Measured Games · Paper 16 of 07 · Experimental economics

Market entry

After the entry game of A. Rapoport and colleagues; laboratory results from J. Sundali, A. Rapoport and D. Seale (1995) and C. Camerer and D. Lovallo (1999)

Abstract

Players decide independently whether to enter a market whose capacity supports only some of them. Entry pays when few enter and loses when many do, and every allocation that exactly fills the capacity is an equilibrium, so nothing in the theory says which one occurs. What laboratory groups do instead is track the capacity closely in aggregate from the earliest rounds, while individual behaviour remains highly variable.

Keywordscoordination without communication · capacity · multiple equilibria · overconfidence

1Setup

Setup

A market, a road, a fishing ground or a conference session has room for a certain number. Each of many people decides independently whether to take part. Taking part pays if few others do and costs if many do. Nobody communicates and nobody sees the others' decisions until it is too late.

Every allocation in which exactly the right number enters is an equilibrium, and there are enormous numbers of them. The theory therefore predicts the total and says nothing whatever about who. That would be an unremarkable observation except for what groups actually do.

2The model

The model

# N players, capacity c, m of them enter enter = k ( c - m ) positive if m < c, negative if m > c stay out = 0 # any m = c is a pure equilibrium, so there are C(N, c) of them # nothing in the payoffs selects between them # the symmetric mixed equilibrium has each entering with probability p ≈ c / N for large N # the observable prediction is only about the aggregate E[m] = c

Coordination problems of this shape usually go badly in the laboratory. This one does not, and Kahneman's remark on watching it is the standard quotation: to a psychologist it looks like magic. The aggregate lands on capacity almost immediately while individual behaviour stays noisy and inconsistent.

Figure 1Decentralised entry under a shared capacity

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Entrants per round against capacity

Distribution of entrant numbers · how tightly the group tracks capacity

Individual entry rates · wide spread behind a stable total

Entrants Capacity Excess entry

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Players N

Capacity c

Learning rate

Overconfidence

Capacity—

Mean entrants—

Standard deviation—

Excess entry—

Spread of individual rates—

Round0

Figure 1. Players adjust a private entry propensity by reinforcement from what they earned and what they would have earned, with no communication and no view of anyone else's rule. The aggregate settles on capacity within a handful of rounds while the individual rates stay spread out, which is the finding. Press Change capacity mid-run and watch the group re-find it. Overconfidence raises each player's estimate of their own standing and reproduces the systematic excess entry reported when payoffs depend on skill.

3Results

Results

The game has an embarrassment of equilibria and no principle for choosing among them, so the interesting result was always going to be empirical. Sundali, Rapoport and Seale (1995) and the related experimental literature found that the number of entrants tracks capacity closely, from very early rounds, across a range of capacities and group sizes.

What makes it striking is the gap between levels. Aggregate entry is close to the equilibrium prediction while individual behaviour is not close to anything: people switch, they do not settle into a stable role, and no individual is playing the symmetric mixed strategy in a recognisable way. Whatever produces the aggregate is a property of the population rather than a description of anybody in it.

Camerer and Lovallo (1999) found the systematic exception. When post-entry payoffs depended on the entrants' own skill rather than on chance, entry rose well above capacity and entrants lost money in aggregate. Their explanation was reference group neglect: subjects judged their own ability correctly enough but failed to adjust for the fact that other people were also selecting themselves in on the same basis.

4Evidence

Evidence

The experimental base is laboratory rather than field, and it is substantial. Sundali, Rapoport and Seale (1995) established the tight aggregate tracking with varying capacity, and later work by Rapoport and colleagues extended it to asymmetric payoffs and to sequential entry, with the coordination result largely surviving.

Camerer and Lovallo (1999) is the important complement because it identifies the boundary. Their design let subjects choose whether to enter knowing that payoffs would be ranked by a skill task, and separately let them self-select into the experiment on that basis. Both manipulations produced excess entry, and the effect was strongest among subjects who had knowingly volunteered for a skill-based contest.

Outside the laboratory the framework is the standard reference for excess entry into small business, where survival rates are low and entrants' stated expectations are well above the base rate. That literature is suggestive rather than a test, since capacity is not observable.

5Limitations

Limitations

The learning rule in the figure is one plausible mechanism, not the mechanism. Several different adaptive rules produce tight aggregate tracking, and the experiments do not identify which one people use. Reproducing the aggregate is weak evidence about individual process, which is the same caution the minority game carries.

Capacity is common knowledge in the experiments and almost never is anywhere else. Where entrants have to estimate the capacity as well as decide about it, the coordination result has much less support.

The excess-entry finding is the more robust and the more useful. It says that competitive settings where success depends on relative skill will attract more entrants than they can support, and that the error is not optimism about oneself but a failure to think about who else is deciding at the same time.

References

Camerer, C., & Lovallo, D. (1999). Overconfidence and excess entry: An experimental approach. The American Economic Review, 89(1), 306–318. https://doi.org/10.1257/aer.89.1.306
Erev, I., & Rapoport, A. (1998). Coordination, "magic," and reinforcement learning in a market entry game. Games and Economic Behavior, 23(2), 146–175. https://doi.org/10.1006/game.1997.0619
Rapoport, A., Seale, D. A., Erev, I., & Sundali, J. A. (1998). Equilibrium play in large group market entry games. Management Science, 44(1), 119–141. https://doi.org/10.1287/mnsc.44.1.119
Selten, R., & Güth, W. (1982). Equilibrium point selection in a class of market entry games. In M. Deistler, E. Fürst, & G. Schwödiauer (Eds.), Games, economic dynamics, and time series analysis (pp. 101–116). Physica-Verlag.
Sundali, J. A., Rapoport, A., & Seale, D. A. (1995). Coordination in market entry games with symmetric players. Organizational Behavior and Human Decision Processes, 64(2), 203–218. https://doi.org/10.1006/obhd.1995.1100
Ochs, J. (1990). The coordination problem in decentralized markets: An experiment. The Quarterly Journal of Economics, 105(2), 545–559. https://doi.org/10.2307/2937800

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