Excess entry in an experimental winner-take-all market

doi:10.1016/j.jebo.2006.05.018

Journal of Economic Behavior & Organization

Volume 67, Issue 1, July 2008, Pages 150-163

https://doi.org/10.1016/j.jebo.2006.05.018 Get rights and content

Abstract

“Winner-take-all” markets (i.e., markets in which the relative and not the absolute performance is decisive) have gained in importance. Such markets have a tendency to provoke inefficiently many entries. We investigate such markets in an experiment and show that there are even more inefficient entries than predicted by the Nash equilibrium. Moreover, this effect increases with group size. Quantal response equilibrium predicts the increase in group size but fails to predict the excess entry in the smaller group. We show that the excess entry is not caused by coordination failures. Furthermore, individual entry behavior is not significantly linked to risk preferences.

Introduction

For the income of a tennis player it is not important how good he is in absolute terms, but whether he beats others or not. If he is better than others he will earn a lot of money; if not, even if he is very good in absolute terms, he will not be able to earn his living by playing tennis. This criterion serves to qualify professional tennis as a “winner-take-all” market, a market that is characterized by two properties: (i) relative performance is more important for payoffs than absolute performance and (ii) the payoff of the best performers is much higher than the payoff of the second best performers. In the fields of sports and performing arts, the existence of winner-take-all markets is most obvious. However, also in the markets for lawyers, for CEOs, or for academics, relative performance is much more important than absolute performance. An excellent overview of the structure and the economic importance of winner-take-all markets can be found in the book “The Winner-Take-All Society” by Frank and Cook (1995). They convincingly argue that an increasing share of labor and other markets show the characteristics of winner-take-all markets. This is problematic because winner-take-all markets tend to produce an inefficiently high number of entrants to the fact that each person who enters a winner-take-all market imposes an externality onto the other people in the market by reducing their probability to win. There is a lot of evidence that “winner-take-all” markets are inefficient; many young people try to become football stars or actors and very few succeed. Economically more important, many new companies fail, in the US about 60 percent in the first 5 years. However, since we do not know the preferences of the market participants, this evidence is not completely unambiguous.

In this study, we present the first experimental investigation of entry behavior in winner-take-all markets. The experimental method is very well suited to this question because we can control many factors that cannot be controlled in the field. For instance, in an existing winner-take-all market it is hard to know the number of (potential) entrants and their abilities, the payoff people expect to get, the winning probabilities, and the beliefs people hold about others’ entry decisions. As a consequence, we cannot determine the efficient number of entries. Likewise, it is impossible to calculate the Nash equilibria for that particular winner-take-all market. In our experiment, we control for the number of potential entrants, their abilities, the winning probabilities and the payoffs. Hence, we can determine Nash equilibria and the social optimum of our experimental winner-take-all market. Moreover, to be able to determine the rationality of an individual's entry decision, we elicit beliefs about the other subjects’ entry decisions.

Frank and Cook conjecture that the problem of inefficient entries in winner-take-all markets increases with the number of potential entrants. We explore this argument by varying the group size. In one treatment there is a group of 7 potential entrants; in the other, the group size is 11. In our experimental winner-take-all game the social optimum is one entry. The Nash equilibria predict an expected number of entries between 3 and 3.8. Interestingly, group size matters neither for the social optimum nor for the bounds of the Nash equilibria.

In the experiment, we find that there are indeed inefficiently many entries in our winner-take-all market. With a group size of 7, the average number of entries is 4.11; with a group size of 11, on average 5.32 subjects enter. Hence, it turned out that even more people entered than predicted by the Nash equilibrium. This result contradicts the findings of a number of experimental studies on market entry games that report quick convergence to the Nash equilibria (e.g., Sundali et al., 1995). Moreover, and also in contrast to the Nash prediction, this excess entry increases with group size. This trend has an important economic implication: if there are winner-take-all markets, an increase in the number of potential entrants will reduce welfare.

Our experimental design allows us to investigate potential sources of excess entry. Since we elicited subjects’ beliefs about the other players’ entry decisions, we can determine the rationality of each entry decision. We find that on average beliefs are unbiased. We can thus conclude that the observed excess entry is not caused by a coordination failure induced by false beliefs. Even if we control for beliefs, we find that subjects heavily deviate from a rational entry pattern. A theory that explicitly deals with ‘random’ errors is the concept of quantal response equilibrium (QRE). We find that QRE can explain the increase of entries in group size but fails to explain excess entry in our treatment with the smaller group size. A regression analysis shows that there is a substantial heterogeneity among the subjects with respect to the entry decision. Surprisingly, a measure of risk preferences cannot account for this heterogeneity. Thus, to understand excess entry one has to assume that at least a fraction of the subjects gets some utility from entering that goes beyond the monetary payoff.

In Section 2, we describe the experiment, in Section 3, we show the main result and in Section 4, we discuss the result and investigate different reasons for the excess entry. In Section 5, we relate our results to the literature and conclude.

Section snippets

The winner-take-all game

In order to test the functioning of winner-take-all markets in the laboratory, we formulate a winner-take-all game. In this game, all players have to decide simultaneously whether to enter a winner-take-all market or to stay out. We denote by n the number of players and by e the number of players who decide to enter the winner-take-all market (the entrants, 0 ≤ e ≤ n). The players who enter can win a high prize. However, only one player, the winner, actually wins this prize. The size of the prize

Main results

Remember that according to HA₁, the number of entries is above the Nash equilibrium, which is between 3 and 3.80. An overview of the entry decisions is given in Table 3, which shows the average number of entries. Each row shows one period, the non-bold columns show session averages, and the bold columns show averages over a whole treatment. We see that in both treatments and in all periods the average number of entries is much higher than the prediction of the pure strategy Nash equilibrium.

Sources of excess entry

In the previous section, we have seen that there is excess entry and that this excess entry increases with group size. We will now deal with different possible sources of excess entry. First we show that the observed excess entry is not caused by an underestimation of the other players’ entry probabilities. Of course, people make errors in their estimates of how many other players will enter. However, these estimations are not biased in any direction. Second, we compare our results to the

Conclusion

In this paper, we have found excess entry in an experimental winner-take-all market. There is not only excess entry with respect to the social optimum; even more subjects enter than predicted by any Nash equilibrium. Furthermore, we have shown that the number of entries increases with group size even though, in equilibrium, no increase is predicted. The analysis in the previous section has shown that there is (i) large heterogeneity in the frequency of entries into the winner-take-all market,

Acknowledgements

We would like to thank Armin Falk, Ernst Fehr, Simon Gächter, Lorenz Götte, David Grether, two anonymous referees and conference participants of the ESA conference in Grenoble and the EEA conference in Vernice for helpful comments. This paper is part of the EU-TMR Research Network ENDEAR (FMRX-CTP98-0238).

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View full text

Excess entry in an experimental winner-take-all market

Abstract

Introduction

Section snippets

The winner-take-all game

Main results

Sources of excess entry

Conclusion

Acknowledgements

Journal of Economic Theory

Labour Economics

Journal of Economic Behavior and Organization

Games and Economic Behavior

Organizational Behavior and Human Decision Processes

Experimental evidence for attractions to chance

German Economic Review

An experimental analysis of intertemporal allocation behavior

Experimental Economics

Tournaments and piece rates: an experimental study

The Journal of Political Economy

Overconfidence and excess entry: an experimental approach

American Economic Review

Anomalous behavior in a traveler's dilemma?

American Economic Review

z-Tree, Zurich toolbox for ready-made economic experiments

Experimental Economics

The Winner-Take-All Society