Greeks and games: Forerunners of modern game theory

Modern game theory is connected with its ancient Greek originals in three respects.

1.	The notion of rationality operative in game theory is the formal notion of consistency, whether of beliefs, desires, or choices. Just as Aristotle’s formal logic is the first system for determining the consistency of beliefs, so his practical syllogism is the first device to affirm a deductive connection of rational choice with desire and belief. Modern rational choice theory is the fulfillment of the idea of the deductive practical syllogism.
2.	Interest in generating measurements of attitudinal states is found in Plato and Epicurus. Kant revived the project in arguing that such measurements could be generated from an agent’s willingness to assume risk. This is the core of the expected utility theory of von Neumann and Morgenstern.
3.	Thucydides had a deep understanding of the logic of individual rational choice in strategic situations, where each agent must make the effort to influence, to anticipate, or to adapt to the decisions of other(s) to serve its own interests. Modern game theory formalizes the sorts of strategic problem Thucydides depicts and analyses in his history.

Even when men have no need of assistance from each other, they desire to live together ... [But] to live together and share all our human affairs is difficult; especially to share ... work and its products ... [T]hey quarrel.Aristotle, Politics 3.4; 2.2.