Chain Store Game Research Articles

Does Informational Equivalence Preserve Strategic Behavior? Experimental Results on Trockel’s Model of Selten’s Chain Store Story

The purpose of this study is to experimentally test Trockel’s game, which is a modelling of the classical Chain Store Game (CSG), and determine whether one of the two theories of Equality and Deterrence may better account for the observed behavior. The CSG is an example of a simple game in extensive form where the actual behavior of well-informed players cannot be expected to agree with the clear results of game theoretical reasoning. To explain the disagreement between the theory and the expected behavior, Trockel’s game is proposed as an alternative modelling of the scenario. The existence of more than one equilibrium in Trockel’s game opens a door for reputation building. This study is the first attempt to experimentally test this alternative game with the same purpose. According to my data, there is some evidence in favor of both Equality and Deterrence Hypotheses. However, since the strategies compatible with the Equality Hypothesis are played more frequently, I observe some patterns which share the same intuition with the Deterrence Hypothesis.

Multiple rounds in a chain store game

In textbook models of reputation, a number of entry games are played sequentially. A multimarket incumbent—the chain store—deters entry of “early” small entrants with a threat of predation. In the last markets of the game, entry occurs stochastically. We show that this stochastic entry is due to a restrictive assumption and vanishes if entrants that initially decided to stay out are allowed to reconsider their decision following entry elsewhere.

Paradox Lost: The Evolution of Strategies in Selten’s Chain Store Game

The classical game theoretic resolutions to Selten's Chain Store game are unsatisfactory; they either alter the game to avoid the paradox or struggle to organize the existing experimental data. This paper applies co-evolutionary algorithms to the Chain Store game and demonstrates that the resulting system's dynamics are neither intuitively paradoxical nor contradicted by the existing experimental data. Specifically, some parameterizations of evolutionary algorithms promote genetic drift. Such drift can lead the system to transition among the game's various Nash Equilibria. This has implications for policy makers as well as for computational modelers.

Chain store game based channel allocation in cognitive radio system

In adaptive channel allocation for secondary user (SU) of cognitive radio (CR) system, it is necessary to consider allocation process from the temporal perspective. In this article, a chain store game is modeled to achieve SU's equilibrium state. Due to the computational complexity of solving equilibrium states, the authors explore the correlated equilibrium (CE) by importing signal mechanisms based on time and sequence number. Also, correlated equilibrium based game algorithms are presented. Simulations show that these algorithms are superior to other allocation algorithms both in channel utilization and communication time.

Reputation and exogenous private learning

Short-run competitors in the chain store game receive noisy signals of the long-run incumbent firm's type. The history of signals, which in the limit is fully revealing, is observable to the competitors but possibly not to the incumbent. As long as there is sufficient noise in the signals, then in any equilibrium a patient weak incumbent obtains a payoff strictly higher than her minmax payoff.

Reputation and impermanent types

I consider a version of the chain store game where the incumbent firm's type evolves according to a Markov process with two states: a “tough” type who always fights entry, and a “weak” type who prefers to accommodate. There exists a minimal level of persistence necessary for the incumbent to be able to sustain any reputation for being tough. Above that level, as the number of markets T increases, in equilibrium play alternates between intervals of entry by competitors and intervals of deterrence. When T is infinite, then regardless of the discount factor there exists a sequential equilibrium in which entry occurs in a positive fraction of the markets. One interpretation is that reputation is not permanent, but must be renewed occasionally.

REPUTATION BY IMITATION: AN EVOLUTIONARY MODEL WITH STRATEGIC MATCHING

This paper shows how strategic matching generates reputation-building behavior in an evolutionary chain-store game. Strategic matching means the possibility for an entrant to choose in a strategic way the local market into which it will move. Players are boundedly rational and follow behavioral rules simply requiring that the frequency of any strategy enjoying the highest payoff should never decrease. In preventing the random entries in markets of "fighting monopolists", strategic matching reinforces the reputation effects. Using the bounded rationality set-up offered by evolutionary game theory, the paper follows Selten (1978)'s intuition underlying the necessity of a limited rationality approach in order to capture reputation effects.

Value of reputation in the chain-store game with multiple incumbents

We extend the basic chain-store game to the two-incumbent case. A highly stylized model is developed to analyze incentives of incumbent firms to maintain reputation for toughness. Entry deterrence has a public good property. Since maintaining reputation is costly, each incumbent has an incentive to free ride on the entry deterring activities of its counterpart. As a result of these incentives, both incumbents accommodate when they both have a relatively high initial reputation for toughness. This extreme form of underinvestment in entry deterrence becomes less likely as the number of markets with potential entry increases. We also demonstrate that an incumbent's payoff is a decreasing function of its reputation over a large range of parameters. This result stands in sharp contrast to the existing versions of the chain-store game where high reputation for toughness always benefits a weak incumbent.

Rationality, Nash Equilibrium and Backwards Induction in Perfect- Information Games

We say that a player is certain of an event A if she assigns probability 1 to A. There is common certainty (CC) of A if the event A occurred, each player is certain of A, each player is certain that every other player is certain of A, and so forth. It is shown that in a generic perfect-information game the set of outcomes that are consistent with common certainty of rationality (CCR) at the beginning of the game coincides with the set of outcomes that survive one deletion of weakly dominated strategies and then iterative deletion of strongly dominated strategies. Thus, the backward induction outcome is not the only outcome that is consistent with CCR. In particular, cooperation in Rosenthal's (1981) centipede game, and fighting in Selten's (1978) chainstore game are consistent with CCR at the beginning of the game. Next, it is shown that, if in addition to CCR, there is CC that each player assigns a positive probability to the true strategies and beliefs of the other players, and if there is CC of the support of the beliefs of each player, then the outcome of the game is a Nash equilibrium outcome.

Learning, reputation and entry deterrence: A chain-store game with correlated entrants

This paper presents a chain-store game in which the entrants' types are correlated. It argues that the uninformed incumbent will experiment to strategically learn (or to remain uninformed about) the entrants' types and play tougher (or softer) initially when another potential entrant exists.

Stability and the Chain Store Paradox

For the Kreps and Wilson version of Selten′s Chain Store Game, every equilibrium of every stable set induces the same outcome. This unique outcome is that induced by the Kreps and Wilson solution. Journal of Economic Literature Classification Numbers: C72.

On the Existence of Predatory Pricing: An Experimental Study of Reputation and Entry Deterrence in the Chain-Store Game

A single monopolist plays a sequence of eight periods against a series of different entrants. There are two types of monopolists, monopolists whose single-period best response is to acquiesce after entry, and monopolists whose dominant strategy is to fight entry. Data show high levels of predatory pricing, defined as weak monopolists fighting all entrants in early periods, both with and without experimenter-induced strong monopolists. We reject a number of predictions of the asymmetric-information, sequential equilibrium model of Kreps and Wilson (1982) and find important deviations from more general sequential equilibrium models as well.

Reputation and imperfect information

A common observation in the informal literature of economics (and elsewhere) is that is multistage “games,” players may seek early in the game to acquire a reputation for being “tough” or “benevolent” or something else. But this phenomenon is not observed in some formal game-theoretic analyses of finite games, such as Selten's finitely repeated chain-store game or in the finitely repeated prisoners' dilemma. We reexamine Selten's model, adding to it a “small” amount of imperfect (or incomplete) information about players' payoffs, and we find that this addition is sufficient to give rise to the “reputation effect” that one intuitively expects.

Games of perfect information, predatory pricing and the chain-store paradox

The thesis of this paper is that finite, noncooperative games possessing both complete and perfect information ought to be treated like one-player decision problems. That is, players ought to assign at every move subjective probabilities to every subsequent choice in the game and ought to make decisions via backward induction. This view is in contrast with the gametheoretic approach of Nash equilibrium. After expanding on this view for games in the abstract in Sections 2 and 3, attention is turned in Section 4 to an example due to Reinhard Selten, called the chain-store paradox, which possesses the flavor of a situation involving a predatory-pricing monopolist. It is argued that for the chain-store game the decision-analytic approach leads, under certain assumptions, to more realistic outcomes than the standard Nash-equilibrium approach.