scholarly journals Discretized Multinomial Distributions and Nash Equilibria in Anonymous Games

2008 ◽  
Author(s):  
Constantinos Daskalakis ◽  
Christos H. Papadimitriou
Keyword(s):  
Nash Equilibria ◽  
Anonymous Games

scholarly journals Strict pure strategy Nash equilibria in large finite‐player games

2021 ◽  
Vol 16 (3) ◽  
pp. 1055-1093
Author(s):  
Guilherme Carmona ◽  
Konrad Podczeck
Keyword(s):  
Nash Equilibria ◽  
Existence Result ◽  
Pure Strategy ◽  
The Other ◽  
Precise Sense ◽  
Equilibrium Distributions ◽  
Payoff Functions ◽  
Anonymous Games ◽  
Differentiability Properties

In the context of anonymous games (i.e., games where the payoff of a player is, apart from his/her own action, determined by the distribution of the actions made by the other players), we present a model in which, generically (in a precise sense), finite‐player games have strict pure strategy Nash equilibria if the number of agents is large. A key feature of our model is that payoff functions have differentiability properties. A consequence of our existence result is that, in our model, equilibrium distributions of non‐atomic games are asymptotically implementable by pure strategy Nash equilibria of large finite‐player games.

scholarly journals Multiagent Learning in Large Anonymous Games

2011 ◽  
Vol 40 ◽  
pp. 571-598 ◽  
Author(s):  
I. A. Kash ◽  
E. J. Friedman ◽  
J. Y. Halpern
Keyword(s):  
Nash Equilibria ◽  
Learning Algorithms ◽  
Efficient Algorithms ◽  
Statistical Information ◽  
Multiagent Learning ◽  
Alternative Approach ◽  
Agent Learning ◽  
Multi Agent ◽  
Large Systems ◽  
Anonymous Games

In large systems, it is important for agents to learn to act effectively, but sophisticated multi-agent learning algorithms generally do not scale. An alternative approach is to find restricted classes of games where simple, efficient algorithms converge. It is shown that stage learning efficiently converges to Nash equilibria in large anonymous games if best-reply dynamics converge. Two features are identified that improve convergence. First, rather than making learning more difficult, more agents are actually beneficial in many settings. Second, providing agents with statistical information about the behavior of others can significantly reduce the number of observations needed.

scholarly journals Approximate Nash equilibria in anonymous games

2015 ◽  
Vol 156 ◽  
pp. 207-245 ◽  
Author(s):  
Constantinos Daskalakis ◽  
Christos H. Papadimitriou
Keyword(s):  
Nash Equilibria ◽  
Approximate Nash Equilibria ◽  
Anonymous Games

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.

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