Question

Identify whether cooperative (collusive) outcomes may be supported as a Nash equilibrium in a repeated game, and explain the roles of trigger strategies, the interest rate, and the presence of an indefinite or uncertain final period in achieving such outcomes.

Short answer

Cooperative outcomes are supported in Nash equilibrium, but the trigger strategies will not lead to Nash equilibrium in a repeated game, and interest rate will lead to Nash equilibrium in a repeated game, in presence of an indefinite final period.

Step-by-step solution

Nash equilibrium

When Nash equilibrium state cannot provide the player with the possible results, where the player can use collaborative results to maximize common interests, it is considered a result. For example, if two players get a high value of $1000 for one player, the other player gets $500. These are joint payments, in addition, if the game is played by a player in unlimited mode, the consequences of conspiracy are not considered legal and risky. All players need to have a good attitude and knowledge of all possible payments so that the consequences of a collision can occur.

Trigger strategy

The trigger strategy is used in non-cooperative repeating games. In trigger strategy, one player collaborates to start the game but later exploits another player who has shown a flaw in the game. Trigger strategies do not lead to cooperative outcomes in a repeated game as cooperation exists only till the opponent works jointly, as soon as the opponent stops working jointly, cooperation ceases to exist.

Interest Rate

The interest rate is used as a discount factor to determine future payments. In repetitive games, each player receives a payout from each game, but even if many game players play, a total rebate pay-out is added in the final period to achieve the result.

Indefinite or Uncertain final period

An indefinite or uncertain final period is when the game is not ended, i.e., it goes on without stopping or ending. There is no distinct stage where the game halts. There is no certainty regarding if there will be a final period or which stage is the final period.

Nash equilibrium is the best for players to play confidently.