nBEPA1 in Single-optimum Coordination Games played in networks

Luis R. Izquierdo & Segismundo S. Izquierdo


To use nBEPA1-SOCG-nw (protocol noisy Best Experienced Payoff, test All, 1 trial, in Single Optimum Coordination Games played in networks), you will have to install NetLogo 6.2.1 (free and open source) and download the model itself. Unzip the downloaded file and click on nbepa1-socg-nw.nlogo


This section explains the formal model that nBEPA1-SOCG-nw implements. The information provided here should suffice to re-implement the same formal model in any sophisticated enough modelling platform. We use bold green italicised arial font to denote parameters (i.e. variables that can be set by the user).


In the model, there is a population of \(N\) agents who are embedded in an undirected network and repeatedly play a Single-Optimum Coordination Game with their neighbors. The type of network is determined by the user setting the parameter network-model, which can have the following values: Erdos-Reny, small-world, preferential-attachment, ring, star, or grid-4-nbrs.

The Game

The Single-Optimum Coordination Game is a 2-player \(n\)-strategy game with the following payoff matrix: \[ \left(\begin{array}{ccccc} 1&0&0&...&0\\ 0&2&0&...&0\\ 0&0&\ddots&&\vdots\\ \vdots&\vdots&&n-1&0\\ 0&0&...&0&n\\ \end{array} \right) \]

Note that the optimal outcome is achieved if both players choose strategy \(n\).

The nBEPA1 revision protocol

From time to time, agents are given the opportunity to revise their strategy, and they do so following the nBEPA1 revision protocol:

Sequence of events

Initially, agents are randomly assigned a strategy according to the initial distribution n-of-players-for-each-strategy = \(\left[a_1, a_2, ..., a_n\right]\) set by the user, where \(a_i\) denotes the number of agents using strategy \(i\). The population size \(N\) and the number of strategies \(n\) in the game are computed from the initial distribution, since \(N = \sum_i a_i\) and \(n\) is the number of elements in the initial distribution.

The model then runs in discrete time-steps called ticks. Within each tick, agents are given the opportunity to revise their strategies. The way agents are scheduled to revise their strategies is specified by the user with parameter updating, which can take three values:

Note that, in every tick, exactly \(N\) revisions take place regardless of the value of updating. This sequence of events is repeated iteratively.






nbepa1-socg-nw is a NetLogo model designed to analyze the nBEPA1 (noisy Best Experienced Payoff, test All, 1 trial) protocol in Single Optimum Coordination Games played in networks.
Copyright (C) 2021 Luis R. Izquierdo & Segismundo S. Izquierdo

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You can download a copy of the GNU General Public License by clicking here; you can also get a printed copy writing to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.

Contact information:
Luis R. Izquierdo
University of Burgos, Spain.
e-mail: lrizquierdo@ubu.es


This program has been designed and implemented by Luis R. Izquierdo & Segismundo S. Izquierdo.


Izquierdo, L. R., Izquierdo, S. S. and Rodríguez, J. (2021). Fast and Scalable Global Convergence in Single-Optimum Decentralized Coordination Problems. Working paper.