The Computation of Approximate Generalized Feedback Nash Equilibria
نویسندگان
چکیده
We present the concept of a generalized feedback Nash equilibrium (GFNE) in dynamic games, extending to games which players are subject state and input constraints. formalize necessary sufficient conditions for (local) GFNE solutions at trajectory level, enable development efficient numerical methods their computation. Specifically, we propose Newton-style method finding game trajectories satisfy an equilibrium, can then be checked against sufficiency conditions. show that evaluation general requires computing series nested, implicitly defined derivatives, quickly becomes intractable. To this end, introduce approximation is amenable and, turn, computation solutions. call approximate quasi-Nash equilibria, In particular, develop sequential linear-quadratic (LQ) approach, LQ local solved each iteration. The relies on ability compute inequality- equality-constrained therefore specific solution these special cases developed detail. demonstrate effectiveness proposed approach arising autonomous driving application.
منابع مشابه
Multi-player Approximate Nash Equilibria
In this paper we study the complexity of finding approximate Nash equilibria in multi-player normal-form games. First, for any constant number n, we present a polynomial-time algorithm for computing a relative ( 1− 1 1+(n−1)n ) -Nash equilibrium in arbitrary nplayer games and a relative ( 1− 1 1+(n−1)n−1 ) -Nash equilibrium in symmetric n-player games. Next, we show that there is an additive ε-...
متن کاملApproximate Nash Equilibria via Sampling
We prove that in a normal form n-player game with m actions for each player, there exists an approximate Nash equilibrium where each player randomizes uniformly among a set of O(logm+log n) pure strategies. This result induces an N log logN algorithm for computing an approximate Nash equilibrium in games where the number of actions is polynomial in the number of players (m = poly(n)), where N =...
متن کاملAn Optimization Approach for Approximate Nash Equilibria
In this paper we propose a new methodology for determining approximate Nash equilibria of non-cooperative bimatrix games and, based on that, we provide an efficient algorithm that computes 0.3393-approximate equilibria, the best approximation till now. The methodology is based on the formulation of an appropriate function of pairs of mixed strategies reflecting the maximum deviation of the play...
متن کاملA Note on Approximate Nash Equilibria
In view of the intractability of finding a Nash equilibrium, it is important to understand the limits of approximation in this context. A subexponential approximation scheme is known [LMM03], and no approximation better than 1 4 is possible by any algorithm that examines equilibria involving fewer than logn strategies [Alt94]. We give a simple, linear-time algorithm examining just two strategie...
متن کاملApproximate Plutocratic and Egalitarian Nash Equilibria
We pose the problem of computing approximate Nash equilibria in bimatrix games with two simultaneous criteria of optimization: minimization of the incentives to deviate from a strategy profile and maximization of a measure of quality of the strategy profile. We consider two natural measures of quality: the maximum and the minimum of the payoffs of the two players. Maximizing the former yields p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Siam Journal on Optimization
سال: 2023
ISSN: ['1095-7189', '1052-6234']
DOI: https://doi.org/10.1137/21m142530x