On the Complexity of Uniformly Mixed Nash Equilibria and Related Regular Subgraph Problems

2005 ◽  
pp. 197-208 ◽  
Author(s):  
Vincenzo Bonifaci ◽  
Ugo Di Iorio ◽  
Luigi Laura
Keyword(s):  
Nash Equilibria ◽  
Regular Subgraph

scholarly journals The complexity of uniform Nash equilibria and related regular subgraph problems

2008 ◽  
Vol 401 (1-3) ◽  
pp. 144-152 ◽  
Author(s):  
Vincenzo Bonifaci ◽  
Ugo Di Iorio ◽  
Luigi Laura
Keyword(s):  
Nash Equilibria ◽  
Regular Subgraph

A Theory of Patronized Goods: Inefficient and Efficient Equilibria

2011 ◽  
pp. 65-87 ◽  
Author(s):  
A. Rubinstein
Keyword(s):  
Nash Equilibrium ◽  
Social Policy ◽  
Nash Equilibria ◽  
Institutional Environment ◽  
Social Motivation ◽  
Pareto Optimal ◽  
Market Failures ◽  
Equilibrium Conditions ◽  
Policy Issues

The article considers some aspects of the patronized goods theory with respect to efficient and inefficient equilibria. The author analyzes specific features of patronized goods as well as their connection with market failures, and conjectures that they are related to the emergence of Pareto-inefficient Nash equilibria. The key problem is the analysis of the opportunities for transforming inefficient Nash equilibrium into Pareto-optimal Nash equilibrium for patronized goods by modifying the institutional environment. The paper analyzes social motivation for institutional modernization and equilibrium conditions in the generalized Wicksell-Lindahl model for patronized goods. The author also considers some applications of patronized goods theory to social policy issues.

Berge and Nash Equilibria in a Linear-Quadratic Differential Game

2020 ◽  
Vol 81 (11) ◽  
pp. 2108-2131
Author(s):  
V. I. Zhukovskiy ◽  
A. S. Gorbatov ◽  
K. N. Kudryavtsev
Keyword(s):  
Differential Game ◽  
Quadratic Differential ◽  
Nash Equilibria ◽  
Linear Quadratic

scholarly journals Expressiveness and Nash Equilibrium in Iterated Boolean Games

2021 ◽  
Vol 22 (2) ◽  
pp. 1-38
Author(s):  
Julian Gutierrez ◽  
Paul Harrenstein ◽  
Giuseppe Perelli ◽  
Michael Wooldridge
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Infinite Sequence ◽  
Multi Agent Systems ◽  
Temporal Logics ◽  
Agent Systems ◽  
Temporal Properties ◽  
Multi Agent ◽  
Game Theoretic ◽  
Boolean Games

We define and investigate a novel notion of expressiveness for temporal logics that is based on game theoretic equilibria of multi-agent systems. We use iterated Boolean games as our abstract model of multi-agent systems [Gutierrez et al. 2013, 2015a]. In such a game, each agent  has a goal  , represented using (a fragment of) Linear Temporal Logic ( ) . The goal  captures agent  ’s preferences, in the sense that the models of  represent system behaviours that would satisfy  . Each player controls a subset of Boolean variables , and at each round in the game, player is at liberty to choose values for variables in any way that she sees fit. Play continues for an infinite sequence of rounds, and so as players act they collectively trace out a model for , which for every player will either satisfy or fail to satisfy their goal. Players are assumed to act strategically, taking into account the goals of other players, in an attempt to bring about computations satisfying their goal. In this setting, we apply the standard game-theoretic concept of (pure) Nash equilibria. The (possibly empty) set of Nash equilibria of an iterated Boolean game can be understood as inducing a set of computations, each computation representing one way the system could evolve if players chose strategies that together constitute a Nash equilibrium. Such a set of equilibrium computations expresses a temporal property—which may or may not be expressible within a particular fragment. The new notion of expressiveness that we formally define and investigate is then as follows: What temporal properties are characterised by the Nash equilibria of games in which agent goals are expressed in specific fragments of  ? We formally define and investigate this notion of expressiveness for a range of fragments. For example, a very natural question is the following: Suppose we have an iterated Boolean game in which every goal is represented using a particular fragment of : is it then always the case that the equilibria of the game can be characterised within ? We show that this is not true in general.

Nash equilibria in electricity pool markets with large-scale wind power integration

Energy ◽  
2021 ◽  
Vol 228 ◽  
pp. 120642
Author(s):  
Evangelos G. Tsimopoulos ◽  
Michael C. Georgiadis
Keyword(s):  
Wind Power ◽  
Large Scale ◽  
Nash Equilibria ◽  
Wind Power Integration

scholarly journals The Evolution of Networks and Local Public Good Provision: A Potential Approach

Games ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 55
Author(s):  
Markus Kinateder ◽  
Luca Paolo Merlino
Keyword(s):  
Public Good ◽  
Nash Equilibria ◽  
Potential Game ◽  
Public Good Provision ◽  
Local Public Good ◽  
Steady State Distribution ◽  
State Distribution ◽  
Long Run ◽  
Split Graphs ◽  
Good Provision

In this paper, we propose a game in which each player decides with whom to establish a costly connection and how much local public good is provided when benefits are shared among neighbors. We show that, when agents are homogeneous, Nash equilibrium networks are nested split graphs. Additionally, we show that the game is a potential game, even when we introduce heterogeneity along several dimensions. Using this result, we introduce stochastic best reply dynamics and show that this admits a unique and stationary steady state distribution expressed in terms of the potential function of the game. Hence, even if the set of Nash equilibria is potentially very large, the long run predictions are sharp.

scholarly journals Nash equilibria for non-binary choice rules

2006 ◽  
Vol 35 (3) ◽  
pp. 455-464 ◽  
Author(s):  
José C. R. Alcantud ◽  
Carlos Alós-Ferrer
Keyword(s):  
Nash Equilibria ◽  
Binary Choice
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