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Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized…
In communication systems where users share common resources, users' selfish behavior usually results in suboptimal resource utilization. There have been extensive works that model communication systems with selfish users as one-shot games…
The distributed task allocation problem, as one of the most interesting distributed optimization challenges, has received considerable research attention recently. Previous works mainly focused on the task allocation problem in a population…
Correlated equilibrium generalizes Nash equilibrium by allowing a central coordinator to guide players' actions through shared recommendations, similar to how routing apps guide drivers. We investigate how a coordinator can learn a…
The paper studies the convergence, as $N$ tends to infinity, of a system of $N$ coupled Hamilton-Jacobi equations, the Nash system. This system arises in differential game theory. We describe the limit problem in terms of the so-called…
We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…
We quantize prisoner dilemma in presence of collective dephasing with dephasing rate $\gamma $. It is shown that for two parameters set of strategies $Q\otimes Q$ is Nash equilibrium below a cut-off value of time. Beyond this cut-off it…
In this paper, we consider the problem of minimizing a smooth function, given as finite sum of black-box functions, over a convex set. In order to advantageously exploit the structure of the problem, for instance when the terms of the…
The paper is devoted to the first-order mean field game system in the case when the distribution of players can contain atoms. The proposed definition of a generalized solution is based on the minimax approach to the Hamilton-Jacobi…
In this paper, we consider the nonlinear constrained optimization problem (NCP) with constraint set $\{x \in \mathcal{X}: c(x) = 0\}$, where $\mathcal{X}$ is a closed convex subset of $\mathbb{R}^n$. We propose an exact penalty approach,…
Game-theoretic techniques and equilibria analysis facilitate the design and verification of competitive systems. While algorithmic complexity of equilibria computation has been extensively studied, practical implementation and application…
In this paper we propose a numerical method to obtain an approximation of Nash equilibria for multi-player non-cooperative games with a special structure. We consider the infinite horizon problem in a case which leads to a system of…
We consider the problem of finding a Nash equilibrium (NE) in a general-sum game, where player $i$'s objective is $f_i(x)=f_i(x_1,...,x_n)$, with $x_j\in\mathbb{R}^{d_j}$ denoting the strategy variables of player $j$. Our focus is on…
Solution methods for generalized Nash equilibrium have been dominated by variational inequalities and complementarity problems. Since these approaches fundamentally rely on the sufficiency of first-order optimality conditions for the…
In this paper, we consider a class of $n$-person noncooperative games, where the utility function of every player is given by a homogeneous polynomial defined by the payoff tensor of that player, which is a natural extension of the bimatrix…
Cooperative games can be distinguished as non-cooperative games in which players can freely sign binding agreements to form coalitions. These coalitions inherit a joint strategy set and seek to maximize collective payoffs. When the payoffs…
The Reward-Penalty-Selection Problem (RPSP) can be seen as a combination of the Set Cover Problem (SCP) and the Hitting Set Problem (HSP). Given a set of elements, a set of reward sets, and a set of penalty sets, one tries to find a subset…
Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constraints (MPCCs). A…
Nash Equilibrium (NE) is the canonical solution concept of game theory, which provides an elegant tool to understand the rationalities. Though mixed strategy NE exists in any game with finite players and actions, computing NE in two- or…
This paper considers a time-varying game with $N$ players. Every time slot, players observe their own random events and then take a control action. The events and control actions affect the individual utilities earned by each player. The…