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For time inconsistent optimal control problems, a quite popular approach is the equilibrium approach, taken by the sophisticated agents. In this short note we construct a deterministic continuous time example where the unique equilibrium is…
As part of an effort to apply the rigorous guarantees of formal verification to multi-agent systems, the field of equilibrium analysis, also called rational verification, studies equilibria in multiplayer games to reason about system-level…
One of the contributions of this work is to formulate the problem of energy-efficient power control in multiple access channels (namely, channels which comprise several transmitters and one receiver) as a stochastic differential game. The…
Time optimal control problems for some non-smooth systems in general form are considered. The non-smoothness is caused by singularity. It is proved that Pontryagin's maximum principle holds for at least one optimal relaxed control. Thus,…
We study repeated games where players use an exponential learning scheme in order to adapt to an ever-changing environment. If the game's payoffs are subject to random perturbations, this scheme leads to a new stochastic version of the…
This paper studies the problem of output agreement in networks of nonlinear dynamical systems under time-varying disturbances. Necessary and sufficient conditions for output agreement are derived for the class of incrementally passive…
In this paper we focus on noncooperative games with uncertain constraints coupling the agents' decisions. We consider a setting where bounded deviations of agents' decisions from the equilibrium are possible, and uncertain constraints are…
We provide a thorough study of a general class of linear-quadratic extended mean field games and control problems in any dimensions where the mean field terms are allowed to be unbounded and there are also presence of cross terms in the…
We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players…
Static potential games are non-cooperative games which admit a fictitious function, also referred to as a potential function, such that the minimizers of this function constitute a subset (or a refinement) of the Nash equilibrium strategies…
Nonzero sum games typically have multiple Nash equilibriums (or no equilibrium), and unlike the zero sum case, they may have different values at different equilibriums. Instead of focusing on the existence of individual equilibriums, we…
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…
According to recent results, convergence in a prespecified or prescribed finite time can be achieved under extreme model uncertainty if control is applied continuously over time. This paper shows that this extreme amount of uncertainty…
We study the problem of characterizing the set of games that are consistent with observed equilibrium play. Our contribution is to develop and analyze a new methodology based on convex optimization to address this problem for many classes…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
This paper investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
In this paper, we investigate constrained control of continuous-time linear stochastic systems. We show that for certain system parameter settings, constrained control policies can never achieve stabilization. Specifically, we explore a…
In repeated-game applications where both the collusive and non-collusive outcomes can be supported as equilibria, researchers must resolve underlying selection questions if theory will be used to understand counterfactual policies. One…
We study a two-player nonzero-sum stochastic differential game where one player controls the state variable via additive impulses while the other player can stop the game at any time. The main goal of this work is characterize Nash…