Related papers: Does bilevel optimization result in more competiti…

The study of games and their equilibria is central to developing insights for understanding many socio-economic phenomena. Here we present a dynamical systems view of the equilibria of two-person, payoff-symmetric games. In particular,…

Electric endurance racing is characterized by severe energy constraints and strong aerodynamic interactions. Determining race-winning policies therefore becomes a fundamentally multi-agent, game-theoretic problem. These policies must…

We introduce an atomic congestion game with two types of agents, cars and trucks, to model the traffic flow on a road over various time intervals of the day. Cars maximize their utility by finding a trade-off between the time they choose to…

We study connections between optimistic bilevel programming problems and Generalized Nash Equilibrium Problems (GNEP)s. We remark that, when addressing bilevel problems, we consider the general case in which the lower level program is not…

We introduce and study incentive equilibria for multi-player meanpayoff games. Incentive equilibria generalise well-studied solution concepts such as Nash equilibria and leader equilibria (also known as Stackelberg equilibria). Recall that…

Much work in AI deals with the selection of proper actions in a given (known or unknown) environment. However, the way to select a proper action when facing other agents is quite unclear. Most work in AI adopts classical game-theoretic…

We study optimal equilibria in multi-player games. An equilibrium is optimal for a player, if her payoff is maximal. A tempting approach to solving this problem is to seek optimal Nash equilibria, the standard form of equilibria where no…

We construct Nash equilibria in feedback form for a class of two-person stochastic games of singular control with absorption, arising from a stylized model for corporate finance. More precisely, the paper focusses on a strategic dynamic…

This paper presents an optimization framework to model Formula 1 racing dynamics, where multiple cars interact physically and strategically. Aerodynamic wake effects, trajectory optimization, and energy management are integrated by means of…

Trajectory planning for autonomous race cars poses special challenges due to the highly interactive and competitive environment. Prior work has applied game theory as it provides equilibria for such non-cooperative dynamic problems. This…

In this article, we revisit a communication-control co-design problem for a class of two-player stochastic differential games on an infinite horizon. Each 'player' represents two active decision makers, namely a scheduler and a remote…

Solution methods for generalized Nash equilibrium have been dominated by variational inequalities and complementarity problems. Since these approaches fundamentally rely on the sufficiency of first-order optimality conditions for the…

To regulate a social system comprised of self-interested agents, economic incentives are often required to induce a desirable outcome. This incentive design problem naturally possesses a bilevel structure, in which a designer modifies the…

Cooperatively planning for multiple agents has been proposed as a promising method for strategic and motion planning for automated vehicles. By taking into account the intent of every agent, the ego agent can incorporate future interactions…

Nash equilibrium is a solution concept in non-strictly competitive, non-cooperative game theory that finds applications in various scientific and engineering disciplines. A non-strictly competitive, non-cooperative game model is presented…

Autonomous driving has a natural bi-level structure. The goal of the upper behavioural layer is to provide appropriate lane change, speeding up, and braking decisions to optimize a given driving task. However, this layer can only indirectly…

Motivated by the increasing attention to overall social benefits in networked multi-agent systems, this paper investigates an optimization problem building on noncooperative games under high-level regulation, which can be formulated in a…

Game theory is a very profound study on distributed decision-making behavior and has been extensively developed by many scholars. However, many existing works rely on certain strict assumptions such as knowing the opponent's private…

Reinforcement learning from self-play has recently reported many successes. Self-play, where the agents compete with themselves, is often used to generate training data for iterative policy improvement. In previous work, heuristic rules are…

We study noncooperative games, in which each player's objective is composed of a sequence of ordered- and potentially conflicting-preferences. Problems of this type naturally model a wide variety of scenarios: for example, drivers at a busy…