Related papers: Teamwise Mean Field Competitions
In the paper we present a model of discrete-time mean-field game with several populations of players. Mean-field games with multiple populations of the players have only been studied in the literature in the continuous-time setting. The…
Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We…
We consider a symmetric $n$-player nonzero-sum stochastic differential game with controlled jumps and mean-field type interaction among the players. Each player minimizes some expected cost by affecting the drift as well as the jump part of…
This work studies the behaviors of two large-population teams competing in a discrete environment. The team-level interactions are modeled as a zero-sum game while the agent dynamics within each team is formulated as a collaborative…
We propose a mean field game (MFG) framework to model the evolution of renewable energy production in competitive electricity markets. Producers interact through the spot price while optimising their profits under production, installation,…
Mean field Master equations for the norm game are investigated. The strategies are: to obey the norm or not and to punish those who break it or not. The punishment, the temptation, the punishment cost and the relaxation of vengeance are…
Information sharing between individuals is crucial to improve performance in collective tasks. However, in a competitive world, individuals may be reluctant to share information with the others, and it is still unclear how the presence of…
We consider mean-field control problems in discrete time with discounted reward, infinite time horizon and compact state and action space. The existence of optimal policies is shown and the limiting mean-field problem is derived when the…
We present ten different strength-based statistical models that we use to model soccer match outcomes with the aim of producing a new ranking. The models are of four main types: Thurstone-Mosteller, Bradley-Terry, Independent Poisson and…
We explore a broad class of values for cooperative games in characteristic function form, known as \emph{compromise values\/}. These values efficiently allocate payoffs by linearly combining well-specified upper and lower bounds on payoffs.…
An open problem in evolutionary game dynamics is to understand the effect of peer pressure on cooperation in a quantitative manner. Peer pressure can be modeled by punishment, which has been proved to be an effective mechanism to sustain…
This paper studies the mean field game (MFG) problem arising from a large population competition in fund management, featuring a new type of relative performance via the benchmark tracking. In the $n$-player model, each agent aims to…
This paper develops a linear programming approach for mean field games with reflected jump-diffusion dynamics. We first prove the equivalence between the mean field equilibria in the linear programming formulation and those in the weak…
This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…
Graph games provide the foundation for modeling and synthesis of reactive processes. Such games are played over graphs where the vertices are controlled by two adversarial players. We consider graph games where the objective of the first…
This paper contributes to the compactification approach to study mean-field control problems with Poissonian common noise. To overcome the lack of compactness and continuity issues caused by common noise, we exploit the point process…
We study a setting in which a principal selects an agent to execute a collection of tasks according to a specified priority sequence. Agents, however, have their own individual priority sequences according to which they wish to execute the…
Multi-round competitions often double or triple the points awarded in the final round, calling it a bonus, to maximize spectators' excitement. In a two-player competition with $n$ rounds, we aim to derive the optimal bonus size to maximize…
Teamwork is vital in many settings, and it is socially beneficial for teams to cooperate in some situations (``good games'') and not in others (``bad games;'' e.g., those that allow for corruption). A team's cooperation in any given game…
The paper proposes a natural measure space of zero-sum perfect information games with upper semicontinuous payoffs. Each game is specified by the game tree, and by the assignment of the active player and of the capacity to each node of the…