Chainstore paradox

The chain -store paradox is a building designed by Reinhard Selten game theoretical case study in the field of economic competition in which the best behavior is contrary to the empirically obvious behavior of rational arguments. The game is the department store chain game ( chain store game) based in which a competitor enters the market and the market leader, the department store chain, before the election is to displace the new competitors through a price war or to tolerate him. At the department store chain play the payouts are chosen so that it would be rational if the leader tolerates the intruder and no leads for both ruinous price war. Now, if a sequence of market entry of several competitors is viewed from the perspective of a department store chain, it seems rational because backward induction, when the department store chain generally tolerated market intruders, which is in strict contrast to the observed in practice, market entry campaigns.

Chainstore Game and conditions

In the paradox underlying this " department store chain game" controlling an entity to market. Now a competitor has the choice to enter the market or to refrain from it. In the latter, the competitor receives the payoff 0, the dominant firm receives 5 ​​If the competitor contrast to the market, the dominant undertaking has the choice to fight this or tolerate. If he opts for the fighting, both receive the payoff 0, it tolerates the competitors, both receive the payment 2 The only subgame perfect Nash equilibrium is the latter variant, ie, the market entry of competitors and the tolerance by the dominant.

Reinhard Selten now created on the basis of this game is a model to examine the rationality of the behavior of dominant firms in market entry of competitors. He imputed the following conditions:

• The number of observed at this game markets is limited
• The entry threats by competitors occur sequentially
• The competitors act isolated ( no cooperation )
• All participants are all expected payoffs are known ( Perfect Information )
• The buying up of competitors by the dominant is not possible

In Selten's original version now has the dominant market 20 branches in different cities. Now considering to enter competitors in the various cities in the market in a sequential order. In the backward induction we now consider first the latter case, after the 19 decisions have already been made previously. In this 20 case, it would now be rational for the dominant to tolerate the intruder. Then the 19 case for the last game, the rational decision must be the same here as well, which continues up to the first case. Thus, an intruder would have to be always tolerated.

Interpretation of the paradox

Reinhard Selten has the contradiction between economic reality and game theoretical model explained by the fact that decision-makers are unable in practice to carry out the backward induction over many periods.

Another approach to interpret this discrepancy is that Selten's simple model is not the factor of reputation includes that can play a role in practice.