The chances solving a problem that involves coordination between people are increased by introducing robotic players that sometimes make mistakes. This finding has implications for real-world coordination problems

A Cassar

CF Camerer

H Shirado

HP Young

JB Van Huyck

JC Harsanyi

M Kandori

M Kearns

P Turchin

S Bowles

S Weidenholzer

Simon Gächter

V Buskens

VP Crawford

Gaechter, Simon

Nottingham eTheses

Occasional errors can benefit coordination

Crossref

Nature

Repository@Nottingham

	 1	Occasional	errors	can	benefit	coordination		[published in slightly revised version as a News & Views article in Nature 545, 18 May 2017, 297-298, doi:	10.1038/545297a]  		The	chances	solving	a	problem	that	involves	coordination	between	people	are	increased	by	introducing	robotic	players	that	sometimes	make	mistakes.	This	finding	has	implications	for	real-world	coordination	problems.	See	Letter	p.XXX		Simon	Gächter		Complex human societies exist because people cooperate with each other and coordinate their activities1. Cooperation involves collaborating for common benefit, whereas coordination requires people to match their collaborative activities in appropriate ways. This often entails solving small, local coordination problems to achieve global coordination. As an example, consider the production of complex goods, which involves coordinating the division of labour across sites. In this instance, error-prone people must solve many, often intricate, local problems such as work processes, or the logistics of production and supply chains, to achieve global coordination. On page XXX, Shirado and Christakis2 use network experiments to highlight the ways in which errors can help to improve global coordination.  The authors set up 230 randomly generated networks, each with 20 nodes. They allocated each of 4,000 participants to a node, and asked them to solve a colour-coordination game3, in which the aim is to make each node one of three colours that differs from the colour of every neighbouring node (Fig. 1).  Players know that they are part of a large network, but see only the colours of their 	 2	neighbours. They can change their node’s colour as often as they like within five minutes. Thus, a player can remove local colour conflicts without solving all colour conflicts glob- ally. People are paid according to how long it takes to solve all colour conflicts in the net- work. This setup is an abstract representation of many real-world coordination problems3, in which the choices optimal for an individual might not solve a global coordination problem whose resolution is in the collective interest.  In addition to human participants, Shirado and Christakis included three autonomous software agents called bots as players in many of the networks. They programmed the bots to play a locally optimal strategy, but to make a random colour choice a certain amount of the time. The authors tested three levels of randomness — 0% (no noise), 10% (low noise) and 30% (high noise). They placed bots at different positions in different networks: in random, peripheral or central locations. Thus, they tested nine combinations of bot randomness and positioning to examine whether noisy bots help human players.  Of 30 control networks that contained only human players, 67% solved their game within 5 minutes. The remaining groups became stuck in locally unresolvable colour conflicts. Placing low-noise bots in the centre of networks improved success rates: 85% of such networks achieved global coordination within 5 minutes. The presence of these bots also increased the speed with which the problem was solved. Interestingly, the low-noise bots helped to resolve colour conflicts not only by deviating from the locally optimal action, but also because their behaviour nudged human players to occasionally deviate, too. The no-noise and high-noise bots were not that helpful, because they created less-than-ideal levels of deviation (not enough or too much, respectively). Bots placed in the centre of the network had more 	 3	influence than peripheral bots because they had more links to human neighbours.  Shirado and Christakis suggest that noisy bots could be used as ‘simple artificial intelligence’ tools to help human decision-makers solve real-world coordination problems. But they could also serve as experimental tools, acting as models for human players who are, for whatever reason, occasionally willing to try something new or to disrupt the situation even if they do not fully understand what they are doing. Indeed, there was evidence that such individuals were present in the authors’ control experiments — some conflicts were resolved because players temporarily deviated from the local optimum. Thus, bots could be used to test how ‘disruptors’ can shift the behaviour of a population in coordination problems.  Noisy play — making mistakes or experimenting with strategies — is also important for the evolution of social outcomes in models of cooperation and coordination based on evolutionary game theory4–7 (a theoretical framework in which strategic behaviours can be analysed in the context of evolutionary selection pressure). It is therefore instructive to compare Shirado and Christakis’s network-based problem with game-theory-based approaches to the study of coordination, such as games in which some endpoints have greater rewards than others8–10.  As a classic game-theoretic example, consider a game in which two players decide simultaneously whether to hunt a stag or a rabbit. Only if both go for the optimal choice, the stag, will they catch it; if one hunter chooses the stag and the other the rabbit, the first gets nothing, but the second gets a rabbit. In this type of game, attempting to coordinate to achieve a collectively optimal solution exposes players to the risk of a loss. Players might therefore opt for a collectively inefficient but safer endpoint, both choosing the rabbit.  	 4	Game-theory-based models in which players occasionally make mistakes predict an inefficient outcome for these games4,5. Experimental evidence confirms this prediction, particularly in large groups in which everyone must play the game with each other person11. But interestingly, efficient coordination can often be achieved if these games are played on large networks in which each person plays only with their neighbours. Here, success becomes more likely as the network becomes more centralized — that is, the more links players have to others12,13.  This suggests a parallel to the current study, in which centralized bots improve global coordination. Thus, central players are crucial for success in both game theory and networked coordination problems. However, a key difference is that most game-theoretic analyses focus on local interactions, whereas Shirado and Christakis focus on coordination success across the whole network.  An interesting avenue for future research could therefore be to combine Shirado and Christakis’s network approach with incentives for both local and global coordination. This could provide a more-realistic model for interaction structures in many real-world local–global coordination problems (such as in integrated supply chains or large organizations), in which people have local incentives for coordination. These incentives might make them unwilling to move away from a locally optimal decision to achieve global coordination, much like the hunters who have an incentive to go alone for the rabbit. The authors’ approach could be broadly applied to help determine the location and level of noise required to obtain the desired outcome in various networks, testing the effects of differences in both centrality and incentives for local and global coordination.   	 5	  			Simon	Gächter	is	in	the	Centre	for	Decision	Research	and	Experimental	Economics,	University	of	Nottingham,	Nottingham	NG7	2RD,	UK.	e-mail:	simon.gaechter@nottingham.ac.uk.		Support	under	ERC-AdG	295707	COOPERATION	is	gratefully	acknowledged.	 		References	1.	 Turchin,	P.	Ultrasociety:	How	10,000	years	of	war	made	humans	the	greatest	cooperators	on	earth.	(Beresta	Books,	LLC,	Chaplin,	CT,	2016).	2.	 Shirado,	H.	&	Christakis,	N.	A.	Locally	noisy	autonomous	agents	improve	global	human	coordination	in	network	experiments.	Nature	(2017).	3.	 Kearns,	M.,	Suri,	S.	&	Montfort,	N.	An	experimental	study	of	the	coloring	problem	on	human	subject	networks.	Science	313,	824	(2006).	4.	 Kandori,	M.,	Mailath,	G.	J.	&	Rob,	R.	Learning,	mutation,	and	long	run	equilibria	in	games.	Econometrica	61,	29	(1993).	5.	 Young,	P.	H.,	Individual	strategy	and	social	structure:	An	evolutionary	theory	of	institutions.	(Princeton	University	Press,	Princeton,	1998).	6.	 Bowles,	S.,	Microeconomics:	Behavior,	institutions,	and	evolution.	(Princeton	University	Press,	Princeton,	2003).	7.	 Weidenholzer,	S.	Coordination	games	and	local	interactions:	A	survey	of	the	game	theoretic	literature.	Games	1,	551	(2010).	8.	 Harsanyi,	J.	&	Selten,	R.,	A	general	theory	of	equilibrium	selection	in	games.	(The	MIT	Press,	Cambridge,	1988).	9.	 van	Huyck,	J.	B.,	Battalio,	R.	C.	&	Beil,	R.	O.	Tacit	coordination	games,	strategic	uncertainty,	and	coordination	failure.	American	Economic	Review.	80,	234	(1990).	10.	 Crawford,	V.	P.	Adaptive	dynamics	in	coordination	games.	Econometrica	63,	103	(1995).		 6	11.	 Devetag,	G.	&	Ortmann,	A.	When	and	why?	A	critical	survey	on	coordination	failure	in	the	laboratory.	Experimental	Economics	10,	331	(2007).	12.	 Cassar,	A.	Coordination	and	cooperation	in	local,	random	and	small	world	networks:	Experimental	evidence.	Games	and	Economic	Behavior	58,	209	(2007).	13.	 Buskens,	V.	&	Snijders,	C.	Effects	of	network	characteristics	on	reaching	the	payoff-dominant	equilibrium	in	coordination	games:	A	simulation	study.	Dynamic	Games	and	Applications	6,	477	(2016).		FIGURE	1	https://www.nature.com/nature/journal/v545/n7654/fig_tab/545297a_F1.html			Figure	1	|	Noise	helps	resolve	coordination	problems.	a,	Shirado	and	Christakis2		set	up	networks	of	nodes	of	three	colours,	such	as	in	this	simplified	example.	Nodes	were	assigned	to	a	human	player,	or	sometimes	to	an	automated	software	agent	called	a	bot.	Players	aimed	to	coordinate	such	that	each	node	was	a	different	colour	to	each	of	its	neighbours	(colour	conflicts	are	indicated	by	red	lines).	b,	Players	could	only	see	the	colour	choices	of	their	neighbours,	and	so	players	(such	as	the	one	starred)	could	remove	local	colour	conflicts	without	solving	all	conflicts	globally.	Some	conflicts	were	locally	unsolvable	(such	as	that	of	the	circled	player).	Bots	played	optimally	most	of	the	time,	but	were	programmed	to	make	random	colour	choices	a	certain	percentage	of	the	time,	as	here,	introducing	noise	into	the	network.	c,	This	noise	helped	resolve	colour	conflicts	—	in	this	instance	by	encouraging	a	player	(triangle)	to	change	colour,	enabling	the	circled	player	to	resolve	their	conflict.					

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Nottingham ePrints

Gaechter, Simon (2017) Occasional errors can benefit coordination. Nature, 545 . pp. 297-298. ISSN 1476-4687 Access from the University of Nottingham repository: http://eprints.nottingham.ac.uk/43071/8/Gaechter%28ErrorsCoordination_Nature2017%29.pdfCopyright and reuse: The Nottingham ePrints service makes this work by researchers of the University of Nottingham available open access under the following conditions.This article is made available under the University of Nottingham End User licence and may be reused according to the conditions of the licence.  For more details see: http://eprints.nottingham.ac.uk/end_user_agreement.pdfA note on versions: The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher’s version. Please see the repository url above for details on accessing the published version and note that access may require a subscription.For more information, please contact eprints@nottingham.ac.uk	 1	Occasional	errors	can	benefit	coordination		[published in slightly revised version as a News & Views article in Nature 545, 18 May 2017, 297-298, doi:	10.1038/545297a]  		The	chances	solving	a	problem	that	involves	coordination	between	people	are	increased	by	introducing	robotic	players	that	sometimes	make	mistakes.	This	finding	has	implications	for	real-world	coordination	problems.	See	Letter	p.XXX		Simon	Gächter		Complex human societies exist because people cooperate with each other and coordinate their activities1. Cooperation involves collaborating for common benefit, whereas coordination requires people to match their collaborative activities in appropriate ways. This often entails solving small, local coordination problems to achieve global coordination. As an example, consider the production of complex goods, which involves coordinating the division of labour across sites. In this instance, error-prone people must solve many, often intricate, local problems such as work processes, or the logistics of production and supply chains, to achieve global coordination. On page XXX, Shirado and Christakis2 use network experiments to highlight the ways in which errors can help to improve global coordination.  The authors set up 230 randomly generated networks, each with 20 nodes. They allocated each of 4,000 participants to a node, and asked them to solve a colour-coordination game3, in which the aim is to make each node one of three colours that differs from the colour of every neighbouring node (Fig. 1).  Players know that they are part of a large network, but see only the colours of their 	 2	neighbours. They can change their node’s colour as often as they like within five minutes. Thus, a player can remove local colour conflicts without solving all colour conflicts glob- ally. People are paid according to how long it takes to solve all colour conflicts in the net- work. This setup is an abstract representation of many real-world coordination problems3, in which the choices optimal for an individual might not solve a global coordination problem whose resolution is in the collective interest.  In addition to human participants, Shirado and Christakis included three autonomous software agents called bots as players in many of the networks. They programmed the bots to play a locally optimal strategy, but to make a random colour choice a certain amount of the time. The authors tested three levels of randomness — 0% (no noise), 10% (low noise) and 30% (high noise). They placed bots at different positions in different networks: in random, peripheral or central locations. Thus, they tested nine combinations of bot randomness and positioning to examine whether noisy bots help human players.  Of 30 control networks that contained only human players, 67% solved their game within 5 minutes. The remaining groups became stuck in locally unresolvable colour conflicts. Placing low-noise bots in the centre of networks improved success rates: 85% of such networks achieved global coordination within 5 minutes. The presence of these bots also increased the speed with which the problem was solved. Interestingly, the low-noise bots helped to resolve colour conflicts not only by deviating from the locally optimal action, but also because their behaviour nudged human players to occasionally deviate, too. The no-noise and high-noise bots were not that helpful, because they created less-than-ideal levels of deviation (not enough or too much, respectively). Bots placed in the centre of the network had more 	 3	influence than peripheral bots because they had more links to human neighbours.  Shirado and Christakis suggest that noisy bots could be used as ‘simple artificial intelligence’ tools to help human decision-makers solve real-world coordination problems. But they could also serve as experimental tools, acting as models for human players who are, for whatever reason, occasionally willing to try something new or to disrupt the situation even if they do not fully understand what they are doing. Indeed, there was evidence that such individuals were present in the authors’ control experiments — some conflicts were resolved because players temporarily deviated from the local optimum. Thus, bots could be used to test how ‘disruptors’ can shift the behaviour of a population in coordination problems.  Noisy play — making mistakes or experimenting with strategies — is also important for the evolution of social outcomes in models of cooperation and coordination based on evolutionary game theory4–7 (a theoretical framework in which strategic behaviours can be analysed in the context of evolutionary selection pressure). It is therefore instructive to compare Shirado and Christakis’s network-based problem with game-theory-based approaches to the study of coordination, such as games in which some endpoints have greater rewards than others8–10.  As a classic game-theoretic example, consider a game in which two players decide simultaneously whether to hunt a stag or a rabbit. Only if both go for the optimal choice, the stag, will they catch it; if one hunter chooses the stag and the other the rabbit, the first gets nothing, but the second gets a rabbit. In this type of game, attempting to coordinate to achieve a collectively optimal solution exposes players to the risk of a loss. Players might therefore opt for a collectively inefficient but safer endpoint, both choosing the rabbit.  	 4	Game-theory-based models in which players occasionally make mistakes predict an inefficient outcome for these games4,5. Experimental evidence confirms this prediction, particularly in large groups in which everyone must play the game with each other person11. But interestingly, efficient coordination can often be achieved if these games are played on large networks in which each person plays only with their neighbours. Here, success becomes more likely as the network becomes more centralized — that is, the more links players have to others12,13.  This suggests a parallel to the current study, in which centralized bots improve global coordination. Thus, central players are crucial for success in both game theory and networked coordination problems. However, a key difference is that most game-theoretic analyses focus on local interactions, whereas Shirado and Christakis focus on coordination success across the whole network.  An interesting avenue for future research could therefore be to combine Shirado and Christakis’s network approach with incentives for both local and global coordination. This could provide a more-realistic model for interaction structures in many real-world local–global coordination problems (such as in integrated supply chains or large organizations), in which people have local incentives for coordination. These incentives might make them unwilling to move away from a locally optimal decision to achieve global coordination, much like the hunters who have an incentive to go alone for the rabbit. The authors’ approach could be broadly applied to help determine the location and level of noise required to obtain the desired outcome in various networks, testing the effects of differences in both centrality and incentives for local and global coordination.   	 5	  			Simon	Gächter	is	in	the	Centre	for	Decision	Research	and	Experimental	Economics,	University	of	Nottingham,	Nottingham	NG7	2RD,	UK.	e-mail:	simon.gaechter@nottingham.ac.uk.		Support	under	ERC-AdG	295707	COOPERATION	is	gratefully	acknowledged.	 		References	1.	 Turchin,	P.	Ultrasociety:	How	10,000	years	of	war	made	humans	the	greatest	cooperators	on	earth.	(Beresta	Books,	LLC,	Chaplin,	CT,	2016).	2.	 Shirado,	H.	&	Christakis,	N.	A.	Locally	noisy	autonomous	agents	improve	global	human	coordination	in	network	experiments.	Nature	(2017).	3.	 Kearns,	M.,	Suri,	S.	&	Montfort,	N.	An	experimental	study	of	the	coloring	problem	on	human	subject	networks.	Science	313,	824	(2006).	4.	 Kandori,	M.,	Mailath,	G.	J.	&	Rob,	R.	Learning,	mutation,	and	long	run	equilibria	in	games.	Econometrica	61,	29	(1993).	5.	 Young,	P.	H.,	Individual	strategy	and	social	structure:	An	evolutionary	theory	of	institutions.	(Princeton	University	Press,	Princeton,	1998).	6.	 Bowles,	S.,	Microeconomics:	Behavior,	institutions,	and	evolution.	(Princeton	University	Press,	Princeton,	2003).	7.	 Weidenholzer,	S.	Coordination	games	and	local	interactions:	A	survey	of	the	game	theoretic	literature.	Games	1,	551	(2010).	8.	 Harsanyi,	J.	&	Selten,	R.,	A	general	theory	of	equilibrium	selection	in	games.	(The	MIT	Press,	Cambridge,	1988).	9.	 van	Huyck,	J.	B.,	Battalio,	R.	C.	&	Beil,	R.	O.	Tacit	coordination	games,	strategic	uncertainty,	and	coordination	failure.	American	Economic	Review.	80,	234	(1990).	10.	 Crawford,	V.	P.	Adaptive	dynamics	in	coordination	games.	Econometrica	63,	103	(1995).		 6	11.	 Devetag,	G.	&	Ortmann,	A.	When	and	why?	A	critical	survey	on	coordination	failure	in	the	laboratory.	Experimental	Economics	10,	331	(2007).	12.	 Cassar,	A.	Coordination	and	cooperation	in	local,	random	and	small	world	networks:	Experimental	evidence.	Games	and	Economic	Behavior	58,	209	(2007).	13.	 Buskens,	V.	&	Snijders,	C.	Effects	of	network	characteristics	on	reaching	the	payoff-dominant	equilibrium	in	coordination	games:	A	simulation	study.	Dynamic	Games	and	Applications	6,	477	(2016).		FIGURE	1	https://www.nature.com/nature/journal/v545/n7654/fig_tab/545297a_F1.html			Figure	1	|	Noise	helps	resolve	coordination	problems.	a,	Shirado	and	Christakis2		set	up	networks	of	nodes	of	three	colours,	such	as	in	this	simplified	example.	Nodes	were	assigned	to	a	human	player,	or	sometimes	to	an	automated	software	agent	called	a	bot.	Players	aimed	to	coordinate	such	that	each	node	was	a	different	colour	to	each	of	its	neighbours	(colour	conflicts	are	indicated	by	red	lines).	b,	Players	could	only	see	the	colour	choices	of	their	neighbours,	and	so	players	(such	as	the	one	starred)	could	remove	local	colour	conflicts	without	solving	all	conflicts	globally.	Some	conflicts	were	locally	unsolvable	(such	as	that	of	the	circled	player).	Bots	played	optimally	most	of	the	time,	but	were	programmed	to	make	random	colour	choices	a	certain	percentage	of	the	time,	as	here,	introducing	noise	into	the	network.	c,	This	noise	helped	resolve	colour	conflicts	—	in	this	instance	by	encouraging	a	player	(triangle)	to	change	colour,	enabling	the	circled	player	to	resolve	their	conflict.					

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Occasional errors can benefit coordination

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