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In his last dialogue, the Laws, Plato views citizens in the polis as players in a game. Just as contemporary game theory, Plato considers games to be states of strategic interaction. Yet the game of the Laws differs from those of game theory in one important respect. Where game theory assumes that players are rational--that they choose strategies, or rules for taking action at each instant of a game, in order to maximize payoffs--Plato explores the conditions under which rationality, as game theory defines it, is possible.
Plato thus agrees with game theory that rational, maximizing behavior is a necessary constituent of civic order, but not that it may simply be assumed. He concurs that rationality can describe the behavior of citizens, but not under any circumstances. It is the task of politics in Plato's city to prepare the conditions for rationality. Only once politics has done its work is maximizing, utilitarian behavior possible. Yet political preparation of the game of the city is exactly what contemporary game theory assumes away.
The Athenian, who leads the discussion, describes the political preparation for rationality as "this moderate old man's game concerning laws." Political preparation of the game of the city is itself a game, because it is never possible to escape strategic interaction. It is, however, a second-order game whose play paves the way for the first-order game of lawful strategic interaction. The second-order, political game at once completes the analysis of rationality and lays the groundwork for rationality to operate.
The politics of the Laws is a game, but one whose actions and players differ from the actions and players of the first-order game. The action of the political game is lawgiving. The players are the gods and god-like men who serve as lawgivers. The second-order, political game also has its own distinct rationality, linked to a payoff that is qualitatively different from the utilitarian payoffs of the first-order game. The Athenian calls the rationality of the second-order game "intelligence." He calls the payoff associated with it "joy," as distinct from the "benefits" associated with utilitarian rationality. The players in the second-order game seek to maximize joy, not benefit. Joy is the experience of play. The payoff of players in the second-order game is the game itself, not a benefit collateral to playing it. The second-order game is a "true" game, one that the players enter in order to play, not to get utilitarian payoffs.
Arthur J. Jacobson,
Origins of the Game Theory of Law and the Limits of Harmony in Plato's Laws,
Cardozo Law Review
Available at: https://larc.cardozo.yu.edu/faculty-articles/93