Dynamical Systems Theory compared to Game Theory: The case of the Salamis’s battle Konstantina Founta1, Loukas Zachilas1 1Dept. of Economics, University of Thessaly, Volos, Greece Email:
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[email protected] 1. Abstract In this paper, we present an innovative non–linear, discrete, dynamical system trying to model the historic battle of Salamis between Greeks and Persians. September 2020 marks the anniversary of the 2500 years that have passed since this famous naval battle which took place in late September 480 B.C. The suggested model describes very well the most effective strategic behavior between two participants during a battle (or in a war). Moreover, we compare the results of the Dynamical Systems analysis to Game Theory, considering this conflict as a “war game”. Keywords: Discrete Dynamical Systems, Modeling Strategic Behavior, Game Theory, Battle of Salamis. 2. Introduction In recent years, many researchers have studied the players’ behavior either through Game theory or through Dynamical Systems. Some of the notable works are Archan and Sagar [2] who present a possible evolutionary game-theoretic interpretation of non- convergent outcomes. They highlight that the evolutionary game dynamics is not about optimizing (mathematically) the fitness of phenotypes, but it is the heterogeneity weighted fitness that must be considered. They mention that heterogeneity can be a measure of diversity in the population. In our research, this is described by the asymmetry in the conflict. In addition, Toupo, Strogatz, Cohen and Rand [3] present how important the role of the environment of the game is for the decision-makers. They suggest simulations of agents who make decisions using either automatic or controlled cognitive processing and who not only compete, as well as affect the environment of the game.