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The investment game was invented by experimental economists Joyce Berg, John Dickhaut and Kevin McCabe to study game theory, particularly considering backward induction and social preferences. It is frequently compared with the Dictator Game and Ultimatum Game. The game essentially works like this:
1. There are two players, who can't communicate (except via the game's formal mechanism of sending money).
2. One player (the Sender) gets \$10. The other player (the Receiver) gets nothing.
3. The Sender can choose to send any amount of their money to the Receiver.
4. Any amount the Sender chooses to send gets tripled.
5. The Receiver can now choose to send any amount of money back to the Sender. This money is not multiplied.
6. They take their money and go home.
For example:
1. Amos is the Sender and Betina is the Receiver.
2. Amos gets \$10.
3. Amos decides to send \$6 to Betina.
4. The \$6 gets tripled, so now Amos is left with \$4, and Betina has \$18.
5. Betina decides to send back \$6, which leaves her with \$12 and Amos with \$10.
Similar to the Ultimatum Game, standard analysis with backward induction and assuming selfish players would say that Amos shouldn't have sent anything. Amos would figure out that no matter what he sent, Betina wouldn't send anything back.

There is still a good deal of analysis about what exactly happens and why in the investment game. The motivating story is based on evolution of trust and reciprocity--that humans should have evolved to trust each other, and to reciprocate with help when help is given (I'll share some of my fish with you because you shared some of your apples with me).

Other analysis tries to break down the effects of altruism versus trust & reciprocity.

In practice, many senders do send some amount, tending to about one-half of what they're given. Receivers often send some back, though it's not at all clear if they send back more when they are sent more, or that it's actually a good investment for the Senders to send.

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