Timed strategic games A new game theory for managing strategic plans in the time dimension

Abstract

Background: Over the last 60+ years a number of wars of different kinds has been taken place worldwide. Scholars refer to the latest ones as 4 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> Generation wars (or warfare) where the confrontation is no longer between state actors, but between non-state actors (mainly guerrilla/insurgents) and state actors. Aims: Since the old strategic game theory (e.g. Prisoner's Dilemma) is not able to explain 4 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> Generation wars because of asymmetry and the lack of a timed framework, we define a variation of this theory that we call Timed Strategic Game with the aim of bringing up the discussion on what it is really needed to plan and manage military campaigns such as Afghanistan, Iraq, Libya, Somalia, Lebanon, Israel-Palestine, and etc. Method: The theory being defined deals with asymmetry and includes a temporal dimension. Our definition is completely new. We did not use an automaton approach as usually done in game theory. We considered a continuous parametric function varying based upon the variable time. The use of the variable time in strategic games is the main novelty of this work. Results: Based upon the definition of “Timed Strategic Game”, we put forward the definition of “Timed Prisoner's Dilemma” and another one that we called IN-OUT game, which was set up specifically to model the main features of 4 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> Generation wars. Furthermore, the contribution of this work is also with the definition of Stable and Unstable Timed Nash Equilibria, which are the extension of “Nash Equilibria” to Timed Strategic Games. Conclusions: In this research we show a way of modeling asymmetric strategic games over time. Even though the suitability of the application of this new theory has to be tried out in practical terms, it is the first step to have a theoretical framework where strategic games can finally be categorized in terms of time. Additional contributions are that the proposed model is general purpose regardless of 4 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> Generation wars; we observed that Timed Strategic Games could also help model value-based management, earned value analysis, and share-market dynamics.