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Published in: Journal of Economic Interaction and Coordination 1/2019

28-12-2017 | Regular Article

Efficient coordination in the lab

Authors: Aurora García-Gallego, Penélope Hernández-Rojas, Amalia Rodrigo-González

Published in: Journal of Economic Interaction and Coordination | Issue 1/2019

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Abstract

We follow the example of Gossner et al. (Econometrica 74(6):1603–1636, 2006) in the design of a finitely repeated 2-player coordination game with asymmetric information. Player 1 and Player 2 and Nature simultaneously decide whether to play 0 or 1 and successful coordination requires that all actions coincide. Nature’s moves are known only by Player 1, while Player 2 observes only the history of Nature and Player 1. In such a theoretical set up, efficient transmission of information takes place when Player 1 uses block codification through signalling mistakes. With this in mind, we test coordination in the lab. We first model and establish the appropriate sequence length played by Nature and the block strategy for lab implementability. We show that the majority rule with 3-length is the optimal block codification for a 55-length sequence. Experimental data supports the main results of the original model with respect to the codification rule using signalling mistakes.

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Appendix
Available only for authorised users
Footnotes
1
See Farrell and Rabin (1996) for an exhaustive survey.
 
2
Grossman (1981) and Milgrom (1981) are seminal papers in this line of research.
 
3
In general, \(\left( \begin{array}{c} m \\ t x \end{array}\right) \) is defined as \(\Gamma (m+1)/(\Gamma (x+1)\Gamma (m-x+1))\). Being \(\Gamma (m)\) the Euler gamma function that satisfies \(\Gamma (m)=\int _{0}^{\infty } t^{m-1}e^{-t}dt\). For \(m(1-q)=1\), we consider \(\left( \begin{array}{c} m(1-q) \\ m(1-q)\frac{1}{2} \end{array}\right) \)\(=2\). That means that with one digit is possible to construct the two basic sequences: 0 and 1.
 
4
The entropy is also useful to approximate a combinatorial number. For \(0<x<1\), the combinatorial number \(\left( \begin{array}{c}m\\ mx\\ \end{array}\right) \) is upper bounded by \(2^{mH(x)}\).
 
5
\(\mathbb {Z}\) denotes the set of positive integer numbers.
 
6
The possible binary sequences of length 3 are: (0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0), (1, 1, 0), (1, 0, 1), (0, 1, 1) and (1, 1, 1). There are four sequences with majority rule 0, and also four with majority rule 1. The probability of the majority rule ‘equals 0’ is given by \(prob(majority=0)=prob(000\cup 001\cup 010\cup 100)=4\frac{1}{8}=\frac{1}{2}\). Similarly, the probability of the majority rule ‘equals 1’is equal to \(prob(majority=1)= prob(110\cup 101\cup 011\cup 111)=4\frac{1}{8}=\frac{1}{2}\). Thus, the probability of two consecutive blocks having the same majority is \(\frac{1}{2}\). The probability of an intended mistake (say x) becoming a random match is equal to: \(P(x=majority=0)P(majority=0)P(majority=0) + P(x=majority=1)P(majority=1)P(majority=1) = \frac{1}{4}\).
 
7
See the translated version from the original in Spanish in “Appendix 2”.
 
8
Subjects were informed about the computerized random process as being like tossing a coin.
 
9
Wilcoxon signed-rank test for the equality of medians: \(z=3.701, p=0.0002\).
 
10
In this algorithm, the applied measure of distance is the sum of absolute differences, known as the L1 distance. Each centroid is the component-wise median of the points in that cluster: \(d(x,c)=\sum _{j=1}^{p} |x_{j}-c_{j}|\).
 
11
It is applied Wilcoxon signed-rank test for the equality of medians.
 
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Metadata
Title
Efficient coordination in the lab
Authors
Aurora García-Gallego
Penélope Hernández-Rojas
Amalia Rodrigo-González
Publication date
28-12-2017
Publisher
Springer Berlin Heidelberg
Published in
Journal of Economic Interaction and Coordination / Issue 1/2019
Print ISSN: 1860-711X
Electronic ISSN: 1860-7128
DOI
https://doi.org/10.1007/s11403-017-0214-3

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