Why is reputation important in repeated games?

Game Theory is a general framework that aids in decision making, when your payoff is dependent on the action(s) of other player(s); creating an interdependence in pricing decisions, it also provides useful ways to monitor employees, make other decisions on advertising, coordination and quality (Baye, 2014).

In Game Theory, there are various games for example A. one shot games and B. repeated games, the later is the focus of discussion. Repeated games are when the underlying game is played more than once, that is; played repeatedly leading to perpetual interaction among players. 

Reputation is an established habit or stature, created from an action/actions of the entity. In this instance a “good” reputation is preferred, as it fosters “goodwill and fair treatment” from others. Time and number of games are relevant to the formation, development and use of reputation in games. 

In said repeated games, players sometimes may jointly try to impose a different and better payoff outcome than what Nash Equilibrium offers; this is called a collusion, hence in this scenario -individual players having a reputation is important. The importance are listed below:

1. Reputation can be used to establish common ground and to deter other player(s) from acting off script.
2. A good reputation (which is the acceptance of incentive to collude, following through with the decisions and prescribed actions of the collusion) prevents the initiating of triggers, a bad reputation (which can attained from one action/round) instigates retaliation. 
3. Players are willing to collude with other players with a reputation of reliability and following through. 
4. It creates groundwork for linking the past and the future of player’s behavior.
5. Outcomes are more predictable in a collusion than Nash equilibrium.
6. With loss of a good reputation by one player, the other player(s) choose the Nash Equilibrium.
7. A bad reputation causes loss of “better” payoff on both sides, due to loss of trust 

It is worthy to note that there are valid reasons to maintain a reputation in repeated games; but finite repeated games are not the same. In finite repeated games, there are a known number of times the games are played and in the last period everyone cheats as there are no avenues for retaliation or initiation of the Nash Equilibrium after it. This triggers backwards to the period before the last period and the one before that, so eventually the threat of retaliation is not credible in any period and collusion is not sustainable. Hence the is no need for a reputation in finitely repeated games (Marinakis, 2014). 

Conclusively, collusion is illegal and a way of cheating the consumers through pricing and it is especially felt in a market with very limited sellers, hence it is no surprise that reputation in these games are fickle as it only takes one round/action to undo.

References

Baye, M. (201  . Managerial Economics And Business Strategy. McGrawhill-Hill Companies, Inc. New York, N.Y.  8th ed. P 365

Marinakis, K. (2014). Industrial Organization: Strategy And Competition In Business - Repeated Games. Retrieved from https://www.coursera.org/learn/industrial-organization/lecture/cOisy/8-repeated-games

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