GTES :
Game-Theoretical Evolutionary Simulation

1.1 Introduction

GTES is a framework for applying Evolutionary Game Theory to the investigation of a complex system (most often, defined with a system dynamics model).

GTES is a simulation technique that combines Monte-Carlo, Game Theory and Evolutionary Algorithms. As explained in my blog or my research paper, it is mostly a "model benchmark", that is a tool to explore what can be said about a very general model.

GTES applies to problems for which a model is conjectured, but with far too many unknown parameters to be useful for a direct simulation. It also adresses the behavior of a set of actors/players, who try to maximize some form of objective function. GTES separates these unknown parameters into three families:

• parameters that are not related to the actors but represent the environment. The GTES approach is to sample these parameters using a Monte-Carlo simulation

• parameters that represent the objective function, i.e. the strategy of the actors. These are the control parameters for the model, those for which a "game theory strategy matrix" is desired. GTES will yield a simulation value for each setting of these parameters.

• so-called tactical parameters that are assigned to each actor, but are "controlled" by the strategy parameters, in the sense that each actor may be assumed to learn the optimal value to best fit its objective function. This is where the "evolutionary algorithms" (or any form of local optimization and meta-heuristic) kick in: GTES solves each optimization sub-problem to find the "best behavior" for each actor according to its strategy parameters.

The beauty of the GTES approach is to reduce the set of parameters that need to be looked at (i.e., the second set). The first set is sampled and the third set is derived from solving a set of optimization problem. The game theoretical part comes from solving each actor's optimization problems at the same time. A simple fixpoint computation (iterating the local moves) may find a Nash equilibrium, but there is no warranty. However, the first application of GTES to various problems using a naive search for Nash equilibrium has proven to be quite interesting. 

1.2  Domains of Application

• CCEM : (Energy/Economy/Climate World model)

• Mobile Market Competition: cf CGS (Cellular Game Simulation).

• Simulation of Smart Grids

• Tender/Auctions for 3G and 4G Licences

• SIFOA (simulation of information flows in organization)

A key application of GTES has been to market equilibriums (equilibria for purists).  Most of the work in the past 5 years has been with CGS (Cellular Game Simulation), a GTES model which represents the competition between phone operators. The major presentation at INRIA in 2010 was dedicated to this topic. My further work on modeling the introduction of Free into the market (cf. CSDM presentation) was based on an even simpler representation of market competition. My goal for the next two years is to deepen my analysis of “market equilibriums”:

• GTES versus classical equilibriums such as Cournot.

  • I want to calibrate the results obtained through GTES simulation against the classical equilibrium from game theory applied to economy (including Bertrand, Stackelberg and others). The goal is two-folds: increase the credibility of GTES by reproducing results from analytical methods with simple market equations, and enrich our set of working market model with insights from economy theory.

• Bids, such as LTE bids in 2011. 

  • GTES was applied at the end of 2011 to help simulate a few bidding strategies when an auction was proposed by ARCEP for LTE frequencies. The complexity of the auction, with rules that govern the bundles of frequencies allocated to bidding operators, translates into an interesting game (although it is a “one-shot” auction, with a unique bid).

1.3  Goals (updated in 2025)

• Improve the characterization of equilibriums (beyhond Nash equilibriums)

• Apply GTES to global warming : GWDG !

• Publish a research paper in English :)

1.4  References

Papers:

• RAIRO (2009):  https://www.rairo-ro.org/articles/ro/abs/2009/04/ro0936/ro0936.html

• CSDM (2012):  https://link.springer.com/chapter/10.1007/978-3-642-34404-6_2

Presentations: 

• UTC Presentation (2014) on Slideshare: https://fr.slideshare.net/slideshow/gtes-utc-2014/42116445

• Presentation about S3G: https://fr.slideshare.net/slideshow/systemic-simulation-of-smart-grids-evolutionary-game-theory/274805104

Blogpost:

• https://organisationarchitecture.blogspot.com/2007/05/un-nouvel-exemple-de-simulation-par.html
  one of the first posts about GTES (2007) in French

• https://informationsystemsbiology.blogspot.com/2013/05/systemic-simulation-of-smart-grids-s3g.html