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Morality Games 295

uncorrelated asymmetries must have. This requires a bit more game theory to illus-
trate; the logic is detailed in the section on categorical distinctions but the implica-
tions are straightforward: Uncorrelated asymmetries must be discrete (as in who
arrived first or whether someone has African ancestry) and cannot be continuous
(who is stronger, whether someone has darker skin). Indeed, we challenge the reader
to identify a case where our sense of rights depends on surpassing a threshold in a
continuous variable (stronger than? darker than?). More generally, an asymmetry
must have the characteristic that, when it occurs, every observer believes it occurred
with a sufficiently high probability, where the exact level of confidence is deter-
mined by the payoffs of the game. This is true of public, explicit speech and hand-
shakes, but not innuendos or rumors. (Formally, explicit speech and handshakes
induce what game theorists term common p-beliefs.)

The Hawk–Dove explanation of our sense of rights also gives useful clarity on
when there will be conflict. Conflict will arise if both players receive opposing sig-
nals regarding the uncorrelated asymmetry, such as two individuals each believing
they arrived first, or when there are two uncorrelated asymmetries that point in
conflicting directions, such as when one person invested more and the other arrived
first. The former source of conflict appears to be the case in the Israeli–Palestinian
conflict. Indeed, both sides pour great resources into demonstrating their early
possession, especially Israel, through investments in and public displays of archeol-
ogy and history. The latter source of conflict appears to be the case in many of the
contested legal disputes in the study by DeScioli and Karpoff (2014) mentioned
above. An example is one person finds an object on another’s land. Indeed, this turns
out to be a source of many legal conflicts over property rights, and a rich legal tradi-
tion has developed to assign precedence to one uncorrelated asymmetry over another
(Descioli & Karpoff, 2014). As usual, we see similar behavior in animals in studies
that provide empirical support for Maynard Smith’s model for animal territoriality:
When two animals are each given the impression they arrived first by, for example,
clever use of mirrors, a fight ensues (Davies, 1978).

Authentic Altruism, Motives, and the Envelope Game

In this section, we present a simple extension of the Repeated Prisoner’s Dilemma
to explain why morality depends not just on what people do but also what they think
or consider.
In the Repeated Prisoner’s Dilemma and other models of cooperation, players
judge others by their actions—whether they cooperate or defect. However, we not
only care about whether others cooperate but also about their decision-making pro-
cess: We place more trust in cooperators who never even considered defecting. To
quote Kant, “In law a man is guilty when he violates the rights of others. In ethics
he is guilty if he only thinks of doing so.”
The Envelope Game (Fig. 3) models why we care about thoughts and consider-
ations and not just actions (Hoffman, Yoeli, & Nowak, 2015). The Envelope Game

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