اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCorrelated Equilibria in Wireless Power Control Games
197
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper, we consider the problem of wireless power control in an interference channel where transmitters aim to maximize their own benefit. When the individual payoff or utility function is derived from the transmission efficiency and the spent power, previous works typically study the Nash equilibrium of the resulting power control game. We propose to introduce concepts of correlated and communication equilibria from game theory to find efficient solutions (compared to the Nash equilibrium) for this problem. Communication and correlated equilibria are analyzed for the power control game, and we provide algorithms that can achieve these equilibria. Simulation results demonstrate that the correlation is beneficial under some settings, and the players achieve better payoffs.
قيم البحث
اقرأ أيضاً
We investigate the computation of equilibria in extensive-form games where ex ante correlation is possible, focusing on correlated equilibria requiring the least amount of communication between the players and the mediator. Motivated by the hardness
results on the computation of normal-form correlated equilibria, we introduce the notion of normal-form coarse correlated equilibrium, extending the definition of coarse correlated equilibrium to sequential games. We show that, in two-player games without chance moves, an optimal (e.g., social welfare maximizing) normal-form coarse correlated equilibrium can be computed in polynomial time, and that in general multi-player games (including two-player games with Chance), the problem is NP-hard. For the former case, we provide a polynomial-time algorithm based on the ellipsoid method and also propose a more practical one, which can be efficiently applied to problems of considerable size. Then, we discuss how our algorithm can be extended to games with Chance and games with more than two players.
Despite the many recent practical and theoretical breakthroughs in computational game theory, equilibrium finding in extensive-form team games remains a significant challenge. While NP-hard in the worst case, there are provably efficient algorithms f
or certain families of team game. In particular, if the game has common external information, also known as A-loss recall -- informally, actions played by non-team members (i.e., the opposing team or nature) are either unknown to the entire team, or common knowledge within the team -- then polynomial-time algorithms exist (Kaneko and Kline, 1995). In this paper, we devise a completely new algorithm for solving team games. It uses a tree decomposition of the constraint system representing each teams strategy to reduce the number and degree of constraints required for correctness (tightness of the mathematical program). Our algorithm reduces the problem of solving team games to a linear program with at most $NW^{w+O(1)}$ nonzero entries in the constraint matrix, where $N$ is the size of the game tree, $w$ is a parameter that depends on the amount of uncommon external information, and $W$ is the treewidth of the tree decomposition. In public-action games, our program size is bounded by the tighter $tilde O(3^t 2^{t(n-1)}NW)$ for teams of $n$ players with $t$ types each. Since our algorithm describes the polytope of correlated strategies directly, we get equilibrium finding in correlated strategies for free -- instead of, say, having to run a double oracle algorithm. We show via experiments on a standard suite of games that our algorithm achieves state-of-the-art performance on all benchmark game classes except one. We also present, to our knowledge, the first experiments for this setting where more than one team has more than one member.
We consider polymatrix coordination games with individual preferences where every player corresponds to a node in a graph who plays with each neighbor a separate bimatrix game with non-negative symmetric payoffs. In this paper, we study $alpha$-appro
ximate $k$-equilibria of these games, i.e., outcomes where no group of at most $k$ players can deviate such that each member increases his payoff by at least a factor $alpha$. We prove that for $alpha ge 2$ these games have the finite coalitional improvement property (and thus $alpha$-approximate $k$-equilibria exist), while for $alpha < 2$ this property does not hold. Further, we derive an almost tight bound of $2alpha(n-1)/(k-1)$ on the price of anarchy, where $n$ is the number of players; in particular, it scales from unbounded for pure Nash equilibria ($k = 1)$ to $2alpha$ for strong equilibria ($k = n$). We also settle the complexity of several problems related to the verification and existence of these equilibria. Finally, we investigate natural means to reduce the inefficiency of Nash equilibria. Most promisingly, we show that by fixing the strategies of $k$ players the price of anarchy can be reduced to $n/k$ (and this bound is tight).
We propose a simple uncertainty modification for the agent model in normal-form games; at any given strategy profile, the agent can access only a set of possible profiles that are within a certain distance from the actual action profile. We investiga
te the various instantiations in which the agent chooses her strategy using well-known rationales e.g., considering the worst case, or trying to minimize the regret, to cope with such uncertainty. Any such modification in the behavioral model naturally induces a corresponding notion of equilibrium; a distance-based equilibrium. We characterize the relationships between the various equilibria, and also their connections to well-known existing solution concepts such as Trembling-hand perfection. Furthermore, we deliver existence results, and show that for some class of games, such solution concepts can actually lead to better outcomes.
We study the problem of checking for the existence of constrained pure Nash equilibria in a subclass of polymatrix games defined on weighted directed graphs. The payoff of a player is defined as the sum of nonnegative rational weights on incoming edg
es from players who picked the same strategy augmented by a fixed integer bonus for picking a given strategy. These games capture the idea of coordination within a local neighbourhood in the absence of globally common strategies. We study the decision problem of checking whether a given set of strategy choices for a subset of the players is consistent with some pure Nash equilibrium or, alternatively, with all pure Nash equilibria. We identify the most natural tractable cases and show NP or coNP-completness of these problems already for unweighted DAGs.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
