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;

Extreme Associated Functions: Optimally Linking Local Extremes to Large-scale Atmospheric Circulation Structures

We present a new statistical method to optimally link local weather extremes to large-scale atmospheric circulation structures. The method is illustrated using July-August daily mean temperature at 2m height (T2m) time-series over the Netherlands and 500 hPa geopotential height (Z500) time-series over the Euroatlantic region of the ECMWF reanalysis dataset (ERA40). The method identifies patterns in the Z500 time-series that optimally describe, in a precise mathematical sense, the relationship with local warm extremes in the Netherlands. Two patterns are identified; the most important one corresponds to a blocking high pressure system leading to subsidence and calm, dry and sunny conditions over the Netherlands. The second one corresponds to a rare, easterly flow regime bringing warm, dry air into the region. The patterns are robust; they are also identified in shorter subsamples of the total dataset. The method is generally applicable and might prove useful in evaluating the performance of climate models in simulating local weather extremes.Comment: 10 pages, 7 figures, 14 eps figure files; to appear in J. Atmos. Chem. Phy

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

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

Social Conformity in Games with Many Players

In the literature of psychology and economics it is frequently observed that individuals tend to imitate similar individuals. A fundamental question is whether the outcome of such imitation can be consistent with self-interested behaviour. We propose that this consistency requires the existence of a Nash equilibrium that introduces a partition of the player set into relatively few groups of similar individuals playing the same or similar strategies. In this paper we define and characterize a family of games admitting existence of approximate Nash equilibria in pure strategies that introduce partitions of the player sets with the desired properties. We also introduce the Conley-Wooders concept of 'crowding types' into our description of players and distinguish between the crowding type of a player - those characteristics of a player that have direct effect on others - and his tastes, taken to directly affect only that player. With the assumptions of 'within crowding type anonymity' and a 'convexity of taste-types' assumption we show that the number of groups can be uniformly bounded.