Attainability in repeated games with vector payoffs

Norman 3. Jan C. Science and Engineering University of Groningen. This paper reframes approachability theory within the context of population games. Thus, whilst a player still aims at driving her average payoff to a predefined set, her opponent is no longer malevolent but instead is extracted randomly at each instant of time from a population of individuals choosing actions in a similar manner.

First, we define the notion of 1st-moment approachabilitya weakening of Blackwell's approachability. Second, since the endogenous evolution of the population's play is then important, we develop a model of two coupled partial differential equations PDEs in the spirit of mean-field game theory: one describing the best-response of every player given the population distribution, the other capturing the macroscopic evolution of average payoffs if every player plays her best response.

Third, we provide a detailed analysis of existence, nonuniqueness, and stability of equilibria fixed points of the two PDEs. Fourth, we apply the model to regret-based dynamics, and use it to establish convergence to Bayesian equilibrium under incomplete information.

AumannUtility theory without the completeness axiom, Econometrica30 Google Scholar. AumannMarkets with a continuum of traders, Econometrica32 BausoObjective function design for robust optimality of linear control under state-constraints and uncertainty, ESAIM: Control, Optimisation and Calculus of Variations17 BardiExplicit solutions of some linear-quadratic mean field games, Network and Heterogeneous Media7 Hofbauer and S.

BlackwellAn analog of the minimax theorem for vector payoffs, Pacific J. BlanchiniSet invariance in control — a survey, Automatica35 DekelLexicographic probabilities and choice under uncertainty, Econometrica59 SchwarzInternet advertising and the generalised second-price auction: Selling billions of dollars worth of keywords, American Economic Review97 KaltonThe existence of value in differential games of pursuit and evasion, J.

Differential Equations12 Jeffrey C.

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VohraRegret in the on-line decision problem, Games and Economic Behavior29 John C. HarsanyiGames with incomplete information played by 'bayesian' players, i—iii. Bayesian equilibrium points, Management Science14 HartAdaptive heuristics, Econometrica73 Huang, P.

Caines and R. RosenthalAnonymous sequential games, Journal of Mathematical Economics17 Le cas stationnaire, Comptes Rendus Mathematique, LionsMean field games, Japanese Journal of Mathematics2 LehrerAllocation processes in cooperative games, International Journal of Game Theory31 LehrerApproachability in infinite dimensional spaces, International Journal of game Theory31 LehrerA wide range no-regret theorem, Games and Economic Behavior42 SolanExcludability and bounded computational capacity strategies, Mathematics of Operations Research31 Lehrer, E.Computational Management Science pp Cite as.

This paper studies population games with vector payoffs. It provides a new perspective on approachability based on mean-field game theory. The model involves a Hamilton-Jacobi-Bellman equation which describes the best-response of every player given the population distribution and an advection equationcapturing the macroscopic evolution of average payoffs if every player plays its best response.

attainability in repeated games with vector payoffs

The work of D. This work has developed during the sabbatical period spent by D. Skip to main content. This service is more advanced with JavaScript available. Advertisement Hide. Population Games with Vector Payoff and Approachability.

attainability in repeated games with vector payoffs

Conference paper. This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access. Acknowledgements The work of D. Aumann, R. Econometrica 32 1—239—50 CrossRef Google Scholar. Bauso, D.

IEEE Trans. Controlin print. Available online at doi: Blackwell, D. Pacific J. Cesa-Bianchi, N. Foster, D. Games Econ. Hart, S. Econometrica 73— CrossRef Google Scholar. Theory 9826—54 CrossRef Google Scholar. Huang, M. Control 9— CrossRef Google Scholar. Jovanovic, B.We hope this content on epidemiology, disease modeling, pandemics and vaccines will help in the rapid fight against this global problem. Click on title above or here to access this collection.

We study the notion of approachability in a repeated game with vector payoffs from a new point of view using techniques recently developed for qualitative differential games. Namely, we relate the sufficient condition for approachability B-set to the notion of discriminating domain for a suitably chosen differential game.

The other goal of the present article is to obtain a new precise link between the strategies in the differential game and in the repeated game preserving approachability properties. Sign in Help View Cart. Article Tools. Add to my favorites. Recommend to Library. Email to a friend. Digg This. Notify Me! E-mail Alerts. RSS Feeds.

SIAM J. Control Optim. Related Databases. Web of Science You must be logged in with an active subscription to view this. Keywords differential gamesrepeated gamesviability. Publication Data. Publisher: Society for Industrial and Applied Mathematics. Dynamic Games and Applications Automatica 84 Dynamic Games and Applications 6 :3, Population Games with Vector Payoff and Approachability. Computational Management Science, Mathematics of Operations Research 40 :3, Dynamic Games and Applications 5 :1, Advances in Zero-Sum Dynamic Games.

Handbook of Game Theory with Economic Applications, Journal of Dynamics and Games 1 :4, Journal of Dynamics and Games 1 Journal of Dynamics and Games 1 :2, Dynamic Games and Applications 3 :1, Journal of Optimization Theory and Applications :3, Dynamic Games and Applications 1 :1, Banner art adapted from a figure by Hinke M.Patrick Van Roy, Full references including those not matched with items on IDEAS More about this item Keywords attainability ; continuous time ; repeated games ; Vector payoffs ; dynamic games ; approachability ; Statistics Access and download statistics Corrections All material on this site has been provided by the respective publishers and authors.

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attainability in repeated games with vector payoffs

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Attainability in Repeated Games with Vector Payoffs

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FRED data. Attainability in Repeated Games with Vector Payoffs. Registered: Eilon Solan Xavier Venel. We introduce the concept of attainable sets of payoffs in two-player repeated games with vector payoffs.

A set of payoff vectors is called attainable by a player if there is a positive integer such that the player can guarantee that in all finite game longer than that integer, the distance between the set and the cumulative payoff is arbitrarily small, regardless of the strategy Player 2 is using. We provide a necessary and sufficient condition for the attainability of a convex set, using the concept of B -sets. We then particularize the condition to the case in which the set is a singleton, and provide some equivalent conditions.

We finally characterize when all vectors are attainable. More about this item Keywords attainability ; continuous time ; repeated games ; Vector payoffs ; dynamic games ; approachability ; Statistics Access and download statistics. Corrections All material on this site has been provided by the respective publishers and authors.

Louis Fed. Help us Corrections Found an error or omission? RePEc uses bibliographic data supplied by the respective publishers.Ehud Lehrer. Contact Info email: jane. Lehrer and B. Weiss - " An e-free Rohlin lemma ", Ergodic Theory Dynamical Systems, 2Lehrer - " Topological mixing and uniquely ergodic systems ", Israel Journal of Mathematics, 57, Lehrer and H.

Pant - " On strictly ergodic models which are not almost topologically conjugate ", Israel Journal of Mathematics, 73, Lehrer and E. Shmaya - " A subjective approach to quantum probability ", Proceedings of the Royal Society A, Lehrer and D.

To appear in Mathematics of Operations Research. International Journal of Game Theory, 18, Lehrer - " Nash Equilibria of n-player repeated games with semi-standard information ", International Journal of Game Theory, 19, Lehrer - " Internal correlation in repeated games ", Lehrer - " On the equilibrium payoffs set of two player repeated games with imperfect monitoring ", International Journal of Game Theory, 20, Lehrer - " Correlated equilibria in two-player repeated games with non-observable actions ", Mathematics of Operations Research, 17, Theoretical Economics, 13, 87— Journal of Economic Theory, Games and Economic Behavior, Repeated games with incomplete information E.

Lehrer - " A note on the monotonicity of Vn ", Economic Letters, 23, Lehrer and S. Sorin - " e-Consistent equilibrium in repeated games ", International Journal of Game Theory, 27, Lehrer and L.The Infona portal uses cookies, i.

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Repeated games over networks with vector payoffs: the notion of attainability. Abstract We introduce the concept of strongly attainable sets of payoffs in two-player repeated games with vector payoffs in continuous time.

attainability in repeated games with vector payoffs

A set of payoffs is called strongly attainable if player 1 has a strategy guaranteeing, even in the worst case, that the distance between the set and the cumulative payoff shrinks with time to zero. We characterize when any vector is strongly attainable and illustrate the motivation of our study on a multi-inventory application.

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Download to disc. High contrast On Off. Close window. Assign to yourself. Assign to other user Search user Invite. Assign Wrong email address.This project builds on the widely accepted idea that when independent and geographically sparse wind farm power producers agree to join coalitions and aggregate their production capacities, they reduce the aggregate volatility and end up bidding less conservatively.

The problem involves a set of independent wind farm producers, which can form coalitions and submit joint bids. A possible configuration is. The grid. In return, financial flows run from the ISO to the coalitions dashed. Each coalition is managed by a cooperative designer. Adaptation and coordination in decentralized organizations. This project deals with the analysis of quantitative models simulating a distributed decision making for manufacturing.

The model simulates the partitioning of the whole project into specific tasks and assign them to multiple independent decision-makers. Case study. A large software project that cannot be developed by a single engineer. The project is decomposed in multiple modules tasks and each module is assigned to a different team. If the software project involves the development of a proprietary operating system, we will have a module focusing on the process manager, another module dealing with the network access and so forth.

On the other hand, all modules will need to be assembled in coherent whole. A higher level of coordination entails an increase in the communication between. Affecting the performance of the organization are two conflicting factors: ii how well. The figure above [Tarraf and Bauso ] displays an assembling process with four final products. Evolutionary game theory models for the Warburg Effect in cancer cells.

T he Warburg effect is an aerobic glycolysis, loss of glucose, in the presence of oxigen, which produces ATP energy. Some scientists conjecture that such an effect is a metabolic strategy used by cancer cells to meet large fluctuations in energy demand observed in tumor environments.

This project deals with the development of cell models describing both the efficient but slow responding aerobic metabolism and the inefficient but fast responding glycolytic metabolism.

The model simulates different tradeoffs between efficiency and speed of metabolic pahtways for the upregulation of ATP. This project originates from a brainstorm with Dr. Challenges include convergence analysis under the influence of external manipulators, malicious agents, stubborn agents, or zealots.

Each producer tries to maximize the production rate when the forecasted demand is high, and total produced quantity by others is low so that the sale price can be increased. Another application domain is "herd behaviors" in social networks.

This is linked to imitation phenomena in mass behaviors, which explains current tendencies in society, fashion, or markets. Mean field games capture this mutual interaction between a population and its individuals.


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