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We consider the interaction among agents engaging in a driving task and we model it as general-sum game. This class of games exhibits a plurality of different equilibria posing the issue of equilibrium selection. While selecting the most…
Mean field equilibrium (MFE) has emerged as a computationally tractable solution concept for large dynamic games. However, computing MFE remains challenging due to nonlinearities and the absence of contraction properties, limiting its…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
Equilibrium in Economics has been seldom addressed in a situation where some variables are discrete. This work introduces a problem related to lot-sizing with several players, and analyses some strategies which are likely to be found in…
Strategic randomization is a key principle in game theory, yet it remains underexplored in large language models (LLMs). Prior work often conflates the cognitive decision to randomize with the mechanical generation of randomness, leading to…
In this paper, we introduce a novel equilibrium concept, called the equilibrium cycle, which seeks to capture the outcome of oscillatory game dynamics. Unlike the (pure) Nash equilibrium, which defines a fixed point of mutual best…
We add the assumption that players know their opponents' payoff functions and rationality to a model of non-equilibrium learning in signaling games. Agents are born into player roles and play against random opponents every period.…
We study the distribution of strategies in a large game that models how agents choose among different double auction markets. We classify the possible mean field Nash equilibria, which include potentially segregated states where an agent…
In a social system, the self-interest of agents can be detrimental to the collective good, sometimes leading to social dilemmas. To resolve such a conflict, a central designer may intervene by either redesigning the system or incentivizing…
Examining the behavior of multi-agent systems is vitally important to many emerging distributed applications - game theory has emerged as a powerful tool set in which to do so. The main approach of game-theoretic techniques is to model…
We develop the fictitious play algorithm in the context of the linear programming approach for mean field games of optimal stopping and mean field games with regular control and absorption. This algorithm allows to approximate the mean…
We compute equilibrium strategies in multi-stage games with continuous signal and action spaces as they are widely used in the management sciences and economics. Examples include sequential sales via auctions, multi-stage elimination…
In this paper we study a type of games regularized by the relative entropy, where the players' strategies are coupled through a random environment variable. Besides the existence and the uniqueness of equilibria of such games, we prove that…
Aligning large language models (LLMs) with human preferences is inherently multi-objective: different users and evaluation criteria impose heterogeneous and often conflicting requirements on model outputs. We propose CAGE (Common-Agency…
We study a dynamic stopping game between a principal and an agent. The agent is privately informed about his type. The principal learns about the agent's type from a noisy performance measure, which can be manipulated by the agent via a…
Strategic classification studies the problem where self-interested individuals or agents manipulate their response to obtain favorable decision outcomes made by classifiers, typically turning to dishonest actions when they are less costly…
Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and…
We study reinforcement learning (RL) for learning a Quantal Stackelberg Equilibrium (QSE) in an episodic Markov game with a leader-follower structure. In specific, at the outset of the game, the leader announces her policy to the follower…
Evolutionary game theory studies populations that change in response to an underlying game. Often, the functional form relating outcome to player attributes or strategy is complex, preventing mathematical progress. In this work, we…
Finite-player dynamic games with dispersed private information are difficult because actions both move payoffs and reshape what opponents learn, generating hierarchies of beliefs about beliefs. This paper provides a recursive representation…