# Talk:Repeated game

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## Overtaking?

The last paragraph in Section 2, beginning with "Overtaking", seems truncated. --Erel Segal (talk) 20:52, 1 August 2015 (UTC)

Dr. Korenok has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

1. Original : "The presence of different equilibrium properties is present because the threat of retaliation is real, since one will play the game again with the same person."

Comment: The sentence is not clear. Here is an alternative version: "Reputation changes the set of equilibria in the repeated game compared to equilibria in the stage game."

2. Original: "Even finitely repeated games are not necessarily finite horizon, the player may just perceive a probability of another cycle and act accordingly. For example, the fact that everyone has a fixed lifetime doesn't mean that all games should be finite horizon. Also, players might act differently when the horizon is far away as opposed to when it is close by, which can probably be thought of as a time modifier function applied to the payoff."

Comment: Very unclear. Either clarify or delete.

3. Original: "The most widely studied repeated games are games that are repeated a possibly infinite number of times."

Comment: Why possibly? "The most widely studied repeated games are games that are repeated infinite number of times."

4. Original: "On many occasions, it is found that the optimal method of playing a repeated game is not to repeatedly play a Nash strategy of the constituent game (look at the Repeated prisoner's dilemma example), but to cooperate and play a socially optimum strategy. This can be interpreted as a "social norm" and one essential part of infinitely repeated games is punishing players who deviate from this cooperative strategy. The punishment may be something like playing a strategy which leads to reduced payoff to both players for the rest of the game (called a trigger strategy)."

Comment: This description is correct for Prisoner's Dilemma. Propose to state this upfront and tighten language a bit. "In iterated prisoner's dilemma games (https://en.wikipedia.org/wiki/Prisoner%27s_dilemma#The_iterated_prisoner.27s_dilemma), it is found that the optimal strategy is not to play a Nash strategy of the stage game, but to cooperate and play a socially optimum strategy. An essential part of optimal strategy in infinitely repeated game is punishing players who deviate from this cooperative strategy. The punishment may be playing a strategy which leads to reduced payoff to both players for the rest of the game (called a trigger strategy)."

5. Original: "There are many different ways in which a preference relation may be modeled in an infinitely repeated game, the main ones are..."

Comment: v(t) is not defined.

6. Original: "In the first class of finitely repeated games where the time period is fixed and known, it is optimal to play the Nash strategy in the last period. When the Nash Equilibrium payoff is equal to the minmax payoff, then the player has no reason to stick to a socially optimum strategy and is free to play a selfish strategy throughout, since the punishment cannot affect him (being equal to the minmax payoff). This deviation to a selfish Nash Equilibrium strategy is explained by the Chainstore paradox."

Comment: Isn't it optimal for all periods due to backward induction? "In the first class of finitely repeated games where the time period is fixed and known, it is optimal to play the Nash strategy of the stage game in all periods."

7. Repeated prisoner's dilemma section.

Comment: There is iterated prisoner's dilemma section on a different wiki page: https://en.wikipedia.org/wiki/Prisoner%27s_dilemma#The_iterated_prisoner.27s_dilemma

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Korenok has published scholarly research which seems to be relevant to this Wikipedia article:

• Reference 1: Asen Ivanov & Douglas D. Davis & Korenok Oleg, 2011. "A Simple Approach for Organizing Behavior and Explaining Cooperation in Repeated Games," Working Papers 1101, VCU School of Business, Department of Economics.
• Reference 2: Douglas Davis & Asen Ivanov & Oleg Korenok, 2014. "Individual Characteristics and Behavior in Repeated Games: An Experimental Study," Working Papers 728, Queen Mary University of London, School of Economics and Finance.

ExpertIdeasBot (talk) 15:37, 24 June 2016 (UTC)

Dr. Normann has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

The distinction of finitely vs. infinitely repeated games is probably more confusing than clarifying. I do not think that the sentence "The second class of finitely repeated games are usually thought of as infinitely repeated games" will be understood by many in a simple Wiki article.

Given the emphasis on finite vs. infinite, it is surprising that the following is missing: finitely repeated games can have (repeated game) SGPNE when the stage game has more thna one Nash equilibrium.

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Normann has published scholarly research which seems to be relevant to this Wikipedia article:

• Reference : Fonseca, Miguel A. & Normann, Hans-Theo, 2012. "Explicit vs. tacit collusion: The impact of communication in oligopoly experiments," DICE Discussion Papers 65, HeinrichHeineUniversitat Dusseldorf, Dusseldorf Institute for Competition Economics (DICE).

ExpertIdeasBot (talk) 18:38, 27 June 2016 (UTC)

Dr. Schlag has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

I would give the title "Repeated games".

I have never heard of the term "iterated game", this should be removed.

The following statement "It can be proved that every strategy that has a payoff greater than the minmax payoff can be a Nash Equilibrium" is incorrect as it only holds for infinitely repeated games with sufficiently high discount factor.

The paragraph on "Finitely vs infinitely repeated games" needs to be redone, it does not contain any description of what a finitely repeated game is.

There is no "optimal method of playing a repeated game".

The overtaking criterion is insufficiently explained and should be dropped as it is only of secondary interest.

The author needs to clearly write how trigger strategies work to sustain cooperation in the repeated prisoners' dilemma.

Repated games are easy to solve, the variious papers on the folk theorem show us how.

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Schlag has published scholarly research which seems to be relevant to this Wikipedia article:

• Reference : Karl Schlag & Andriy Zapechelnyuk, 2010. "On the Impossibility of Regret Minimization in Repeated Games," Working Papers 676, Queen Mary University of London, School of Economics and Finance.

ExpertIdeasBot (talk) 18:58, 27 June 2016 (UTC)

## Title Change?

As mentioned in Dr. Schlag's expert comments, perhaps the title should be changed to "Repeated Games". I am not sure if this is possible to change on this page, or if a new page would have to be created to implement this change.

Benvanschaayk (talk) 23:55, 15 December 2016 (UTC)