Ahmer Tarar

I present a game-theoretic analysis of Socrates’ moral theory, using the cooperate/defect framework of Prisoner’s Dilemma and Stag Hunt, the two most commonly used game-theoretic models in moral and political philosophy. Based on Plato’s Apology, Crito, and Gorgias, I argue that Socrates presents a preference ordering even more cooperative than that of Stag Hunt. One version is consistent with what Vlastos (1991) calls the Identity Thesis, where an agent’s virtue is the only determinant of her happiness, and the other is consistent with the Sufficiency Thesis, whereby the agent’s virtue is the major determinant of her happiness, but conventional goods also affect this. A repeated-game analysis suggests that, contrary to Vlastos, and consistent with Annas (1999), the Identity Thesis better represents Socrates’ moral theory than does the Sufficiency Thesis, in that only with the former does the agent always cooperate (act justly) in every equilibrium with every type of opponent, consistent with a core Socratic moral principle of never committing an injustice under any circumstance, even in retaliation for having an injustice committed against oneself.

In A Treatise of Human Nature, Hume argues that morality pertains primarily to character, and that actions have moral content only to the extent that they signal good or bad character. I formalize his signalling theory of moral/immoral actions using simple game-theoretic models. Conditions exist under which there is a separating equilibrium in which actions do indeed credibly signal character, but conditions also exist in which there is only a pooling or semi-separating equilibrium. A tradeoff is identified between the signalling value of actions, and the consequentialist goal of incentivizing all character types to choose beneficial actions.

Formal analyses of Pascal’s Wager have almost all been decision-theoretic, with a human as the sole decision-maker. This paper analyses Pascal’s Wager in a game-theoretic setting in which the deity whose existence the human is considering wagering on is also a decision-maker. There is an equilibrium in which the human chooses to wager that the deity exists and Pascal’s Wager thus operates, but also one in which the human does not wager. Thus, in a game-theoretic setting, Pascal’s Wager is indeterminate: wagering and not wagering are both consistent with equilibrium behaviour.