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[1808.09004] Downstream Effects of Affirmative Action
We study a two-stage model, in which students are 1) admitted to college on the basis of an entrance exam which is a noisy signal about their qualifications (type), and then 2) those students who were admitted to college can be hired by an employer as a function of their college grades, which are an independently drawn noisy signal of their type. Students are drawn from one of two populations, which might have different type distributions. We assume that the employer at the end of the pipeline is rational, in the sense that it computes a posterior distribution on student type conditional on all information that it has available (college admissions, grades, and group membership), and makes a decision based on posterior expectation. We then study what kinds of fairness goals can be achieved by the college by setting its admissions rule and grading policy. For example, the college might have the goal of guaranteeing equal opportunity across populations: that the probability of passing through the pipeline and being hired by the employer should be independent of group membership, conditioned on type. Alternately, the college might have the goal of incentivizing the employer to have a group blind hiring rule. We show that both goals can be achieved when the college does not report grades. On the other hand, we show that under reasonable conditions, these goals are impossible to achieve even in isolation when the college uses an (even minimally) informative grading policy.

--would make a nice example in a game theory class.
decison_theory  game_theory  algorithmic_fairness  discrimination  affirmative_action  economics  computer_science  teaching 
8 weeks ago by rvenkat
[1506.03414] An evolutionary advantage of cooperation
Cooperation is a persistent behavioral pattern of entities pooling and sharing resources. Its ubiquity in nature poses a conundrum. Whenever two entities cooperate, one must willingly relinquish something of value to the other. Why is this apparent altruism favored in evolution? Classical solutions assume a net fitness gain in a cooperative transaction which, through reciprocity or relatedness, finds its way back from recipient to donor. We seek the source of this fitness gain. Our analysis rests on the insight that evolutionary processes are typically multiplicative and noisy. Fluctuations have a net negative effect on the long-time growth rate of resources but no effect on the growth rate of their expectation value. This is an example of non-ergodicity. By reducing the amplitude of fluctuations, pooling and sharing increases the long-time growth rate for cooperating entities, meaning that cooperators outgrow similar non-cooperators. We identify this increase in growth rate as the net fitness gain, consistent with the concept of geometric mean fitness in the biological literature. This constitutes a fundamental mechanism for the evolution of cooperation. Its minimal assumptions make it a candidate explanation of cooperation in settings too simple for other fitness gains, such as emergent function and specialization, to be probable. One such example is the transition from single cells to early multicellular life.
evolution_of_cooperation  evolutionary_biology  game_theory 
10 weeks ago by rvenkat
The ecology of the microbiome: Networks, competition, and stability | Science
The human gut harbors a large and complex community of beneficial microbes that remain stable over long periods. This stability is considered critical for good health but is poorly understood. Here we develop a body of ecological theory to help us understand microbiome stability. Although cooperating networks of microbes can be efficient, we find that they are often unstable. Counterintuitively, this finding indicates that hosts can benefit from microbial competition when this competition dampens cooperative networks and increases stability. More generally, stability is promoted by limiting positive feedbacks and weakening ecological interactions. We have analyzed host mechanisms for maintaining stability—including immune suppression, spatial structuring, and feeding of community members—and support our key predictions with recent data
microbiome  networks  ecology  evolution_of_cooperation  game_theory  for_friends 
10 weeks ago by rvenkat
Probabilistic Theory of Mean Field Games with Applications I | SpringerLink
"This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions.
"Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. 
"Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games."
to:NB  books:noted  downloaded  game_theory  re:do-institutions-evolve  stochastic_processes 
10 weeks ago by cshalizi
Twenty Lectures on Algorithmic Game Theory by Tim Roughgarden
"Computer science and economics have engaged in a lively interaction over the past fifteen years, resulting in the new field of algorithmic game theory. Many problems that are central to modern computer science, ranging from resource allocation in large networks to online advertising, involve interactions between multiple self-interested parties. Economics and game theory offer a host of useful models and definitions to reason about such problems. The flow of ideas also travels in the other direction, and concepts from computer science are increasingly important in economics. This book grew out of the author's Stanford University course on algorithmic game theory, and aims to give students and other newcomers a quick and accessible introduction to many of the most important concepts in the field. The book also includes case studies on online advertising, wireless spectrum auctions, kidney exchange, and network management."
to:NB  books:noted  downloaded  game_theory  theoretical_computer_science  re:computational_complexity_of_communism 
11 weeks ago by cshalizi
[1811.05008] Choosing to grow a graph: Modeling network formation as discrete choice
We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another node, based on (generic) features of the other nodes available to make a connection. This perspective on network formation unifies existing models such as preferential attachment, triadic closure, and node fitness, which are all special cases, and thereby provides a flexible means for conceptualizing, estimating, and comparing models. The lens of discrete choice theory also provides several new tools for analyzing social network formation; for example, mixtures of existing models can be estimated by adapting known expectation-maximization algorithms, and the significance of node features can be evaluated in a statistically rigorous manner. We demonstrate the flexibility of our framework through examples that analyze a number of synthetic and real-world datasets. For example, we provide rigorous methods for estimating preferential attachment models and show how to separate the effects of preferential attachment and triadic closure. Non-parametric estimates of the importance of degree show a highly linear trend, and we expose the importance of looking carefully at nodes with degree zero. Examining the formation of a large citation graph, we find evidence for an increased role of degree when accounting for age.

--seems related to some of M.O. Jackson's constructions...
networks  dynamics  optimization  game_theory  via:clauset 
november 2018 by rvenkat
Algorithms, games, and evolution
Theoretical biology was founded on the mathematical tools of statistics and physics. We believe there are productive connections to be made with the younger field of theoretical computer science, which shares with it an interest in complexity and functionality. In this paper, we find that the mathematical description of evolution in the presence of sexual recombination and weak selection is equivalent to a repeated game between genes played according to the multiplicative weight updates algorithm, an algorithm that has surprised computer scientists time and again in its usefulness. This equ...
algorithmic_game_theory  algorithms  evolutionary_computation  game_theory  Everything 
july 2018 by jpowerj
[1401.4770] Opinion Exchange Dynamics
We survey a range of models of opinion exchange. From the introduction: "The exchange of opinions between individuals is a fundamental social interaction... Moreover, many models in this field are an excellent playground for mathematicians, especially those working in probability, algorithms and combinatorics. The goal of this survey is to introduce such models to mathematicians, and especially to those working in discrete mathematics, information theory, optimization, probability and statistics."
opinion_dynamics  opinion_formation  interating_particle_system  game_theory  review 
july 2018 by rvenkat
The Non-Existence of Representative Agents by Matthew O. Jackson, Leeat Yariv :: SSRN
We characterize environments in which there exists a representative agent: an agent who inherits the structure of preferences of the population that she represents. The existence of such a representative agent imposes strong restrictions on individual utility functions -- requiring them to be linear in the allocation and additively separable in any parameter that characterizes agents' preferences (e.g., a risk aversion parameter, a discount factor, etc.). Commonly used classes of utility functions (exponentially discounted utility functions, CRRA or CARA utility functions, logarithmic functions, etc.) do not admit a representative agent.

non-equilibrium  statistical_mechanics  interating_particle_system  game_theory  economics  macro_from_micro  collective_dynamics  matthew.jackson 
july 2018 by rvenkat

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