...  The authors would like to thank Leonid Gurvits for insightful comments and pointers to the literature.  ... 
fatcat:bwb3ird345fkfk24tojlisu6km

Satiation in Fisher Markets and Approximation of Nash Social Welfare [article]

Jugal Garg, Martin Hoefer, Kurt Mehlhorn
2019 arXiv   pre-print
We show how (approximate) equilibria can be rounded and provide the first constant-factor approximation algorithm (with a factor of 2.404) for maximizing Nash social welfare when agents have budget-additive  ...  Beyond natural applications in economics, these markets arise in the context of maximizing Nash social welfare when allocating indivisible items to agents.  ...  REFERENCES [1] Nima Anari, Shayan Oveis Gharan, Amin Saberi, and Mohit Singh. Nash social welfare, matrix permanent, and stable polynomials. In Proc. 8th Symp. Innovations in Theoret.  ... 
arXiv:1707.04428v3 fatcat:qqsywhxufvexrkaxz3qzba5gie

Game-theoretic insights into the role of environmentalism and social-ecological relevance: A cognitive model of resource consumption

Talha Manzoor, Elena Rovenskaya, Abubakr Muhammad
2016 Ecological Modelling  
Our model demonstrates, in a stylized fashion, how profound preference to social information can help avert free-riding behaviour and result in globally stable resource consumption dynamics.  ...  depending on their level of environmental concern, and relative importance placed on social and ecological information.  ...  The Jacobian matrix of (3) is given by is a quadratic polynomial in > 0. As > 0, the graph of q(•) points upwards and the roots are either complex conjugates or both real and positive.  ... 
doi:10.1016/j.ecolmodel.2016.09.007 fatcat:hgj3my757jdopbnc3dvf6dy5xi

Real Stable Polynomials and Matroids: Optimization and Counting [article]

Damian Straszak, Nisheeth K. Vishnoi
2016 arXiv   pre-print
Two notable examples are a result by Gurvits on the van der Waerden conjecture for real stable g when B is a single element and a result by Nikolov and Singh for multilinear real stable polynomials when  ...  We show that roughly, when g is a real stable polynomial with non-negative coefficients and B is a matroid, the integrality gap of our relaxation is finite and depends only on m (and not on the coefficients  ...  . , x m y m ). (7) A similar relaxation was used in [NS16] in the context of subdeterminant maximization and in [AOSS16] for the Nash Social Welfare problem.  ... 
arXiv:1611.04548v1 fatcat:bownuefvfrdrzaegj3su3j4zzy

Porter Hypothesis vs Pollution Haven Hypothesis: Can There Be Environmental Policies Getting Two Eggs in One Basket?

Claudia Ranocchia, Luca Lambertini
2021 Environmental and Resource Economics  
AbstractThe Porter hypothesis and the pollution haven hypothesis seem to predict opposite reactions by firms facing environmental regulation, as the first invokes the arising of a win–win solution while  ...  We illustrate the possibility of designing policies (taking the form of either emission taxation or environmental standards) able to eliminate firms' incentives to relocate their plants abroad and create  ...  the optimal sharing rule NBS 1 determined by the Nash Bargaining solution requires solving a FOC which contains a quintic polynomial in 1 , as it must maximise the Nash product V = C 1 − N 1 C 2 − N 2  ... 
doi:10.1007/s10640-020-00533-x fatcat:gsgr2j6xpzcltprzmz66cqxcsy

A Tight Analysis of Bethe Approximation for Permanent [article]

Nima Anari, Alireza Rezaei
2019 arXiv   pre-print
We show this by proving that the Bethe approximation of the permanent, a quantity computable in polynomial time, is at least as large as the permanent divided by √(2)^n.  ...  Our bound is tight, and when combined with previously known inequalities lower bounding the permanent, fully resolves the quality of Bethe approximation for permanent.  ...  [Ana+17b] used a particular approximation of the permanent to attack the problem of maximizing Nash social welfare; a key property used in their algorithm was that this approximation of per(A) was log-concave  ... 
arXiv:1811.02933v2 fatcat:7hxms2beffdynjxhgl5pygrthi

Maximizing Determinants under Matroid Constraints [article]

Vivek Madan, Aleksandar Nikolov, Mohit Singh, Uthaipon Tantipongpipat
2020 arXiv   pre-print
To show the approximation guarantee, we utilize recent works on strongly log-concave polynomials and show new relationships between different convex programs studied for the problem.  ...  ,v_n∈R^d and a matroid M=([n],I), we study the problem of finding a basis S of M such that (∑_i ∈ Sv_i v_i^) is maximized.  ...  References [AB13] [AGSS16] Nima Anari, Shayan Oveis Gharan, Amin Saberi, and Mohit Singh. Nash social welfare, matrix permanent, and stable polynomials.  ... 
arXiv:2004.07886v1 fatcat:2z4i3t4wujggvpwd4lst7m6uf4

Towards a dynamics of social behaviour: Strategic and genetic models for the evolution of animal conflicts

P SCHUSTER
1985 Journal of Social and Biological Systems  
Game dynamics provides a suitable framework to accomodate for the dynamic urp..i, of permanence and uninvadability, to model the evolution of phenotypes with frequency äependent fitness and to relate the  ...  persistence of behavioural traits in animal societies rather than optimality of reproductive success is described in terms of the game-theoretic notion of evolutionarily stable strategy.  ...  John Maynard Smith and Dr Peter Hammerstein for fruitful discussions.  ... 
doi:10.1016/0140-1750(85)90070-3 fatcat:yv6htkei4beelom4zwfj7r3fxq

Three Puzzles on Mathematics, Computation, and Games [article]

Gil Kalai
2018 arXiv   pre-print
In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years.  ...  Given an n by n matrix A, let per(A) denote the permanent of A. Let M be a complex n × m matrix, m ≥ n with orthonormal rows.  ...  The majority gives asymptotically "most rational" social preferences among generalized social welfare functions based on strong voting games with vanishing maximal Banzhaf power.  ... 
arXiv:1801.02602v1 fatcat:zeicivye4zhjjc6t32tyhu2pn4

Chapter 34 New econometric approaches to stabilization policy in stochastic models of macroeconomic fluctuations [chapter]

John B. Taylor
1986 Handbook of Econometrics  
The government sets g and the private sector takes g as given. The government then maximizes its social welfare function across different values of g.  ...  Note that this procedure or solving (2.95) can be stated quite simply in two steps: (1) factor the lag polynomial into two stable polynomials, one involving positive powers of L (lags) and the other involving  ... 
doi:10.1016/s1573-4412(86)03014-3 fatcat:l2bdvoosvnhq5ghszmqi6y75oy

Can We Identify the Fed's Preferences?

Jean-Bernard Chatelain, Kirsten Ralf
2017 Social Science Research Network  
A pre-test of Ramsey optimal policy versus time-consistent policy rejects timeconsistent policy and (optimal) simple rule for the U.S.  ...  Estimating a structural VAR for Ramsey optimal policy during Volcker-Greenspan period, the new-Keynesian Phillips curve slope parameter and the Fed's preferences (weight of the volatility of the output  ...  The characteristic polynomial of matrix M a : (X ) X 2 1 a X + 1 = 0 Matrix M a has two stable roots with bounded discounted quadratic loss function (below q 1 imply U = 1+ p 1 4 a 2 2 a = 1 R > q 1 .  ... 
doi:10.2139/ssrn.2914592 fatcat:4bg53mrs4zg6rhwtxmdc6xsrmq

On Achieving Fairness and Stability in Many-to-One Matchings [article]

Shivika Narang, Arpita Biswas, Y Narahari
2021 arXiv   pre-print
In fact, when additivity and non-negativity are the only assumptions on the valuations, we show that, unless P=NP, no efficient polynomial factor approximation is possible.  ...  The past few years have seen a surge of work on fairness in social choice literature.  ...  That is, u i (c j ) = 1 for all choices of i and j. This ensures that all the (complete) matchings are stable, as no student has an incentive to switch. The  ... 
arXiv:2009.05823v3 fatcat:6zfxgnciizb6xlynxkoo5kka7q

Achieving Diverse Objectives with AI-driven Prices in Deep Reinforcement Learning Multi-agent Markets [article]

Panayiotis Danassis, Aris Filos-Ratsikas, Boi Faltings
2021 arXiv   pre-print
resource wastefulness, fairness, buyers' and sellers' welfare, etc.  ...  To evaluate our approach, we design a realistic market with multiple and diverse buyers and sellers.  ...  We also remark that while similar in spirit, the market equilibrium is a different notion from the well-known notion of the Nash equilibrium [45] ; the former is a stable point of the market supply and  ... 
arXiv:2106.06060v1 fatcat:n3recajdyzh77ocujp42xowxvy

The Tragedy of the Commons, Livestock Cycles and Sustainability

M. Fafchamps
1998 Journal of African Economies  
. _ ______________ † I benefitted from comments from participants to various conferences and to seminars in Berkeley and Stanford.  ...  This paper revisits the tragedy of the commons and examines the conditions under which externalities contribute to livestock cycles.  ...  To summarize: Proposition 3: (1) Except for a set of parameter configurations of measure zero, the characteristic matrix exists and is non-singular. (2) A steady state is locally stable if one of the roots  ... 
doi:10.1093/oxfordjournals.jae.a020957 fatcat:72i3tyf54ffp3cxdpexwucuhz4
« Previous Showing results 1 — 15 out of 204 results