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In this work, we study a class of stationary mean-field games of singular stochastic control under model uncertainty. The representative agent adjusts the dynamics of an It\^o diffusion via one-sided singular stochastic control, aiming to…
The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…
Optimal behavior in (competitive) situation is traditionally determined with the help of utility functions that measure the payoff of different actions. Given an ordering on the space of revenues (payoffs), the classical axiomatic approach…
Here we present a ground-breaking new postulate for game theory. The first part of this postulate contains the axiomatic observation that all games are created by a designer, whether they are: e.g., (dynamic/static) or…
Dynamic game theory is an increasingly popular tool for modeling multi-agent, e.g. human-robot, interactions. Game-theoretic models presume that each agent wishes to minimize a private cost function that depends on others' actions. These…
This research investigates the impact of dynamic, time-varying interactions on cooperative behaviour in social dilemmas. Traditional research has focused on deterministic rules governing pairwise interactions, yet the impact of interaction…
In the paper, we use the equivalent formulation of a finite state mean field game as a control problem with mixed constraints to study the dependence of solutions to finite state mean field game on an initial distribution of players. We…
The actions of an autonomous vehicle on the road affect and are affected by those of other drivers, whether overtaking, negotiating a merge, or avoiding an accident. This mutual dependence, best captured by dynamic game theory, creates a…
This brief discusses evolutionary game theory as a powerful and unified mathematical tool to study evolution of collective behaviours. It summarises some of my recent research directions using evolutionary game theory methods, which include…
Von Neumann founded both game theory and the theory of self-reproducing automata, but the two programs never merged. This paper provides the synthesis. The Theory of Strategic Evolution analyzes strategic replicators: entities that optimize…
Causality and game theory are two influential fields that contribute significantly to decision-making in various domains. Causality defines and models causal relationships in complex policy problems, while game theory provides insights into…
Trajectory planning involving multi-agent interactions has been a long-standing challenge in the field of robotics, primarily burdened by the inherent yet intricate interactions among agents. While game-theoretic methods are widely…
Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination…
We introduce a new paradigm for game theory -- Bayesian satisfaction. This novel approach is a synthesis of the idea of Bayesian rationality introduced by Aumann, and satisfaction games. The concept of Bayesian rationality for which, in…
The timing of strategic exit is one of the most important but difficult business decisions, especially under competition and uncertainty. Motivated by this problem, we examine a stochastic game of exit in which players are uncertain about…
Self-determination theory (SDT), a psychological theory of human motivation, is a prominent paradigm in human-computer interaction (HCI) research on games. However, our prior literature review observed a trend towards shallow applications…
The majority game, modelling a system of heterogeneous agents trying to behave in a similar way, is introduced and studied using methods of statistical mechanics. The stationary states of the game are given by the (local) minima of a…
Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural…
Game theory ideas provide a useful framework for studying evolutionary dynamics in a well-mixed environment. This approach, however, typically enforces a strictly fixed overall population size, deemphasizing natural growth processes. We…
We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become…