Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userWeighted and Near Weighted Potential Games with Application to Game Theoretic Control
68
0
0.0
(
0
)
Added by
Daizhan Cheng Dr
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
An algorithm is proposed to verify whether a finite game is a weighted potential game (WPG) without pre-knowledge on its weights. Then the algorithm is also applied to find the closest WPG for a given finite game. The concept and criterion of near weighted potential games (NWPGs) are given, indicating the evolutionary equivalence between a finite game and its closest WPG. Based on this, a method is proposed for replacing PGs by NWPGs in game theoretic control, which improved the applicability of PG-based optimization.
rate research
Read More
This study investigates simple games. A fundamental research question in this field is to determine necessary and sufficient conditions for a simple game to be a weighted majority game. Taylor and Zwicker (1992) showed that a simple game is non-weighted if and only if there exists a trading transform of finite size. They also provided an upper bound on the size of such a trading transform, if it exists. Gvozdeva and Slinko (2011) improved that upper bound; their proof employed a property of linear inequalities demonstrated by Muroga (1971).In this study, we provide a new proof of the existence of a trading transform when a given simple game is non-weighted. Our proof employs Farkas lemma (1894), and yields an improved upper bound on the size of a trading transform. We also discuss an integer-weight representation of a weighted simple game, improving the bounds obtained by Muroga (1971). We show that our bound on the quota is tight when the number of players is less than or equal to five, based on the computational results obtained by Kurz (2012). Furthermore, we discuss the problem of finding an integer-weight representation under the assumption that we have minimal winning coalitions and maximal losing coalitions.In particular, we show a performance of a rounding method. Lastly, we address roughly weighted simple games. Gvozdeva and Slinko (2011) showed that a given simple game is not roughly weighted if and only if there exists a potent certificate of non-weightedness. We give an upper bound on the length of a potent certificate of non-weightedness. We also discuss an integer-weight representation of a roughly weighted simple game.
We study strategic games on weighted directed graphs, in which the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed non-negative integer bonus for picking a given strategy. These games capture the idea of coordination in the absence of globally common strategies. We identify natural classes of graphs for which finite improvement or coalition-improvement paths of polynomial length always exist, and, as a consequence, a (pure) Nash equlibrium or a strong equilibrium can be found in polynomial time. The considered classes of graphs are typical in network topologies: simple cycles correspond to the token ring local area networks, while open chains of simple cycles correspond to multiple independent rings topology from the recommendation G.8032v2 on the Ethernet ring protection switching. For simple cycles these results are optimal in the sense that without the imposed conditions on the weights and bonuses a Nash equilibrium may not even exist. Finally, we prove that the problem of determining the existence of a Nash equilibrium or of a strong equilibrium in these games is NP-complete already for unweighted graphs and with no bonuses assumed. This implies that the same problems for polymatrix games are strongly NP-hard.
We investigate a class of weighted voting games for which weights are randomly distributed over the standard probability simplex. We provide close-formed formulae for the expectation and density of the distribution of weight of the $k$-th largest player under the uniform distribution. We analyze the average voting power of the $k$-th largest player and its dependence on the quota, obtaining analytical and numerical results for small values of $n$ and a general theorem about the functional form of the relation between the average Penrose--Banzhaf power index and the quota for the uniform measure on the simplex. We also analyze the power of a collectivity to act (Coleman efficiency index) of random weighted voting games, obtaining analytical upper bounds therefor.
Weighted voting games (WVG) are coalitional games in which an agents contribution to a coalition is given by his it weight, and a coalition wins if its total weight meets or exceeds a given quota. These games model decision-making in political bodies as well as collaboration and surplus division in multiagent domains. The computational complexity of various solution concepts for weighted voting games received a lot of attention in recent years. In particular, Elkind et al.(2007) studied the complexity of stability-related solution concepts in WVGs, namely, of the core, the least core, and the nucleolus. While they have completely characterized the algorithmic complexity of the core and the least core, for the nucleolus they have only provided an NP-hardness result. In this paper, we solve an open problem posed by Elkind et al. by showing that the nucleolus of WVGs, and, more generally, k-vector weighted voting games with fixed k, can be computed in pseudopolynomial time, i.e., there exists an algorithm that correctly computes the nucleolus and runs in time polynomial in the number of players and the maximum weight. In doing so, we propose a general framework for computing the nucleolus, which may be applicable to a wider of class of games.
We introduce a game-theoretic approach to the study of recommendation systems with strategic content providers. Such systems should be fair and stable. Showing that traditional approaches fail to satisfy these requirements, we propose the Shapley mediator. We show that the Shapley mediator fulfills the fairness and stability requirements, runs in linear time, and is the only economically efficient mechanism satisfying these properties.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
