Cooperate Without Looking Why we care what people

“Will you do me this favor? ” “What’s in it for me? ” “Let

VS. “Act in such a way that you treat humanity… never merely as a

Cannot be explained by… C D b-c -c b 0 δ C D C

“The Envelope Game” High Temptation Low Temptation C a, b D c H, d

1. Model variation in costs of cooperation

2 2. Model player 1’s choice of whether to “look” Crucial assumption: others (player

2 3. Player 1 then chooses whether to cooperate or defect 2 is again

The strategy pair (CWOL) Player 1: Don’t look and cooperate Player 2: Exit if

The strategy pair (CWL) Player 1: Look and cooperate Player 2: Exit if player

The strategy pair (ONLYL) Player 1: Look and cooperate iff temptation is low Player

The strategy pair (ALLD) Player 1: Defect Player 2: Exit is always a stationary,

CWOL, CWL, ONLYL, and ALLD are the only stationary, subgame perfect equilibria of the

Why? Is game theory relevant? Multiple equilibria. Does CWOL emerge?

2. Strategies “evolve” according to replicator

3. Start at random point in parameter region and solve replicator

Part of broader approach: apply game theory to preferences and ideologies Questions or comments?

Slides: 43

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Cooperate Without Looking Why we care what people think and not just what they do Moshe Hoffman, Erez Yoeli, and Martin Nowak Program for Evolutionary Dynamics, Harvard University

Motivation…

“Will you do me this favor? ” “What’s in it for me? ” “Let me think about it… OK. ” “Who else is coming? ” VS. “Of course, no problem!” “Action from duty has its moral worth not in the purpose to be attained by it but in the maxim in accordance with which it is decided upon”

VS. “Act in such a way that you treat humanity… never merely as a means to an end, but always at the same time as an end. ”

VS.

Cannot be explained by… C D b-c -c b 0 δ C D C b-c -c D b 0 δ C D b-c -c b 0 δ …

Our model…

“The Envelope Game” High Temptation Low Temptation C a, b D c H, d c L, d c. H > c. L > a> 0 bp + d(1–p) < 0 < b

1. Model variation in costs of cooperation

2 2. Model player 1’s choice of whether to “look” Crucial assumption: others (player 2) can observe whether player 1 looked

2 3. Player 1 then chooses whether to cooperate or defect 2 is again able to observe High Temptation Low Temptation C a, b D c H, d c L, d c. H > c. L > a> 0 bp + d(1–p) < 0 < b

4. Model others’ “trust” in Player 1

Results…

The strategy pair (CWOL) Player 1: Don’t look and cooperate Player 2: Exit if player 1 looks or defects is a stationary, subgame perfect equilibrium iff: a/(1 -w) > pc. L + (1 -p)c. H

The strategy pair (CWL) Player 1: Look and cooperate Player 2: Exit if player 1 defects is a stationary, subgame perfect equilibrium iff: a/(1 -w) > c. H

The strategy pair (ONLYL) Player 1: Look and cooperate iff temptation is low Player 2: Exit if player 1 defects when temptation is high is a stationary, subgame perfect equilibrium iff: pb + (1 -p)d < 0

The strategy pair (ALLD) Player 1: Defect Player 2: Exit is always a stationary, subgame perfect equilibrium

CWOL, CWL, ONLYL, and ALLD are the only stationary, subgame perfect equilibria of the envelope game Then…

The strategy pair (CWOL) Player 1: Don’t look and cooperate Player 2: Exit if player 1 looks or defects is the only cooperative equilibrium provided: c. H > a/(1 -w) > pc. L + (1 -p)c. H pb + (1 -p)d < 0

The strategy pair (CWOL) Player 1: Don’t look and cooperate Player 2: Exit if player 1 looks or defects is the only cooperative equilibrium provided: large rare temptations defection is harmful

Dynamics…

Why? Is game theory relevant? Multiple equilibria. Does CWOL emerge?