Talk:Chainstore paradox

logical inescapability of the induction argument
" The logical inescapability of the induction argument is unable to destroy the allure of the deterrence theory ".......I wonder what this means in plain words. 82.38.112.68 11:12, 7 July 2007 (UTC) mikeL
 * I would love to know this, too. I don't agree that the game theory payoffs presented in the first section is complete as stated. The deterrence argument is based on the idea that each competitor expects the chain store to act irrationally. The major failing of saying that "the deterrence explains this better than game theory" is that game theory is predicated on complete information. The probability that the chain store will retaliate is not known, and thus the payoff numbers given cannot be applied!--Agamemnus (talk) 03:49, 14 January 2011 (UTC)
 * So, in other words, if we assume that each player acts rationally (and I believe they do, in the final analysis), then the problem as presented does not completely define the payoff matrix. To be able to calculate the payoff matrix, we must know the full strategy of the monopolist -- how he responds to his competitor's decision. In the case of multiple games, the initial payoff matrix is insufficient because the monopolist's strategy is a result of not just one company's response, but of all the companies' responses.--Agamemnus (talk) 08:07, 15 January 2011 (UTC)
 * Ok. This is an incredible article!  I think I might know why this is difficult to understand.  But since it has been around since 1974, I would think it is explained somewhere.  I'll state the basic idea first, as I see it.  The basic idea that Selten demonstrates to me is simply "economic behavior" with and without perceived shortages.  In any time-limited game, such the Chain store game, time becomes scarce.   At move 20, in this game.  There is no more time.  This is easily perceived by the players.  That is, if the chain store owner decides to act AGGRESSIVE, this information influences no future players, so deterrence has no value.
 * Does this make sense? However, at move 1,  the decisions of 19 other players still occur over 19 other time periods.   AGGRESSIVE behavior at move 1 could result in the perception of the threat of aggression to other players.  If so, this perception will discourage the other players, along the way.  And Player A will receive a higher payoff when the deterrence works.  At move 20 it no longer is needed and both Player A and Player 20 probably perceives this.  By induction Player 19 also probably perceives this as well at move 19.  The perception blurs as you go backward in time so that at moves 1 and 2, time seems less limited.
 * Here is another time limited game. I was watching some hummingbirds last night at a hummingbird feeder.  During the day, they act aggressive to try to frighten each other off the feeder so they can control it exclusively.  However, as night begins to fall, they are less interested in deterrence of other hummingbirds.  As darkness falls, in fact, 5 of them sit on the feeder at once and others wait patiently 15 feet away for their chance.
 * In sum, economic behavior is influenced by the perception of shortages.
 * To help eliminate confusion, I'd say just forget the word "theory" in the article. As Selten uses it, I think simply  explains the influence that the perception of a future shortage has on decisions and behavior. This use is not to explain some "economic theory" but to explain a player's own theory in making an economic decision. The idea is simply this perception influences their economic decision making.  Friedman's "consumer confidence" idea is a similar idea (see J. Brad DeLong's "Friedman completes Keynes")(I've yet to see Friedman applied to hummingbirds, where as Selten's article seems applicable, to me.  RichardKatz (talk) 18:04, 19 March 2011 (UTC)

removed two sections explaining paradox
I pulled out this and this, which were recently added. I don't completely understand what they're saying, but there's some mistakes in them which I think are substantive.

First, this is quintessentially a dynamic game, and so would not typically be represented in payoff matrices. If one chose to depict it graphically rather than with words (as is done in the article), it would be represented by a cumbersomely large game tree instead. And in this, the editor who added that material and I might be in agreement-that thinking in terms of a one-period payoff matrix isn't very helpful.

This material included the text, Player A's competitors look at Player A's actions in previous game rounds to determine what course of action to take: this information is missing from the payoff matrix! The way the game s described, and as a game of complete information, the previous actions will not affect Player B's payoffs. They will affect affect Player A's payoffs but not in a strategically relevant way because whatever they've earned in the previous rounds will be a constant added to Player A's payoffs regardless of what A or their competitor does in the current round. Basically, they're a sunk cost (or sunk benefit, depending).

I'm not sure I fully understand what the edits were trying to say, so I might be misunderstanding. Or, if you're not familiar with the chain-store paradox from other sources, the description in this article might be confusing to you. C RETOG 8(t/c) 10:13, 25 February 2011 (UTC)
 * You should not remove entire sections on a whim... I'm not very happy to see this section, which I carefully worked on and worded, entirely gone without any sort of discussion. Let me address your concerns instead.
 * First of all, what is wrong with this?
 * "And in this, the editor who added that material and I might be in agreement-that thinking in terms of a one-period payoff matrix isn't very helpful."
 * So... why remove this part if you agree???
 * "The way the game s described, and as a game of complete information, the previous actions will not affect Player B's payoffs." This is where you make the mistake: saying "player B". There is no player B. There are competitors to Player A. The previous rounds ("actions" as you say) do affect the payoff matrix (you say "payoffs") of the later rounds, as described in the "deterrence theory" section: the key point here is that Player A is playing one game of X decisions with his competitors, not repeated games with Player B. I describe this as clearly as possible. :-\ --Agamemnus (talk) 09:00, 28 February 2011 (UTC)
 * "Or, if you're not familiar with the chain-store paradox from other sources, the description in this article might be confusing to you." I'm not sure what you're saying here. If the description of the game is confusing, rewrite that section instead of blanking my work.
 * And as you mentioned in your undo comment: there is no visible payoff matrix image, but it is described in the initial paragraphs. If you want to add a payoff matrix image, be my guest!
 * If you're going to blank something, you should blank the description of "Selten's" explanation, because it's complete nonsense.
 * --Agamemnus (talk) 09:00, 28 February 2011 (UTC)


 * The description of the game describes a dynamic game: "They do so in sequential order and one at a time.". Such games can be depicted with matrices, but usually aren't because it's not a very useful way to show them. Instead, they're normally shown with game trees.
 * You're right, I got sloppy referring to "Player B". I meant "the competitor of player A who is currently under consideration". How about we call them "Player i", where i=1,2,3,...,20? According to standard analysis, Player 19 doesn't need to think about what's happened with Players 1, 2, ..., 18, but only needs to think about what will happen for themself and Player 20. The way the game is set up, what happened previously doesn't affect Player 19's payoffs, and affects Player A's payoffs in a not-strategically-relevant way.
 * Phrasing needs to be really careful: Game theory is a large field, with different ways of looking at problems, including behavioral game theory where the players might not behave a a traditionally "rational" fashion. So, we don't want to attribute something to simply "game theory" but to something more narrow. That narrowness can come from specificity, in this case probably attributing it to subgame perfect equilibrium, or I'd often rephrase things more generally to "standard game-theory analysis" or something like that.
 * It's still possible that the main problem is that I don't quite understand what you're trying to say, otherwise, I could try to help figure out how to rephrase it. C RETOG 8(t/c) 15:51, 28 February 2011 (UTC)
 * In the "deterrence theory" paragraph, there is a description that shows Player i does know what strategy Player A took in regards to Player i-1's strategy: "If a few do test the chain store early in the game, and see that they are greeted with the aggressive strategy, the rest of the competitors are likely not to test any further.". That is the root of the paradox: it is initially implied that each round is separate, but in fact it is not. In your terms, there is no "subgame perfect equilibrium" in this game.--Agamemnus (talk) 18:43, 28 February 2011 (UTC)
 * Agamemnus clearly is unfamiliar with game theory, which is unusual for writing a game theory article. The use of induction shows that an SPE exists (contrary to Agamemnus’s claim that none exists). In explaining what is wrong with this: first of all the word optimal is used very loosely; its definition seems to vary from sentence to sentence. Perhaps Agamemnus does not realise that it is a technical term. Secondly, it is incorrect to assert that “game theory states that induction ... should be optimal”; this is most famously refuted by the Prisoner's Dilemma. Lastly, I point out that ‘induction’ is not a strategy itself. In the least, this section is very poorly expressed. --furthermost (talk) 5:11, 31 August 2011 (UTC)
 * I second Cretog8's initial deletion  --furthermost (talk) 5:14, 31 August 2011 (UTC)

Complete information indeed
In reading the previous section of this talk page, I am confused about who did what to whose sections of the article and who is on whose side of the argument. All I know for sure is my position: the payoff matrix as presented in the article is complete and it is a perfect information game. And it doesn't matter to me whether you refer to the 20 competitors collectively as Player B or as Players B through U.

I have always understood chess to be the quintessential example of a perfect information deterministic game. The rules as published by FIDE completely describe how the game is played and who wins or draws. There is no requirement in those rules that each player has to reveal to the other player before the game begins what his/her strategy is and how (s)he would respond to any particular sequence of moves of the opponent. Aside from the fact that this would take more time to do than my entire life expectancy, I don't believe I know how I would respond to every possible position of the board (that is, the positions of all the pieces, whether either player has castled, etc.) presented to me. If I did, I wouldn't take any time at all to speak of to make a move, or to solve the chess puzzles (white to play and win in 3 moves, etc.) in newspapers. None of this changes the fact that the published rules of chess are complete, and the game is one of perfect information in the game-theoretic sense. And so is the chainstore game. -Hccrle (talk) 03:00, 2 December 2011 (UTC)

Nash Equilibrium
The article claims that the deterrence strategy is not a Nash equilibrium; I am not convinced this is true. If you assume a status pro ante that player A is always aggressive and player B always chooses "out", then no player can improve their outcome by changing only their strategy, which is the definition of a Nash equilibrium (according to its Wikipedia page).

(A scenario where B always chooses "in" and A always cooperates is also a Nash equilibrium, of course.) --Antistone (talk) 04:53, 8 June 2017 (UTC)


 * I agree. The single occurrence where one competitor chooses to enter or not and the monopolist responds has multiple pure strategy Nash equilibria. One is  and one is . However,  is the subgame-perfect Nash equilibrium. This should probably be included in the article.
 * The distinction here is that this is a repeated game. It seems more likely to be a Bayesian game, where the monopolist is one of two possible types, one aggressive and one not.
 * I think I will read the original description by Selton and see if I can clean this article up a little. Tommy2024 (talk) 03:43, 30 March 2024 (UTC)

Chainstore Paradox vs Ultimatum Game
It seems to me that the Chainstore Paradox is basically just a more complicated version of the Ultimatum Game.

In the Ultimatum Game, the game-theoretic solution is for the proposer to offer the smallest possible positive amount to the responder, and then for the responder to accept, because any positive amount is better than nothing. In reality, human beings rarely behave that way (either because they are irrational, or because they are acting rationally in a context that is broader than the game being played), and so this strategy doesn't work in real life.

In the Chainstore Paradox, the game-theoretic solution is for B to always choose "in" and for A to always cooperate. If all players mutually believe that all other players are acting rationally within the context of the game, then this solution is 100% correct. But in real life, a deterrence strategy is likely to work, because once A starts going aggressive, player B will no longer believe that player A is a rational actor (within the context of the game), and the backwards-induction proof establishing B's strategy is only valid under the assumption that player A is a rational actor.

Both games illustrate that real people don't always behave rationally (within the bounds of the game), and that the optimal strategy against a rational player is not necessarily optimal against an irrational one. --Antistone (talk) 05:14, 8 June 2017 (UTC)

Chain store vs Chainstore
Shelton originally described this thought experiment as the "chain store" paradox, not the "chainstore" paradox. Should this be fixed? Tommy2024 (talk) 03:33, 30 March 2024 (UTC)