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After the PD has taken place, a player can choose to punish her opponent, which consists in paying a cost
$\epsilon_1$ to make the opponent incur a cost$\delta_1$ . -
Assume that
$\epsilon_1<\delta_1$ . -
CP cooperates in the PD, and punishes a co-player who defected in the game.
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AP defects in the PD, and punishes a co-player who cooperated in the game.
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pure cooperator (C) and pure defector (D) (i.e. they do not use the punishment option).
Commitment strategy (denoted by COM)
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First offer to commit, then cooperate, proposer pays cost
$\epsilon_2$ ; -
adversary accepts commitment but does not cooperate, compensation cost
$\delta_2$ ; -
if does not accept commitment, interaction will not occur, both parties gain 0;
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first assume adversary will cooperate.
Unconditional cooperators (C)
- always commit when being proposed a commitment deal, cooperate whenever the PD is played, but do not propose commitment themselves.
Unconditional defectors (D),
- do not accept commitment, defect when the PD takes place, and do not propose commitment.
Fake committers(FAKE),
- False committers, pretending to accept a commitment and then reneging on it;
- compensated by payment of cost
$\delta_2$ for accepting a promise to renege.
Commitment free-riders (FREE)
- defect unless being proposed a commitment, which they then accept and cooperate subsequently in the PD;
- In other words, these players are willing to cooperate when a commitment is proposed but are not prepared to pay the cost of setting it up;
- No cooperation if you are not committed.
