Strategic Cooperation in Repeated Games and Market Dynamics

Part 3: Strategic Cooperation

The Rationale for Cooperation

Why cooperation? It may offer ways out of inefficient market solutions. For example, cooperation is crucial when:

• Buying inputs from a supplier.
• Deciding on price and quality of goods.
• Formulating advertising strategy in a competitive market.

Repeated Games

Definition: A strategy in a multi-stage game for Player I indicates, for each stage of the game and for each possible sequence of prior moves, how the player will move.

The Backward Induction Problem: Backward induction would typically imply an aggressive strategy only, because in the last stage, cooperation is not a Nash equilibrium. A way out of this dilemma is that it is often not obvious when the last round takes place. Therefore, backward induction is often considered a too simple concept for real-world strategic interactions.

The Axelrod Tournament

The Axelrod tournament involved participants playing their strategies against each other in a repeated Prisoner's Dilemma game. Several key results emerged from Axelrod's repeated tournaments, forming the basis of successful cooperative strategies:

1. Be Nice: Start out by being cooperative; do not be the first to play aggressively.
2. Don't Allow Exploitation: Answer an aggressive move by the opponent in the next stage with an aggressive step (retaliation).
3. Forgive: If the other player returns to cooperation after prior aggression, respond to this “peace offer” by choosing cooperation again.
4. Don’t Be Envious: The Tit-for-Tat strategy does not necessarily win individual matches, but it performs robustly overall.
5. Be Simple: Tit-for-Tat has the advantage of being simple and thus being quickly understood by the opponent, fostering trust and predictability.

Factors Favoring Cooperation

Several conditions increase the likelihood and stability of cooperative behavior:

• Many Repetitions: A long-term interaction with suppliers, competitors, and customers encourages the development of cooperation.
• Importance of Future Payoffs: Low discounting (valuing future rewards highly) is better for cooperation.
• Knowledge of Prior Moves: Adequate reaction is only possible if the actions of the other party can be monitored. Problems may emerge in cases like cartels (secret discounts) or arms control (hidden arms).
• Knowledge of the Other's Identity: A correct reaction is only possible if the current business partner is known and identifiable.
• Clustering of "Nice People": Tit-for-Tat players are particularly successful when clustered together.
• Low Reward for Aggressiveness: Mechanisms for punishment, beyond simple revenge (like playing aggressively), encourage cooperation, even if the Prisoner's Dilemma structure is not completely set off.

Recent Experimental Research on Cooperation

Experimental research contrasts traditional and bounded rationality models:

Traditional Rationality

• Assumption: Beliefs about the behavior of others and the environment are correct, aiming to best satisfy one's preferences.
• Type of Player: Self-regarding player.

Bounded Rationality

• Assumption: Beliefs may be biased, and behavior may deviate from trying to best satisfy one's preferences.
• Type of Player: Strong reciprocator.

The impact on game outcomes depends significantly on the characteristics of the game and the frequency distribution of the types of players involved.