arXiv subjects

Giulio Salizzoni

Publications and source records attributed to Giulio Salizzoni.

6 recordsLinked to original sources

arXiv2026

Refundable Deposits: How to Restore Cooperation in Finitely Repeated Games

While infinitely repeated games admit a rich set of Nash equilibria, finitely repeated games typically have a much smaller and often inefficient one. We show how to enlarge this set using deposits: in each period a player may place a refundable sum with a neutral intermediary, returned when the game ends and forfeited following a deviation. Paying these deposits is voluntary and incentive compatible at every stage, so no commitment by the players is assumed, the only commitment required being that of the intermediary to a refund rule fixed before play begins. The mechanism sustains payoff profiles more efficient than those of the standard equilibria, without altering the underlying game and without transfers between players. We demonstrate it on the prisoner's dilemma, a congestion game, and a public goods game, all settings where cooperation cannot emerge in the standard finitely repeated version. We also apply it to a dynamic common-pool resource, suggesting that the construction extends beyond repeated stage-games.

cs.GT↗

arXiv2025

On Linear Quadratic Potential Games

Our paper addresses characterizing conditions for a linear quadratic (LQ) game to be a potential game. The desired properties of potential games in finite action settings, such as convergence of learning dynamics to Nash equilibria, and the challenges of learning Nash equilibria in continuous state and action settings motivate us to characterize LQ potential games. Our first contribution is to show that the set of LQ games with full-state feedback that are potential games is very limited, essentially differing only slightly from an identical interest game. Given this finding, we restrict the class of LQ games to those with decoupled dynamics and decoupled state information structure. For this subclass, we show that the set of potential games strictly includes non-identical interest games and characterize conditions for the LQ games in this subclass to be potential. We further derive their corresponding potential function and prove the existence of a Nash equilibrium. Meanwhile, we highlight the challenges in the characterization and computation of Nash equilibrium for this class of potential LQ games.

math.OC↗

arXiv2025

Bridging Finite and Infinite-Horizon Nash Equilibria in Linear Quadratic Games

Finite-horizon linear quadratic (LQ) games admit a unique Nash equilibrium, while infinite-horizon settings may have multiple. We clarify the relationship between these two cases by interpreting the finite-horizon equilibrium as a nonlinear dynamical system. Within this framework, we prove that its fixed points are exactly the infinite-horizon equilibria and that any such equilibrium can be recovered by an appropriate choice of terminal costs. We further show that periodic orbits of the dynamical system, when they arise, correspond to periodic Nash equilibria, and we provide numerical evidence of convergence to such cycles. Finally, simulations reveal three asymptotic regimes: convergence to stationary equilibria, convergence to periodic equilibria, and bounded non-convergent trajectories. These findings offer new insights and tools for tuning finite-horizon LQ games using infinite-horizon.

cs.MA↗

arXiv2025

Chance-constrained Linear Quadratic Gaussian Games for Multi-robot Interaction under Uncertainty

We address safe multi-robot interaction under uncertainty. In particular, we formulate a chance-constrained linear quadratic Gaussian game with coupling constraints and system uncertainties. We find a tractable reformulation of the game and propose a dual ascent algorithm. We prove that the algorithm converges to a feedback generalized Nash equilibrium of the reformulated game, ensuring the satisfaction of the chance constraints. We test our method in driving simulations and real-world robot experiments. Our method ensures safety under uncertainty and generates less conservative trajectories than single-agent model predictive control.

cs.RO↗

arXiv2025

Nash equilibria in scalar discrete-time linear quadratic games

An open problem in linear quadratic (LQ) games has been characterizing the Nash equilibria. This problem has renewed relevance given the surge of work on understanding the convergence of learning algorithms in dynamic games. This paper investigates scalar discrete-time infinite-horizon LQ games with two agents. Even in this arguably simple setting, there are no results for finding $\textit{all}$ Nash equilibria. By analyzing the best response map, we formulate a polynomial system of equations characterizing the linear feedback Nash equilibria. This enables us to bring in tools from algebraic geometry, particularly the Gröbner basis, to study the roots of this polynomial system. Consequently, we can not only compute all Nash equilibria numerically, but we can also characterize their number with explicit conditions. For instance, we prove that the LQ games under consideration admit at most three Nash equilibria. We further provide sufficient conditions for the existence of at most two Nash equilibria and sufficient conditions for the uniqueness of the Nash equilibrium. Our numerical experiments demonstrate the tightness of our bounds and showcase the increased complexity in settings with more than two agents.

cs.GT↗

arXiv2024

A Policy Iteration Algorithm for N-player General-Sum Linear Quadratic Dynamic Games

We present a policy iteration algorithm for the infinite-horizon N-player general-sum deterministic linear quadratic dynamic games and compare it to policy gradient methods. We demonstrate that the proposed policy iteration algorithm is distinct from the Gauss-Newton policy gradient method in the N-player game setting, in contrast to the single-player setting where under suitable choice of step size they are equivalent. We illustrate in numerical experiments that the convergence rate of the proposed policy iteration algorithm significantly surpasses that of the Gauss-Newton policy gradient method and other policy gradient variations. Furthermore, our numerical results indicate that, compared to policy gradient methods, the convergence performance of the proposed policy iteration algorithm is less sensitive to the initial policy and changes in the number of players.

math.OC↗