scholarly journals Evolutionary Network Games: Equilibria from Imitation and Best Response Dynamics

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Giulio Cimini
Keyword(s):  
Large Scale ◽  
Nash Equilibria ◽  
Evolutionary Dynamics ◽  
Mean Field ◽  
Coordination Games ◽  
Coordination Game ◽  
Strategic Substitutes ◽  
Response Dynamics ◽  
Scale Free ◽  
Best Response

We consider games of strategic substitutes and complements on networks and introduce two evolutionary dynamics in order to refine their multiplicity of equilibria. Within mean field, we find that for the best-shot game, taken as a representative example of strategic substitutes, replicator-like dynamics does not lead to Nash equilibria, whereas it leads to a unique equilibrium for complements, represented by a coordination game. On the other hand, when the dynamics becomes more cognitively demanding, predictions are always Nash equilibria: for the best-shot game we find a reduced set of equilibria with a definite value of the fraction of contributors, whereas, for the coordination game, symmetric equilibria arise only for low or high initial fractions of cooperators. We further extend our study by considering complex topologies through heterogeneous mean field and show that the nature of the selected equilibria does not change for the best-shot game. However, for coordination games, we reveal an important difference: on infinitely large scale-free networks, cooperative equilibria arise for any value of the incentive to cooperate. Our analytical results are confirmed by numerical simulations and open the question of whether there can be dynamics that consistently leads to stringent equilibria refinements for both classes of games.

scholarly journals Large-Scale Dynamics of Mean-Field Games Driven by Local Nash Equilibria

2013 ◽  
Vol 24 (1) ◽  
pp. 93-115 ◽  
Author(s):  
Pierre Degond ◽  
Jian-Guo Liu ◽  
Christian Ringhofer
Keyword(s):  
Large Scale ◽  
Nash Equilibria ◽  
Mean Field ◽  
Mean Field Games

ANTI-COORDINATION GAMES AND DYNAMIC STABILITY

2007 ◽  
Vol 09 (04) ◽  
pp. 667-688 ◽  
Author(s):  
FUHITO KOJIMA ◽  
SATORU TAKAHASHI
Keyword(s):  
Dynamic Stability ◽  
Mixed Strategy ◽  
Large Population ◽  
Initial Distribution ◽  
Coordination Games ◽  
Coordination Game ◽  
Initial State ◽  
Coordination Property ◽  
Best Response ◽  
Best Response Dynamic

We introduce the class of anti-coordination games. A symmetric two-player game is said to have the anti-coordination property if, for any mixed strategy, any worst response to the mixed strategy is in the support of the mixed strategy. Every anti-coordination game has a unique symmetric Nash equilibrium, which lies in the interior of the set of mixed strategies. We investigate the dynamic stability of the equilibrium in a one-population setting. Specifically we focus on the best response dynamic (BRD), where agents in a large population take myopic best responses, and the perfect foresight dynamic (PFD), where agents maximize total discounted payoffs from the present to the future. For any anti-coordination game we show (i) that, for any initial distribution, BRD has a unique solution, which reaches the equilibrium in a finite time, (ii) that the same path is one of the solutions to PFD, and (iii) that no path escapes from the equilibrium in PFD once the path reaches the equilibrium. Moreover we show (iv) that, in some subclasses of anti-coordination games, for any initial state, any solution to PFD converges to the equilibrium. All the results for PFD hold for any discount rate.

NETWORK FORMATION, COST-SHARING AND ANTI-COORDINATION

2009 ◽  
Vol 11 (01) ◽  
pp. 53-76 ◽  
Author(s):  
DUNIA LÓPEZ-PINTADO
Keyword(s):  
Cost Sharing ◽  
Nash Equilibria ◽  
Network Formation ◽  
Extreme Case ◽  
Coordination Games ◽  
Unique Equilibrium ◽  
Social Game ◽  
Best Response ◽  
Link Cost ◽  
The Cost

The objective of this work is to analyze how social networks coevolve with other dimensions of agents' choice. We present a model where agents choose their neighbors as well as a mode of behavior in 2 × 2 anti-coordination games, i.e. games where an individual's best response is to behave differently than the opponent. Links are costly. The cost of a link is shared between the two individuals involved in it, but not necessarily in a symmetric way. We characterize the set of Nash equilibria of the resulting social game and show how this set shrinks as the shares of the link cost are more equal. In the extreme case in which each agent pays half of the cost, there is a unique equilibrium. We also show that, as usual in the literature of network formation, there is a general misalignment between the stable and efficient states of the game.

scholarly journals The Frequency of Convergent Games under Best-Response Dynamics

2021 ◽  
Author(s):  
Samuel C. Wiese ◽  
Torsten Heinrich
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Pure Strategy ◽  
Response Dynamics ◽  
Novel Approach ◽  
Best Response ◽  
Random Games ◽  
Payoff Matrices ◽  
Best Response Dynamic ◽  
Strategy Nash Equilibrium

AbstractWe calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of n-player, m-strategy normal-form games. To obtain the ensemble, we generate payoff matrices at random. Games with a unique pure strategy Nash equilibrium converge to the Nash equilibrium. We then consider a wider class of games that converge under a best-response dynamic, in which each player chooses their optimal pure strategy successively. We show that the frequency of convergent games with a given number of pure Nash equilibria goes to zero as the number of players or the number of strategies goes to infinity. In the 2-player case, we show that for large games with at least 10 strategies, convergent games with multiple pure strategy Nash equilibria are more likely than games with a unique Nash equilibrium. Our novel approach uses an n-partite graph to describe games.

scholarly journals Pure Nash Equilibria and Best-Response Dynamics in Random Games

2021 ◽  
Author(s):  
Ben Amiet ◽  
Andrea Collevecchio ◽  
Marco Scarsini ◽  
Ziwen Zhong
Keyword(s):  
Nash Equilibria ◽  
Approximation Error ◽  
Pure Nash Equilibrium ◽  
Response Dynamics ◽  
Asymptotic Results ◽  
Finite Games ◽  
Best Response Dynamics ◽  
Best Response ◽  
Random Games ◽  
Pure Equilibria

In finite games, mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large number of players can each choose one of two possible strategies and the payoffs are independent and identically distributed with the possibility of ties. We provide asymptotic results about the random number of pure Nash equilibria, such as fast growth and a central limit theorem, with bounds for the approximation error. Moreover, by using a new link between percolation models and game theory, we describe in detail the geometry of pure Nash equilibria and show that, when the probability of ties is small, a best-response dynamics reaches a pure Nash equilibrium with a probability that quickly approaches one as the number of players grows. We show that various phase transitions depend only on a single parameter of the model, that is, the probability of having ties.

scholarly journals COOPERATION IN THE PRISONER'S DILEMMA GAME IN RANDOM SCALE-FREE GRAPHS

2010 ◽  
Vol 20 (03) ◽  
pp. 849-857 ◽  
Author(s):  
JULIA PONCELA ◽  
JESÚS GÓMEZ-GARDEÑES ◽  
YAMIR MORENO ◽  
LUIS MARIO FLORÍA
Keyword(s):  
Prisoner's Dilemma ◽  
Evolutionary Dynamics ◽  
Mean Field ◽  
Prisoner’S Dilemma ◽  
Mean Field Approximation ◽  
Prisoner’S Dilemma Game ◽  
Scale Free ◽  
Scale Free Networks ◽  
Prisoner's Dilemma Game ◽  
Random Scale

In this paper we study the cooperative behavior of agents playing the Prisoner's Dilemma game in random scale-free networks. We show that the survival of cooperation is enhanced with respect to random homogeneous graphs but, on the other hand, decreases when compared to that found in Barabási–Albert scale-free networks. We show that the latter decrease is related to the structure of cooperation. Additionally, we present a mean field approximation for studying evolutionary dynamics in networks with no degree-degree correlations and with arbitrary degree distribution. The mean field approach is similar to the one used for describing the disease spreading in complex networks, making a further compartmentalization of the strategists partition into degree-classes. We show that this kind of approximation is suitable to describe the behavior of the system for a particular set of initial conditions, such as the placement of cooperators in the higher-degree classes, while it fails to reproduce the level of cooperation observed in the numerical simulations for arbitrary initial configurations.

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 On the Throughput Optimization in Large-Scale Batch-Processing Systems

2021 ◽  
Vol 48 (3) ◽  
pp. 128-129
Author(s):  
Sounak Kar ◽  
Robin Rehrmann ◽  
Arpan Mukhopadhyay ◽  
Bastian Alt ◽  
Florin Ciucu ◽  
...  
Keyword(s):  
Large Scale ◽  
Mean Field ◽  
Queueing Network ◽  
Processing System ◽  
Batch Size ◽  
System Throughput ◽  
Throughput Optimization ◽  
Mean Field Model ◽  
Optimal Batch Size ◽  
Globally Attractive

We analyze a data-processing system with n clients producing jobs which are processed in batches by m parallel servers; the system throughput critically depends on the batch size and a corresponding sub-additive speedup function that arises due to overhead amortization. In practice, throughput optimization relies on numerical searches for the optimal batch size which is computationally cumbersome. In this paper, we model this system in terms of a closed queueing network assuming certain forms of service speedup; a standard Markovian analysis yields the optimal throughput in w n4 time. Our main contribution is a mean-field model that has a unique, globally attractive stationary point, derivable in closed form. This point characterizes the asymptotic throughput as a function of the batch size that can be calculated in O(1) time. Numerical settings from a large commercial system reveal that this asymptotic optimum is accurate in practical finite regimes.

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