scholarly journals Nash blocks

2021 ◽  
Author(s):  
Peter Wikman
Keyword(s):  
Nash Equilibria ◽  
Consideration Set ◽  
Essential Component ◽  
Link Type ◽  
Large Populations ◽  
Pure Strategies ◽  
Science Article

AbstractA product set of pure strategies is a Nash block if it contains all best replies to the Nash equilibria of the game in which the players are restricted to the strategies in the block. This defines an intermediate block property, between curb (Basu and Weibull, Econ Lett 36(2):141–146, 10.1016/0165-1765(91)90179-O, http://www.sciencedirect.com/science/article/pii/016517659190179O, 1991) and coarse tenability (Myerson and Weibull (2015) Econometrica 83(3):943–976, 10.3982/ECTA11048). While the new concept is defined without reference to the consideration-set framework that defines tenability, the framework can be used to characterize Nash blocks in terms of potential conventions when large populations of individuals recurrently interact. Although weaker than curb, Nash blocks nevertheless maintain several robustness properties of curb sets. For example, every Nash block contains an essential component and is robust against payoff perturbations.

Exponential Families and Game Dynamics

1982 ◽  
Vol 34 (2) ◽  
pp. 374-405 ◽  
Author(s):  
Ethan Akin
Keyword(s):  
Game Theory ◽  
Evolutionary Game ◽  
Payoff Matrix ◽  
Exponential Families ◽  
Von Neumann ◽  
Rational Player ◽  
Large Populations ◽  
Pure Strategies ◽  
Classical Game ◽  
Classical Game Theory

A symmetric game consists of a set of pure strategies indexed by {0, …, n} and a real payoff matrix (aij). When two players choose strategies i and j the payoffs are aij and aji to the i-player and j-player respectively. In classical game theory of Von Neumann and Morgenstern [16] the payoffs are measured in units of utility, i.e., desirability, or in units of some desirable good, e.g. money. The problem of game theory is that of a rational player who seeks to choose a strategy or mixture of strategies which will maximize his return. In evolutionary game theory of Maynard Smith and Price [13] we look at large populations of game players. Each player's opponents are selected randomly from the population, and no information about the opponent is available to the player. For each one the choice of strategy is a fixed inherited characteristic.

scholarly journals THE EMERGENCE OF MONEY: A DYNAMIC ANALYSIS

2017 ◽  
Vol 23 (07) ◽  
pp. 2573-2596 ◽  
Author(s):  
Maurizio Iacopetta
Keyword(s):  
Dynamic Analysis ◽  
Nash Equilibria ◽  
Commodity Money ◽  
Novel Method ◽  
Pure Strategies ◽  
Dynamic Equilibria ◽  
Selection Of

This paper studies the role of liquidity in triggering the emergence of money in a Kiyotaki-Wright economy. A novel method computes the dynamic Nash equilibria of the economy by setting up an iteration of the agents' profile of (pure) strategies and of the distribution of commodities across agents. The analysis shows that the evolving state of liquidity can spark the acceptance of a high-cost-storage commodity as money or cause the disappearance of a commodity money. It also reveals the existence of multiple dynamic equilibria with pure strategies. Several simulations clarify how history and the coordination of beliefs matter for the selection of a particular equilibrium.

Nash Equilibria in Pure Strategies

2003 ◽  
Vol 55 (3) ◽  
pp. 311-317 ◽  
Author(s):  
Abderrahmane Ziad
Keyword(s):  
Nash Equilibria ◽  
Pure Strategies

An Improved Quasi-Polynomial Algorithm for Approximate Well-Supported Nash Equilibria

2019 ◽  
Vol 33 ◽  
pp. 1926-1932
Author(s):  
Michail Fasoulakis ◽  
Evangelos Markakis
Keyword(s):  
Nash Equilibrium ◽  
Polynomial Time ◽  
Nash Equilibria ◽  
Polynomial Algorithm ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Bimatrix Games ◽  
Approximate Nash Equilibria ◽  
Pure Strategies ◽  
Approximation Parameter

We focus on the problem of computing approximate Nash equilibria in bimatrix games. In particular, we consider the notion of approximate well-supported equilibria, which is one of the standard approaches for approximating equilibria. It is already known that one can compute an ε-well-supported Nash equilibrium in time nO (log n/ε2), for any ε > 0, in games with n pure strategies per player. Such a running time is referred to as quasi-polynomial. Regarding faster algorithms, it has remained an open problem for many years if we can have better running times for small values of the approximation parameter, and it is only known that we can compute in polynomial-time a 0.6528-well-supported Nash equilibrium. In this paper, we investigate further this question and propose a much better quasi-polynomial time algorithm that computes a (1/2 + ε)-well-supported Nash equilibrium in time nO(log logn1/ε/ε2), for any ε > 0. Our algorithm is based on appropriately combining sampling arguments, support enumeration, and solutions to systems of linear inequalities.

scholarly journals An Analysis of the Replicator Dynamics for an Asymmetric Hawk-Dove Game

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Ikjyot Singh Kohli ◽  
Michael C. Haslam
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Nash Equilibria ◽  
Systems Approach ◽  
Replicator Dynamics ◽  
Equilibrium Points ◽  
Detailed Account ◽  
Full Account ◽  
Local Bifurcations ◽  
Pure Strategies

We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. We give a full account of the equilibrium points and their stability and derive the Nash equilibria. We also give a detailed account of the local bifurcations that the system exhibits based on choices of the typical Hawk-Dove parameters v and c. We also give details on the connections between the results found in this work and those of the standard two-strategy Hawk-Dove game. We conclude the paper with some examples of numerical simulations that further illustrate some global behaviours of the system.

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