STRAT S13

Repeated Games (Iterated Games)

Static games (one-off decisions) often result in a Nash Equilibrium that is not Pareto optimal. However, when a game is repeated multiple times, the strategic environment changes.

• Long-term Payoffs: Players consider long-term gains rather than just immediate payoffs, which can lead to different behaviors.

• Repetition Effects: Iteration creates opportunities for Learning, Expectations, and Trust. It also allows for "Trust Threats" to enforce agreements.

• Cooperation: Repeated interactions can create stability in collusive agreements (cooperation) even without formal contracts.

Static Models

Focus on immediate outcomes. They often fail to explain how firms maintain prices above competitive levels without formal collusion.

Dynamic Models

Address the intensity of price competition over time and focus on how price cooperation can be sustained.

Short-term vs. Long-term

Short-term profits in a static model are often followed by negative long-term effects in a dynamic setting.

Sustainable Cooperation Strategies

Cooperation is often a superior long-term strategy for oligopolies (e.g., electric, telecom, or financial industries), whereas a failure to cooperate can damage an industry long-term (e.g., airlines).

Tit-for-Tat

A player mimics the rival’s previous move. If the rival cooperates, you cooperate; if they defect, you defect. The mere possibility of a player using this strategy can incentivize rivals to cooperate if the time horizon is long enough.

Trigger-Grim (Grim Trigger) Strategy

A player threatens a rival with a "worse" punishment forever if they deviate from an agreed action just once.

The End-Game Problem

Cooperation is a good strategy unless players know the game is about to end, at which point the incentive to defect increases.

Pure Strategy

Assume strategies are chosen with the same probability.

Mixed Strategy

A Nash Equilibrium where each player assigns a specific probability to each strategy.

Benefit: It prevents rivals from easily predicting your moves and keeps payoffs balanced (e.g., Firm 1 non-advertises with 60% probability while Firm 2 does so with 70%).

Bertrand Model Paradox

This model focuses on Price Competition between two firms in a duopoly.

• Assumptions: Homogeneous products (perfect substitutes), identical marginal costs (MC), and simultaneous price-setting.

• The Paradox: Because products are perfect substitutes, if one firm lowers its price even slightly below the other, it captures the entire market.

• Equilibrium (P1=P2=MC): Firms will bid prices down until they reach the Marginal Cost. At this point, Return on Investment (ROI) is zero, and firms make no profit despite being in a duopoly.

Cournot Oligopoly Model

Unlike Bertrand, the Cournot model focuses on Quantity Competition.

• Strategic Decision: Firms set the production quantity (q1,q2) simultaneously.

• Reaction Function: The best quantity for one firm depends on the quantity produced by the other.

• Profit Calculation:

  1. Calculate Total Revenue for both firms.

  2. Calculate Marginal Revenue and Marginal Cost.

  3. Set Marginal Revenue = Marginal Cost to find the Reaction Function.

• Comparison of Quantities: Monopoly Quantity (QM) < Cournot Quantity (QD) < Perfect Competition Quantity (QC). Consequently, the Cournot equilibrium price is lower than a monopoly price but higher than a perfectly competitive price.

Key Principles for the Exam

• Reputation Matters: In games with revealed partners, trust and cooperation increase. With anonymous partners, trust and cooperation decrease.

• Failure to Cooperate: Often results from rapidly shifting demand or cost conditions, as seen in the airline industry.

• Information Asymmetry: Signaling theory (communicating information to a receiver) is used to create commitment and trust to sustain Nash Equilibria over time.