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In this paper, a gentle introduction to Game Theory is presented in the formof basic concepts and examples. Minimax and Nash's theorem are introduced asthe formal definitions for optimal strategies and equilibria in zero-sum andnonzero-sum games. Several elements of cooperative gaming, coalitions, votingensembles, voting power and collective efficiency are described in brief.Analytical (matrix) and extended (tree-graph) forms of game representation isillustrated as the basic tools for identifying optimal strategies and"solutions" in games of any kind. Next, a typology of four standard nonzero-sumgames is investigated, analyzing the Nash equilibria and the optimal strategiesin each case. Signaling, stance and third-party intermediates are described asvery important properties when analyzing strategic moves, while credibility andreputation is described as crucial factors when signaling promises or threats.Utility is introduced as a generalization of typical cost/gain functions and itis used to explain the incentives of irrational players under the scope of"rational irrationality". Finally, a brief reference is presented for severalother more advanced concepts of gaming, including emergence of cooperation,evolutionary stable strategies, two-level games, metagames, hypergames and theHarsanyi transformation.

Elements of Game Theory - Part I: Foundations, acts and mechanisms