The Chain Store Paradox

It is the purpose of this paper to present the 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. A story about a fictitious chain store and its potential competitors is a convenient way to describe the game. This expositionary device should not be misunderstood as a model of a real situation. In view of the story the game will be called "the chain store game". The disturbing disagreement between plausible game behavior and game theoretical reasoning constitutes the "chain store paradox". The chain store paradox throws new light on the well known difficulties which arise in connection with the finite supergame of prisoners' dilemma game. A limited rationality approach seems to be needed in order to explain human strategic behavior. An attempt shall be made to discuss the possibility of a "tree-level theory of decision making" as an explanation of discrepancies between game theoretic analysis and human behavior.

Multistage Game Models and Delay Supergames

Prize Lecture to the memory of Alfred Nobel, December 9, 1994.Game Theory;

Individual Behavior of First-Price Sealed-Bid Auctions: The Importance of Information Feedback in Experimental Markets

This article reports the results of a first-price sealed-bid auction experiment, which has been designed to test the Nash equilibrium predictions of individual bidding behavior. Subjects faced in 100 auctions always the same resale value and competed with computerized bids. Three treatments were considered which varied with the conditions of information feedback. In earlier experimental work an overbidding above the risk neutral Nash equilibrium has been frequently reported. Our data provide evidence that this overbidding regularity can be a consequence of the standard information feedback in auction experiments of revealing only the winning bid after each auction. By means of learning direction theory we explain the individual bidding dynamics. Finally we apply impulse balance theory and make long run predictions of the individual bidding behavior.Experimental economics, first-price sealed-bid auctions, independent private value model, computerized competitors, bidding theory, risk aversion

Risk in a Simple Temporal Framework for Expected Utility Theory and for SKAT, the Stages of Knowledge Ahead Theory

The paper re-expresses arguments against the normative validity of expected utility theory in Robin Pope (1983, 1991a, 1991b, 1985, 1995, 2000, 2001, 2005, 2006, 2007). These concern the neglect of the evolving stages of knowledge ahead (stages of what the future will bring). Such evolution is fundamental to an experience of risk, yet not consistently incorporated even in axiomatised temporal versions of expected utility. Its neglect entails a disregard of emotional and financial effects on well-being before a particular risk is resolved. These are arguments are complemented with an analysis of the essential uniqueness property in the context of temporal and atemporal expected utility theory and a proof of the absence of a limit property natural in an axiomatised approach to temporal expected utility theory. Problems of the time structure of risk are investigated in a simple temporal framework restricted to a subclass of temporal lotteries in the sense of David Kreps and Evan Porteus (1978). This subclass is narrow but wide enough to discuss basic issues. It will be shown that there are serious objections against the modification of expected utility theory axiomatised by Kreps and Porteus (1978, 1979). By contrast the umbrella theory proffered by Pope that she has now termed SKAT, the Stages of Knowledge Ahead Theory, offers an epistemically consistent framework within which to construct particular models to deal with particular decision situations. A model by Caplin and Leahy (2001) will also be discussed and contrasted with the modelling within SKAT (Pope, Leopold and Leitner 2006).

Impulse Balance Equilibrium and Feedback in First Price Auctions

Experimental sealed-bid first-price auctions with private values in which feedback on the losing bids is provided yield lower revenues than auctions where this feedback is not given. The concept of weighted impulse balance equilibrium, which is based on a principle of ex post rationality and incorporates a concern for social comparison, captures the data.Auctions; Overbidding; Feedback; Experiments; Ex-post rationality; Bounded rationality; Social comparison

Experimentally Observed Imitation and Cooperation in Price Competition on the Circle

This paper reports an experiment on a location game, the so-called "Price-Competition on the Circle." There are n symmetric firms equidistantly located on a circle. Consumers are uniformly distributed. Each consumer buys one and only one unit from that firm whose price, including the cost of transportation, is the lowest, provided such a price is below a maximum willingness to pay. Experiments, extended over 200 periods, were run with 3, 4, and 5 participants. Subjects did not receive any information about the relationship between prices and profits, but they received feedback on prices and profits of two neighbors after each period. The evaluation compares predictions derived from imitation equilibrium (Selten and Ostmann 2001) and Cournot equilibrium, as well as symmetric joint-profit maximization. The results qualitatively favor imitation equilibrium, as long as no cooperation is observed.Imitation, Cooperation, Location, Experiments

Experimental Investigation of a Cyclic Duopoly Game

The notion of a cyclic game has been introduced by Selten and Wooders (2001). They illustrate the concept by the analysis of a cyclic  duopoly game. The experiments reported concern this game. The game was played by eleven matching groups of six players each. The observed choice fre- quencies were compared with the predictions of Nash equilibrium, impulse balance equilibrium (Selten, Abbink and Cox (2005), Selten and Chmura (2007)) and two-sample equilbrium (Osborne and Rubinstein(1998)). Pair- wise comparisons by the Wilcoxon Signed-rank test show that impulse balance equilibrium as well as two-sample equilibrium have a significantly better predictive success than Nash equilibrium. The difference between impulse balance equilibrium and two-sample equilibrium is not   significant.In each matching group three players acted only in uneven periods and   the other three only in even periods. This game has two pure strategy equi- libria in which both types of players behave differently. The data exhibit a weak but significant tendency in the direction of coordination at a   pure strategy equilibrium.cyclic game duopoly experiment, impulse balance equilibrium, two-sample equilibrium

Die konzeptionellen Grundlagen der Spieltheorie einst und jetzt

Das fundamentale Werk von John von Neumann und Oskar Morgenstern (1944) hat die Spieltheorie als Gebiet begründet. Es gab zwar vorher schon den in deutscher Sprache veröffentlichen Beitrag von John Neumann (1928) " Zur Theorie der Gesellschaftsspiele", aber erst mit dem Buch aus dem Jahre 1944 wurde in der wissen-schaftlichen Welt genügend Aufmerksamkeit erregt, um einen breiteren Strom von Forschung in Gang zu setzen. Die offenen Fragen, vor allem im Bereich der kooperativen von Neumann-Morgenstern-Lösungen, boten Anknüpfungspunkte für mathematisch anspruchsvolle weiterführende Forschung. In diesem Beitrag soll dargestellt werden, wodurch sich das spieltheoretische Konzept von von Neumann und Morgenstern von den heute vorherrschenden Auffassungen unterscheidet, und wie es aus der damaligen Zeit heraus verstanden werden kann.kooperative Spieltheorie, kardinale Nutzentheorie, Zwei-Personen-Nullsummenspiele, von Neumann-Morgenstern-Lösungen, charakteristische Funktion

Learning in experimental 2 x 2 games

In this paper, we introduce two new learning models: impulse-matching learning and action-sampling learning. These two models together with the models of self-tuning EWA and reinforcement learning are applied to 12 different 2 x 2 games and their results are compared with the results from experimental data. We test whether the models are capable of replicating the aggregate distribution of behavior, as well as correctly predicting individuals' round-by-round behavior. Our results are two-fold: while the simulations with impulse-matching and action-sampling learning successfully replicate the experimental data on the aggregate level, individual behavior is best described by self-tuning EWA. Nevertheless, impulse-matching learning has the second highest score for the individual data. In addition, only self-tuning EWA and impulse-matching learning lead to better round-by-round predictions than the aggregate frequencies, which means they adjust their predictions correctly over time.learning, 2 x 2 games, Experimental data

Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games

The concept of a perfect equilibrium point has been introduced in order to exclude the possibility that disequilibrium behavior is prescribed on unreached subgames. (Selten 1965 and 1973). Unfortunately this definition of perfectness does not remove all difficulties which may arise with respect to unreached parts of the game. It is necessary to reexamine the problem of defining a satisfactory non-cooperative equilibrium concept for games in extensive form. Therefore a new concept of a perfect equilibrium point will be introduced in this paper. In retrospect the earlier use of the word "perfect" was premature. Therefore a perfect equilibrium point in the old Sense will be called "subgame perfect". The new definition of perfectness has the property that a perfect equilibrium point is always subgame perfect but a subgame perfect equilibrium point may not be perfect. It will be shown that every finite extensive game with perfect recall has at least one perfect equilibrium point. Since subgame perfectness cannot be detected in the normal form, it is clear that for the purpose of the investigation of the problem of perfectness, the normal form is an inadequate representation of the extensive form. It will be convenient to introduce an "agent normal form" as a more adequate representation of games with perfect recall.