Chainstore paradox
The chainstore paradox is a game-theoretical case study designed by Reinhard Selten in the field of economic competition , in which the best behavior based on rational arguments is in contradiction to empirically obvious behavior. The game is based on the chain store game , in which a competitor enters the market and the market leader, the department store chain, is faced with the choice of either ousting or tolerating the new competitor through a price war. In the department store chain game, the payouts are chosen in such a way that it would be rational for the market leader to tolerate the intruder and not lead a price war that is ruinous for both of them. If a consequence of the market entry of several competitors is considered from the point of view of a department store chain, it seems rational, due to backward induction , if the department store chain generally tolerates market intruders, which is in stark contrast to the market entry battles observed in practice.
Chainstore game and framework
In the “department store chain game” underlying this paradox, a company dominates the market. A competitor now has a choice between entering the market or not. In the latter case, the competitor receives the payout 0, the dominant player receives 5. If the competitor enters the market, on the other hand, the dominant market has the choice of fighting or tolerating it. If he decides to fight, both receive the payout 0, if he tolerates the competitor, both receive the payout 2. The only subgame-perfect Nash equilibrium is the latter variant, i.e. the competitor's entry into the market and tolerance by the dominant.
| Price war | Market division | |
|---|---|---|
| Stay away | 0; 5 | 0; 5 |
| access | 0; 0 | 2; 2 |
Reinhard Selten now created a model on the basis of this game to examine the rationality of the behavior of dominant companies when a competitor enters the market. He assumed the following framework conditions:
- The number of markets considered in this game is limited
- The threats to enter by competitors occur sequentially
- Competitors act in isolation (no cooperation)
- All parties involved are aware of all expected payouts ( perfect information )
- It is not possible for the dominant player to buy up the competitors
In the original version of Selten, the market leader now has 20 branches in different cities. In sequential order, competitors in the various cities are now considering entering the market. In the case of backward induction, the last case is now considered first after the 19 decisions have already been made. In this 20th case, it would be rational for the dominant player to tolerate the intruder. Then the 19th case becomes the last game, whereby the rational decision must be the same here as well, which continues until the first case. So an intruder would always have to be tolerated.
Interpretation of the paradox
Reinhard Selten explained the contradiction between economic reality and the game theory model by stating that in practice decision-makers are not able to carry out the backward induction over many periods.
Another approach to interpret this discrepancy is that Selten's simple model does not include the factor of reputation , which can play a role in practice. However, in the chain store model, the chain store's reputation is worthless in the last period because the game will not continue, and the chain store owner will not invest in reputation by foregoing profits for the purpose of deterrence. This then applies to all periods using backward induction.
An essential prerequisite for the applicability of the backward induction is that the number of repetitions is known. This does not have to be the case: in reality, the market leader usually does not know how many competitors he will have to defend against. In this case he may also fight the last competitor to maintain his reputation - he does not know that he has no other competitors.
literature
- Siegfried K. Berninghaus, Karl-Martin Ehrhart, Werner Güth: Strategic games: An introduction to game theory. Springer, Berlin / Heidelberg 2006, ISBN 3-540-28414-1 .
Individual evidence
- ↑ a b Reinhard Selten: The chain store paradox. In: Theory and Decision , 9, pp. 127–159, 1978 ( doi: 10.1007 / BF00131770 )
- ↑ Thorsten W. Pries: Combat price abuse in the economized EC cartel law. Mohr Siebeck, 2009, ISBN 3-16-150166-7 , p. 25 ff.
- ^ A b Siegfried K. Berninghaus, Karl-Martin Ehrhart, Werner Güth: Strategic games: An introduction to game theory. Springer, Berlin / Heidelberg 2006, ISBN 3-540-28414-1 , pp. 107-112