Related papers: Competitive Equilibrium for Chores: from Dual Eise…
This paper investigates the distributed Nash equilibrium seeking problem for two-network zero-sum games with set constraints, where the two networks have the opposite nonsmooth cost functions. The interaction of the agents in each network…
The works of (Daskalakis et al., 2009, 2022; Jin et al., 2022; Deng et al., 2023) indicate that computing Nash equilibria in multi-player Markov games is a computationally hard task. This fact raises the question of whether or not…
Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite…
We study techniques to incentivize self-interested agents to form socially desirable solutions in scenarios where they benefit from mutual coordination. Towards this end, we consider coordination games where agents have different intrinsic…
We consider the problem of fairly dividing a set of items. Much of the fair division literature assumes that the items are `goods' i.e., they yield positive utility for the agents. There is also some work where the items are `chores' that…
The Fisher market equilibrium for private goods and the Lindahl equilibrium for public goods are classic and fundamental solution concepts for market equilibria. While Fisher market equilibria have been well-studied, the theoretical…
The Frank-Wolfe algorithm is a popular method for minimizing a smooth convex function $f$ over a compact convex set $\mathcal{C}$. While many convergence results have been derived in terms of function values, hardly nothing is known about…
Market equilibria of matching markets offer an intuitive and fair solution for matching problems without money with agents who have preferences over the items. Such a matching market can be viewed as a variation of Fisher market, albeit…
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…
There has been significant recent progress in algorithms for approximation of Nash equilibrium in large two-player zero-sum imperfect-information games and exact computation of Nash equilibrium in multiplayer strategic-form games. While…
We study the fair division of indivisible goods with conflicts between pairs of goods, represented by a graph $G = (V, E)$. We consider ``soft'' conflicts: assigning two adjacent goods to the same agent is allowed, but we seek allocations…
We introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash…
We propose a novel generalization of the conditional gradient (CG / Frank-Wolfe) algorithm for minimizing a smooth function $f$ under an intersection of compact convex sets, using a first-order oracle for $\nabla f$ and linear minimization…
Online learning algorithms are widely used in strategic multi-agent settings, including repeated auctions, contract design, and pricing competitions, where agents adapt their strategies over time. A key question in such environments is how…
In this paper, we investigate a competitive market involving two agents who consider both their own wealth and the wealth gap with their opponent. Both agents can invest in a financial market consisting of a risk-free asset and a risky…
In fair division problems, we are given a set $S$ of $m$ items and a set $N$ of $n$ agents with individual preferences, and the goal is to find an allocation of items among agents so that each agent finds the allocation fair. There are…
Recent literature on computational notions of fairness has been broadly divided into two distinct camps, supporting interventions that address either individual-based or group-based fairness. Rather than privilege a single definition, we…
The leximin solution -- which selects an allocation that maximizes the minimum utility, then the second minimum utility, and so forth -- is known to provide EFX (envy-free up to any good) fairness guarantee in some contexts when allocating…
Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer(2009) that mixed-binary quadratic programs…
This paper addresses black-box smooth optimization problems, where the objective and constraint functions are not explicitly known but can be queried. The main goal of this work is to generate a sequence of feasible points converging…