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We introduce graphs associated to transport problems between discrete marginals, that allow to characterize the set of all optimizers given one primal optimizer. In particular, we establish that connectivity of those graphs is a necessary…
Computing approximate Nash equilibria in multi-player general-sum Markov games is a computationally intractable task. However, multi-player Markov games with certain cooperative or competitive structures might circumvent this…
The distributed computation of a Nash equilibrium in aggregative games is gaining increased traction in recent years. Of particular interest is the mediator-free scenario where individual players only access or observe the decisions of…
We consider a dynamical approach to game in extensive forms. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding…
We study the convergence to local Nash equilibria of gradient methods for two-player zero-sum differentiable games. It is well-known that such dynamics converge locally when $S \succ 0$ and may diverge when $S=0$, where $S\succeq 0$ is the…
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…
Generalized Nash equilibrium problem (GNEP) is fundamental for practical applications where multiple self-interested agents work together to make optimal decisions. In this work, we study GNEP with shared distributionally robust chance…
This paper resolves a longstanding open question pertaining to the design of near-optimal first-order algorithms for smooth and strongly-convex-strongly-concave minimax problems. Current state-of-the-art first-order algorithms find an…
We study stochastic Nash equilibrium problems with expected valued cost functions whose pseudogradient satisfies restricted monotonicity properties which hold only with respect to the solution. We propose a forward-backward algorithm and…
We present a simple primal-dual algorithm for computing approximate Nash-equilibria in two-person zero-sum sequential games with incomplete information and perfect recall (like Texas Hold'em Poker). Our algorithm is numerically stable,…
In single-agent Markov decision processes, an agent can optimize its policy based on the interaction with environment. In multi-player Markov games (MGs), however, the interaction is non-stationary due to the behaviors of other players, so…
This work considers a stochastic Nash game in which each player solves a parameterized stochastic optimization problem. In deterministic regimes, best-response schemes have been shown to be convergent under a suitable spectral property…
We propose a stochastic first-order algorithm to learn the rationality parameters of simultaneous and non-cooperative potential games, i.e., the parameters of the agents' optimization problems. Our technique combines (i.) an active-set step…
Multi-robot coordination often exhibits hierarchical structure, with some robots' decisions depending on the planned behaviors of others. While game theory provides a principled framework for such interactions, existing solvers struggle to…
In this note, we study a class of deterministic finite-horizon linear-quadratic difference games with coupled affine inequality constraints involving both state and control variables. We show that the necessary conditions for the existence…
The finitely repeated Prisoners' Dilemma is a good illustration of the discrepancy between the strategic behaviour suggested by a game-theoretic analysis and the behaviour often observed among human players, where cooperation is maintained…
Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, finding applications in diverse fields such as economics, political science, and biology. However, the Nash…
Optimization problems aim to find the optimal solution, which is becoming increasingly complex and difficult to solve. Traditional evolutionary optimization methods always overlook the granular characteristics of solution space. In the real…
In this paper, we deal with the equilibrium selection problem, which amounts to steering a population of individuals engaged in strategic game-theoretic interactions to a desired collective behavior. In the literature, this problem has been…
In this paper, we investigate distributed generalized Nash equilibrium (GNE) computation of monotone games with affine coupling constraints. Each player can only utilize its local objective function, local feasible set and a local block of…