Nash Equilibrium Seeking for Quadratic Games and Applications to Oligopoly Markets and Vehicle Deployment

2012 ◽  
pp. 161-179
Author(s):  
Shu-Jun Liu ◽  
Miroslav Krstic
Keyword(s):  
Nash Equilibrium ◽  
Oligopoly Markets

BERGE–ZHUKOVSKII EQUILIBRIA: EXISTENCE AND CHARACTERIZATION

2014 ◽  
Vol 16 (04) ◽  
pp. 1450012 ◽  
Author(s):  
RABIA NESSAH ◽  
MOUSSA LARBANI
Keyword(s):  
Nash Equilibrium ◽  
Normal Form ◽  
The Other ◽  
Environmental Externalities ◽  
Normal Form Games ◽  
Oligopoly Markets

In this paper, we investigate the existence of Berge–Zhukovskii equilibrium in general normal form games. We characterize its existence via the existence of a symmetric Nash equilibrium of some n-person subgame derived of the initial game. The significance of the obtained results is illustrated by two applications. One in economy with environmental externalities and the other in oligopoly markets.

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.

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.

Stackelberg-Nash equilibrium and quasi harmonic games

2021 ◽  
Author(s):  
Lina Mallozzi ◽  
Armando Sacco
Keyword(s):  
Nash Equilibrium

scholarly journals Economic Analysis of Accident Law: A New Liability Rule that Induces Socially Optimal Behaviour in Case of Limited Information

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Astha Srivastava ◽  
Ankur Srivastava
Keyword(s):  
Nash Equilibrium ◽  
Economic Analysis ◽  
Standard Of Care ◽  
Limited Information ◽  
Liability Rule ◽  
Rule Based ◽  
Liability Rules ◽  
Levels Of Care ◽  
Unique Nash Equilibrium ◽  
Optimal Behaviour

AbstractIn accident law, we seek a liability rule that will induce both the parties to adopt socially optimal levels of precaution. Economic analysis, however, shows that none of the commonly used liability rules induce both parties to adopt optimal levels, if courts have access only to ‘Limited Information’ on. In such a case, it has also been established (K. (2006). Efficiency of liability rules: a reconsideration. J. Int. Trade Econ. Dev. 15: 359–373) that no liability rule based on cost justified untaken precaution as a standard of care can be efficient. In this paper, we describe a two-step liability rule: the rule of negligence with the defence of relative negligence. We prove that this rule has a unique Nash equilibrium at socially optimal levels of care for the non-cooperative game, and therefore induces both parties to adopt socially optimal behaviour even in case of limited information.

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