Measured Games  ·  Paper 17 of 07  ·  Experimental economics

Focal points

After T. C. Schelling (1960); measured by J. Mehta, C. Starmer and R. Sugden (1994)

Abstract

In a pure coordination game every matching pair of choices is an equilibrium and the payoffs cannot distinguish between them. What people use instead is salience: some option stands out, and the reasoning runs through what each expects the other to notice rather than through what either prefers. Coordination rates in experiments substantially exceed both chance and the rate implied by people's own preferences over the same options.

Keywordssalience · pure coordination · equilibrium selection · team reasoning · experiment

1Setup

Setup

Two people must name the same thing without communicating, and both are paid only if they match. Any option will do provided both choose it. Nothing in the payoffs distinguishes the options from one another, so nothing in the payoffs can tell either person what to do.

People solve these problems anyway, and at rates far above chance. Asked to name a place in London to meet a stranger, or to pick heads or tails, or to divide a hundred pounds into two shares, respondents converge on particular answers. What they are using is not preference but conspicuousness: each is looking for whatever the other is most likely to notice.

2The model

The model

# pure coordination over n options, payoff 1 if the pair matches, else 0 every matching pair is a Nash equilibrium # with n options there are n of them, and the payoffs rank none above another # let option i carry salience wᵢ. two ways of choosing: picking pi ∝ wi choose what you like coordinating pi ∝ wiλ choose what stands out, λ > 1 # the chance two independent choosers match coordination rate = Σ pi2 random choice → 1/n

The testable content is the comparison rather than the level. If people coordinate by choosing what they personally prefer, the matching rate should equal what their own preferences predict. If they instead sharpen towards whatever is most conspicuous, the rate should be higher than that. The two make different numerical predictions from the same population.

Figure 1Salience against the picking baseline

Choice distribution over the options, under the current rule

Coordination rate against sharpening · hover to read any point

Measured matching in randomly drawn pairs

Choice share Coordinating Picking baseline Chance, 1/n

Charts are focusable. With a chart focused, use the left and right arrow keys to read values along the horizontal axis.

Predicted rate—
Measured rate—
Picking baseline—
Chance—
Most chosen option—
Pairs drawn0
Figure 1. Pairs are drawn independently and matched, so the coordination rate is counted rather than computed. The comparison that matters is between the two rules on the same salience profile: switching from picking to coordinating raises the matching rate without changing anything about the options, which is the experimental result. Flatten the salience towards zero concentration and both rules collapse to chance, because there is nothing left to be conspicuous.
3Results

Results

Schelling (1960) introduced the problem and the informal evidence: asked where in New York to meet a stranger on a given day with no prior arrangement, a large share of his respondents named the same place and time. His point was that game theory as then constituted had nothing to say about this, since the payoffs are symmetric across the options and formal reasoning cannot break the tie.

Mehta, Starmer and Sugden (1994) turned it into a measurement. They ran the same sets of options under two instructions. In the picking treatment subjects chose whatever they liked, with no coordination incentive; in the coordinating treatment they were paid for matching an anonymous partner. If coordination worked by everyone independently following their own tastes, the two treatments would produce the same matching rate. They did not. Coordination rates were substantially higher, meaning subjects were sharpening towards conspicuous options rather than reporting preferences.

The theoretical readings differ. One treats salience as a source of shared beliefs that feed ordinary individual reasoning. The other, team reasoning, holds that subjects switch to asking what we should do and then play their part. The experiments constrain the accounts but do not settle between them.

4Evidence

Evidence

Mehta, Starmer and Sugden (1994) is the primary evidence and remains the cleanest design, because the picking treatment supplies the right null. Their results across a range of question types, numbers, letters, places and divisions, consistently showed coordination above the picking baseline.

Bardsley and colleagues (2010) revisited the question with designs intended to separate the two theoretical accounts, using variations in payoff structure that individual salience-based reasoning and team reasoning predict differently. They found evidence bearing on both and no clean verdict, which is roughly where the literature still sits.

The evidence base here is entirely experimental, and this paper is the only one in the collection with no field counterpart at all. Schelling's original examples are memorable and are not data.

5Limitations

Limitations

Salience is not measured independently in most of this work, which is the central difficulty. If the conspicuous option is identified from the choices themselves, the theory risks being circular: whatever people converge on is called salient. The picking treatment is what rescues it, because preferences are elicited separately and produce a genuine null, and any design without that comparison is much weaker.

Cultural and linguistic context does all the work in specific cases. The famous answers depend on shared background, and none of them transfers. That is a fact about the phenomenon rather than a flaw in the theory, but it limits what can be predicted in advance for a group whose common ground you do not share.

The simulator models salience as a given number, which is exactly the step the literature cannot take for granted. Read it as showing what follows once options differ in conspicuousness, not as explaining why they do.

Related This model shares its mechanism with Bank runs (Paper 11) and The winner's curse (Paper 13) and Brood parasitism (Paper 18). In each of them, what an agent can infer, rather than what they are paid, decides the outcome.

 References

References

  1. Bacharach, M. (2006). Beyond individual choice: Teams and frames in game theory (N. Gold & R. Sugden, Eds.). Princeton University Press.
  2. Bardsley, N., Mehta, J., Starmer, C., & Sugden, R. (2010). Explaining focal points: Cognitive hierarchy theory versus team reasoning. The Economic Journal, 120(543), 40–79. https://doi.org/10.1111/j.1468-0297.2009.02304.x
  3. Crawford, V. P., Gneezy, U., & Rottenstreich, Y. (2008). The power of focal points is limited: Even minute payoff asymmetry may yield large coordination failures. The American Economic Review, 98(4), 1443–1458. https://doi.org/10.1257/aer.98.4.1443
  4. Mehta, J., Starmer, C., & Sugden, R. (1994). The nature of salience: An experimental investigation of pure coordination games. The American Economic Review, 84(3), 658–673.
  5. Schelling, T. C. (1960). The strategy of conflict. Harvard University Press.
  6. Sugden, R. (1995). A theory of focal points. The Economic Journal, 105(430), 533–550. https://doi.org/10.2307/2235016

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