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The laws of chance are often subtle and deceptive. This is why games of chance work. People are convinced that they obey seemingly intuitive laws, while the underlying mathematical structure reveals a different and more complex reality.…

History and Overview · Mathematics 2023-09-06 Paolo Bartesaghi

This paper investigates a robust incentive Stackelberg stochastic differential game problem for a linear-quadratic mean field system, where the model uncertainty appears in the drift term of the leader's state equation. Moreover, both the…

Optimization and Control · Mathematics 2026-03-31 Na Xiang , Jingtao Shi

We introduce a mean field game for a family of filtering problems related to the classic sequential testing of the drift of a Brownian motion. To the best of our knowledge this work presents the first treatment of mean field filtering games…

Optimization and Control · Mathematics 2024-03-28 Steven Campbell , Yuchong Zhang

We study first order evolutive Mean Field Games where the Hamiltonian is non-coercive. This situation occurs, for instance, when some directions are "forbidden" to the generic player at some points. We establish the existence of a weak…

Analysis of PDEs · Mathematics 2018-12-03 Paola Mannucci , Claudio Marchi , Carlo Mariconda , Nicoletta Tchou

Wealthy individuals may be less tempted to defect than those with comparatively low payoffs. To take this into consideration, we introduce coevolutionary success-driven multigames in structured populations. While the core game is always the…

Physics and Society · Physics 2014-10-17 Attila Szolnoki , Matjaz Perc

We analyze a cooperative game, where the cooperative act is not based on the previous behaviour of the co-player, but on the similarity between the players. This system has been studied in a mean-field description recently [A. Traulsen and…

Statistical Mechanics · Physics 2007-05-23 Arne Traulsen , Jens Christian Claussen

In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the…

Optimization and Control · Mathematics 2014-07-28 Alain Bensoussan , Michael Chau , Phillip Yam

In this paper, we analyse inspection games with an evolutionary perspective. In our evolutionary inspection game with a large population, each individual is not a rational payoff maximiser, but periodically updates his strategy if he…

Optimization and Control · Mathematics 2013-06-19 Vassili Kolokoltsov , Hemant Passi , Wei Yang

Mean field type models describing the limiting behavior, as the number of players tends to $+\infty$, of stochastic differential game problems, have been recently introduced by J-M. Lasry and P-L. Lions. Numerical methods for the…

Numerical Analysis · Mathematics 2012-07-13 Yves Achdou , Fabio Camilli , Italo Capuzzo Dolcetta

We propose a novel quadratic programming formulation for estimating the corruption levels in group synchronization, and use these estimates to solve this problem. Our objective function exploits the cycle consistency of the group and we…

Machine Learning · Statistics 2022-06-22 Yunpeng Shi , Cole Wyeth , Gilad Lerman

Game-theoretical models where the rules of the game and the interaction structure both coevolves with the game dynamics -- multiadaptive games -- capture very flexible situations where cooperation among selfish agents can emerge. In this…

Populations and Evolution · Quantitative Biology 2012-10-10 Sungmin Lee , Petter Holme , Zhi-Xi Wu

This paper is devoted to finite horizon deterministic mean field games in which the state space is a network. The agents control their velocity, and when they occupy a vertex, they can enter into any incident edge. The running and terminal…

Optimization and Control · Mathematics 2023-11-21 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

We prove well-posedness of a class of kinetic-type Mean Field Games, which typically arise when agents control their acceleration. Such systems include independent variables representing the spatial position as well as velocity. We consider…

Analysis of PDEs · Mathematics 2024-03-20 David M. Ambrose , Megan Griffin-Pickering , Alpár R. Mészáros

Trust models are widely used in various computer science disciplines. The main purpose of a trust model is to continuously measure trustworthiness of a set of entities based on their behaviors. In this article, the novel notion of "rational…

Cryptography and Security · Computer Science 2017-09-26 Mehrdad Nojoumian

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…

Probability · Mathematics 2020-11-03 Masaaki Fujii

We study the stochastic multi-armed bandits problem in the presence of adversarial corruption. We present a new algorithm for this problem whose regret is nearly optimal, substantially improving upon previous work. Our algorithm is agnostic…

Machine Learning · Computer Science 2019-03-29 Anupam Gupta , Tomer Koren , Kunal Talwar

Predictive policing systems are increasingly used to determine how to allocate police across a city in order to best prevent crime. Discovered crime data (e.g., arrest counts) are used to help update the model, and the process is repeated.…

Computers and Society · Computer Science 2017-12-25 Danielle Ensign , Sorelle A. Friedler , Scott Neville , Carlos Scheidegger , Suresh Venkatasubramanian

Effective enforcement of laws and policies requires expending resources to prevent and detect offenders, as well as appropriate punishment schemes to deter violators. In particular, enforcement of privacy laws and policies in modern…

Computer Science and Game Theory · Computer Science 2013-03-06 Jeremiah Blocki , Nicolas Christin , Anupam Datta , Ariel D. Procaccia , Arunesh Sinha

We use an evolutionary game model to study the interplay between corporate environmental compliance and enforcement promoted by the policy maker in a country facing a pollution trap, i.e., a scenario in which the vast majority of firms do…

Physics and Society · Physics 2018-02-27 Gabriel Meyer Salomão , André Barreira da Silva Rocha

Two models are introduced to investigate graph matching in the presence of corrupt nodes. The weak model, inspired by biological networks, allows one or both networks to have a positive fraction of molecular entities interact randomly with…

Statistics Theory · Mathematics 2023-11-02 Taha Ameen , Bruce Hajek
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