Team	Reasoning:	Theory	and	Evidence Jurgis	Karpus	and	Natalie	Gold for	Routledge Handbook on Social Cognition, ed. Julian Kiverstein February	15th,	2016 Introduc7on Orthodox game theory idenAfies raAonal soluAons to interpersonal and strategically interdependent decision	problems,	games,	using	the	noAon	of	individualisAc	best-response	reasoning.	When	each	player's chosen	strategy	in	a	game	is	a	best	response	to	the	strategies	chosen	by	other	players,	they	are	said	to	be	in a Nash equilibrium-a point at	which no player can benefit by unilaterally changing his or her strategy. Consider the Hi-Lo and the Prisoner's Dilemma two-player games illustrated in Figures 1 and 2. The strategies available to	one	of the two	players are idenAfied	by rows and those available to the	other by columns.	The	numbers	in	each	cell	represent	payoffs	to	the	row	and	the	column	players	respecAvely	in	each of	the	four	possible	outcomes	in	these	games. There	are	two	Nash	equilibria	in	the	Hi-Lo	game,	(Hi,	Hi)	and	(Lo,	Lo),	since,	for	either	player,	the	strategy	Hi is	the	best	response	to	the	other	player's	choice	of	Hi	and	the	strategy	Lo	is	the	best	response	to	the	other's choice	of	Lo.1	As	such,	individualisAc	best-response	reasoning	idenAfies	two	raAonal	soluAons	of	this	game but	does	not	resolve	it	definiAvely	for	the	interacAng	players.	For	many	people,	however,	(Lo,	Lo)	does	not appear	to	be	a	raAonal	soluAon	and	it	seems	that	the	outcome	(Hi,	Hi)	is	a	clear	definiAve	resoluAon	of	this game.	In the case	of the	Prisoner's	Dilemma	game, there is	only	one	Nash	equilibrium, (D,	D), since, for either player, the strategy	D is the best response to	whatever the other player is going to do. As such, individualisAc	best-response	reasoning	resolves this	game	definiAvely.	However,	due	to the inefficiency	of the	outcome	(D,	D)	compared	to	the	outcome	(C,	C)-both	players	are	beXer	off	in	the	laXer	than	they	are in	the	former-for	some	the	outcome	(C,	C)	is	not	obviously	irraAonal	and	there	is	a	division	of	opinion	(at least outside the circle of professional game theorists) about	what a raAonal player ought to do in this game. Orthodox game theory's inability to resolve these games saAsfactorily, in parAcular its inability to definiAvely	resolve	the	Hi-Lo	game,	moAvated	the	development	of	the	theory	of	team	reasoning.2	According 1 These	are	Nash	equilibria	in	pure	strategies.	There	is	a	third	Nash	equilibrium	in	mixed	strategies, in	which	both players	randomize	between	the	two	available	strategies	by	playing	Hi	with	probability	1/3	and	Lo	with	probability 2/3. 2 For	some	of	the	early	and	later	theoreAcal	developments	see	Bacharach	(1999,	2006),	Sugden	(1993,	2000,	2003, 2011,	2015),	Gold	and	Sugden	(2007a,	2007b),	and	Gold	(2012). 1 C D C 2,	2 0,	3 D 3,	0 1,	1 Figure	2:	The	Prisoner's	Dilemma	game Hi Lo Hi 2,	2 0,	0 Lo 0,	0 1,	1 Figure	1:	The	Hi-Lo	game Team	Reasoning:	Theory	and	Evidence to the theory of team reasoning, people may not always be employing individualisAc best-response reasoning in games. The theory allows that people may, instead, idenAfy raAonal soluAons from the perspecAve	of	a	team,	a	group	of	individuals	acAng	together	in	the	aXainment	of	the	best	outcome(s)	for that	group.	This, in	turn,	enables	team	reasoning	to	show	how	the	Hi-Lo	game	can	be	raAonally	resolved definiAvely	and	how	the	outcome	(C,	C)	in	the	Prisoner's	Dilemma	game	can	be	raAonalized. The	theory	of	team	reasoning	gives	a	new	account	of	why	coordinaAon	and	cooperaAon	can	be	raAonal	by introducing	the	possibility	of	mulAple	levels	of	agency	into	classical	game	theory.	But	it	is	also	supposed	to tell	us	something	about	how	people	reason.	It	is	a	model	of	decision-making,	which	abstracts	and	simplifies, but	"it	captures	salient	features	of	real	human	reasoning"	(Sugden,	2000,	p.	178).	We	might	think	of	team reasoning	as	operaAng	at	Marr's	(1982)	computaAonal	level,	specifying	the	goal	of	the	system	and	the	logic behind the output, but leaving open	how the computaAon is implemented and	how it is realised in the brain	(Gold,	in	press). A	number	of	different	versions	of	the	theory	of	team	reasoning	have	been	proposed	and	developed.	These differ	with respect to	what triggers decision-makers' adopAon	of the team	mode	of reasoning and	what team-reasoning individuals try	to	achieve.	We	review	these	developments in	the	first	part	of this	chapter (SecAons	1	to	3).	There	is	also	a	nascent	but	growing	body	of	experiments	that	aXempt	to	test	the	theory. We	review	some	of	these	studies	in	the	second	part	(SecAons	4	to	6).	Finally,	with	SecAon	7	we	conclude and	present	a	suggesAon	for	further	experimental	work	in	this	field. I.	Theory 1.	What	is	Team	Reasoning? The	individualisAc	best-response	reasoning	of	orthodox	game	theory	is	based	on	the	quesAon	of	which	of the	available	strategies	in	a	game	a	parAcular	player	should	take,	given	his	or	her	individual	preferences	and his	or	her	beliefs	about	what	the	other	players	are	going	to	do.	Each	player's	personal	moAvaAons	in	games are represented by the payoff numbers they associate with the available outcomes, and the opAmal strategy	is	that	which	gives	the	player	in	quesAon	the	highest	expected	payoff.	In	this	light,	the	best	strategy for an individualisAcally reasoning player in the Hi-Lo game (see Figure 1 above) is condiAonal on that player's	belief	about	what	the	other	player	is	going	to	do:	play	Hi	or	play	Lo.	In	the	Prisoner's	Dilemma	game (see	Figure	2)	the	best	strategy	is	uncondiAonally	to	play	D. Team	reasoning,	on the	other	hand, is	based	on	the	quesAon	of	what is	opAmal for the	group	of	players acAng	together	as	a	team.	A	team	reasoner	first idenAfies	an	outcome	of	a	game	that	best	promotes	the interests	of	the	team	and	then	chooses	the	strategy	that	is	his	or	her	part	of	aXaining	that	outcome.	If	the outcome (Hi,	Hi) is idenAfied as uniquely opAmal for the team, then team reasoning resolves the Hi-Lo game	definiAvely.	Similarly,	if	any	of	the	outcomes	associated	with	the	play	of	C	in	the	Prisoner's	Dilemma game,	e.g.,	the	outcome	(C,	C),	are	ranked	at	the	top	from	the	point	of	view	of	the	team,	the	strategy	C	can be	raAonalized. It is important to note that reasoning as a	member of a team is not a	mere transformaAon of players' personal	payoff	numbers	associated	with	the	available	outcomes	in	games.	To	see	this,	consider	again	the Hi-Lo	game.	Suppose	that, from	the	point	of	view	of	the	team,	the	outcome	(Hi,	Hi) is	deemed	to	be	the 2 Team	Reasoning:	Theory	and	Evidence best, the outcome (Lo, Lo) is deemed to be the second-best and the outcomes (Hi, Lo) and (Lo,	Hi) the worst. Replacing the two players' original payoff numbers with numbers that correspond to the team's ranking	of	the	four	outcomes	in	the	game	does	not	change	the	payoff	structure	of	the	original	game	in	any way,	since	the	players'	individual	payoffs	are	already	in	line	with	the	valuaAon	of	outcomes	from	the	team's perspecAve.	The	key	difference	here	is	that	individualisAc	reasoning	is	based	on	evaluaAng	and	choosing	a parAcular	strategy	based	on	the	associated	expected	personal	payoff,	whereas	team	reasoning	is	based	on evaluaAng	the	outcomes	of	the	game	from	the	perspecAve	of	the	team,	and	then	choosing	a	strategy	that	is associated	with	the	opAmal	outcome	for	the	team. There	are	two	important	quesAons	that	the	theory	of	team	reasoning	needs	to	address:	"when	do	people reason	as	members	of	a team?"	and	"what	do	people try to	achieve	when	they	reason	as	members	of	a team?".	In	other	words, is it	possible	to	idenAfy	circumstances	or	types	of	games	in	which	the	interacAng players	are	likely	to	adopt	team	reasoning	and	the	mechanism	by	which	they	adopt	it,	and,	once	they	team reason,	is	it	possible	to	specify	a	funcAonal	representaAon	of	what	they	take	the	goals	of	the	team	to	be? We	turn	to	reviewing	the	various	proposals	for	answering	these	quesAons	in	the	following	two	secAons. 2.	What	Triggers	Team	Reasoning? Different	versions	of	the	theory	of	team	reasoning	have	different	answers	to	the	quesAon	of	when	people team reason. One answer, mainly associated with Bacharach (2006), is that the mode of reasoning an individual	uses is	a	maXer	of that	decision-maker's	psychological	make-up,	which in turn	may	depend	on certain	features	of	the	context in	which	decisions	are	made,	but	otherwise lies	outside	of	the individual's conscious control. A second answer, proffered by Sugden (2003), is that an individual may choose to endorse a parAcular	mode of reasoning based on consideraAons about the potenAal benefits of one or another	possible	mode	of	reasoning	and	his	or	her	beliefs	about	the	modes	of	reasoning	endorsed	by	other players, but this choice is outside of raAonal evaluaAon. A third possibility, proposed by Hurley (2005a, 2005b), is that individual decision-makers come to choose the team mode of reasoning as a result of raAonal	deliberaAon	itself. The	first	posiAon,	the	idea	that	the	adopAon	of	team	reasoning	is	outside	of	an	individual's	control,	can	be found in	the	version	of the	theory	of team	reasoning	presented	by	Bacharach	(2006)	and	Smerilli (2012). Here	the	mode	of	reasoning	that	an	individual	adopts	is	a	maXer	of	a	psychological	frame	through	which	he or she sees a decision problem.	The idea is similar to that	of Tversky	and	Kahneman (1981,	p.453),	who define	a frame	as, "the	decision-maker's concepAon	of the	acts,	outcomes,	and	conAngencies	associated with	a	parAcular	choice".	In	Tversky	and	Kahneman's	Prospect	Theory,	framing	a	decision	in	terms	of	losses or	gains	affects	the	part	of	the	value	funcAon	that	decision-makers	apply, thus affecAng their choices. In Bacharach's theory of team reasoning, framing	a	decision	in	terms	of	"we"	or	"I"	affects	the	goals	that	decisionmakers	aim	to	achieve,	which	one	might	think	of	as	using	the	individual or	the	group	value	funcAon,	and	the	mode	of	reasoning	that	they	apply. If	the	individual	frames	the	decision	problem	as	a	problem	for	him	or	her individually,	i.e.,	in	terms	of	individualisAc	best-response	reasoning,	then he	or	she	idenAfies	soluAons	offered	by	that	mode	of	reasoning	alone.	If, on the other hand, the individual frames the decision problem as a 3 Figure	3:	The	goblet	illusion Team	Reasoning:	Theory	and	Evidence problem	for	a	group	of	players	acAng	together	as	a	team,	i.e., in	terms	of	team	reasoning,	then	he	or	she idenAfies	soluAons	offered	by	team	reasoning	and	not	by	individualisAc	reasoning.	This	idea	can	be	likened to	that	of	seeing	either	a	goblet	or	two	faces	in	the	goblet	illusion	picture	illustrated	in	Figure	3	(also	known as	the	Rubin's	vase).	Looking	at	this	picture	it	is	possible	to	see	either	a	goblet	or	two	faces	opposite	from each	other,	but	only	one	of	these	images	at	a	Ame	and	not	both	of	them	simultaneously.	In	the	same	way,	a decision-maker is said to frame a decision problem	either from the point of view	of individualisAc bestresponding	or	from	the	point	of	view	of	reasoning	as	a	member	of	a	team,	but	not	in	terms	of	both	these perspecAves	at	the	same	Ame.3 The	psychological	frame	through	which	an	individual	analyzes	a	parAcular	decision	problem	may	depend	on factors	that	lie	outside	of	the	descripAon	of	a	game,	but	it	can	be	influenced	by	the	payoff	structure	of	the game itself: Bacharach menAons as possible triggers the strong interdependence and double-crossing features.	Roughly	speaking,	strong	interdependence	occurs	when	there is	a	Nash	equilibrium	that	is	worse than	some	other	outcome	in	the	game	from	every	player's	individual	point	of	view.	Both	the	Hi-Lo	and	the Prisoner's	Dilemma	games	have	this	feature:	in	Hi-Lo,	the	Nash	equilibrium	(Lo,	Lo)	is	worse	for	both	players than the outcome (Hi, Hi); in the Prisoner's Dilemma, the outcome (D, D) is worse for both than the outcome	(C,	C).	This	means	that	the	outcomes	(Lo,	Lo)	and	(D,	D)	are	not	Pareto	efficient.	(An	outcome	of	a game is said to be Pareto efficient if there is no other outcome available that	would	make some player beXer-off	without at the same	Ame	making any other player	worse-off.) According to Bacharach, strong interdependence	increases	the	likelihood	that	an	individual	would	frame	a	decision-problem	as	a	problem for	a	team. The double-crossing feature is the possibility of an individual personally benefiAng from a unilateral deviaAon from the team reasoning soluAon. It is the incenAve to act on individual reasoning	when one believes	that	the	other	player	is	acAng	on	team	reasoning.	This	feature	is	present	in	the	Prisoner's	Dilemma but not the Hi-Lo game. In the Prisoner's Dilemma, each individual would personally benefit from a unilateral deviaAon from the cooperaAve play of (C,	C). There is an incenAve to double-cross the other player,	playing	D	if	the	other	player	is	expected	to	play	C.	According	to	Bacharach,	the	possibility	of	double crossing	decreases	the	likelihood	of	a	parAcular	decision-maker	framing	a	decision	problem	as	a	problem	for a team. Smerilli (2012) formalizes this intuiAon, providing a model where the double-crossing feature causes	players	to	vacillate	between	frames. Another possibility, suggested by	Bardsley (2000, Ch. 5, SecAon 6), is that payoff	differences	within cells introduce an inter-individual aspect to game situaAons and Pareto superior outcomes a collecAve one, which	respecAvely	inhibit	or	promote	team	reasoning.	Zizzo	and	Tan	(2007)	introduce	the	noAon	of	"game harmony",	a	generic	game	property	describing	how	conflictual	or	non-conflictual	the	players'	interests	are, and suggest some	ways	of	measuring it, the	simplest	one	being just the	correlaAon	between	the	players' payoffs	across	outcomes. They show that game	harmony	measures can	predict cooperaAon in some	2x2 games	(i.e.	two-player	games	with	two	strategies	available	to	each	player).	Note	that	this	is	a	different	idea 3 However,	see	Bacharach	(1997)	for	a	model	where,	as	well	as	the	"I	frame"	and	the	"we	frame",	there	is	also	an	"S (superordinate)	frame",	which	is	acAve	when	someone	manages	to	see	a	problem	from	both	the	"I"	and	the	"we" perspecAves.	Someone	in	the	"S	frame"	is	sAll	compelled	only	to	evaluate	the	outcomes	from	either	an	"I"	or	a "we"	perspecAve,	and	the	cooperaAve	opAon	is	chosen	by	a	player	in	the	"S	frame"	if	it	is	the	best	opAon	from	the perspecAve	of	team	reasoning	and	not	worse	than	any	other	raAonal	soluAon	in	terms	of	individualisAc	bestresponding. 4 Team	Reasoning:	Theory	and	Evidence from	Bacharach's strong interdependence	and	double crossing features (as	noted	by	Bacharach,	2006,	p. 83).	The	measures	agree	in	pure	coordinaAon	games,	where	players'	interests	are	perfectly	aligned,	and	in zero-sum	games,	where	players'	interests	are	perfectly	opposed.	However,	in	mixed	moAve	games,	the	two ideas	do	not	always	point	in	the	same	direcAon.	Bacharach	is	clear	that	common	interest	is	strong	when	the possible gains from	coordinaAon	are	high	or the losses from	coordinaAon failure are great,	which leaves open	how	consensual	players'	interests	are	in	general,	whereas	game	harmony	is	simply	a	measure	of	how consensual players' interests are and does not take into account the size of the potenAal gains from cooperaAon. In addiAon to the structural features of games themselves, priming group or individualisAc thinking in decision-makers	could	be	expected	to	also	play	an	important	role	in	determining	which	frame	of	mind	the individuals	would	be	in	and	which	mode	of	reasoning	they	would	use	in	games.	Bacharach	(2006)	surveys the	literature	from	social	psychology	on	group	idenAty,	the	effect	of	social	categorizaAon	and	the	minimal group	paradigm,	and	took	himself	to	be	contribuAng	to	that	literature.	Group	idenAty	may	be	triggered	by players' recogniAon of belonging to the same social group or a parAcular category, having common interests, being subject to a common fate or simply having face-to-face contact. For Bacharach, group idenAty is a "framing	phenomenon" (2006,	p. 81). To	group idenAfy is to conceive	of	oneself as a group member:	to	represent	oneself	as	a	group	member	and	have	group	concepts	in	one's	frame.	Hence,	for	him, all these	factors	that	trigger	group idenAty	may	cause	a	shio	from	the	"I frame"	to	a	"we	frame"	(see, in parAcular,	Bacharach,	2006,	pp.	76-81). Sugden (2003,	2011,	2015) takes the second	posiAon	described	above:	an individual	decision-maker	may choose	to	endorse	team	reasoning,	but	there	is	no	basis	for	raAonal	evaluaAon	of	this	choice.	For	Sugden, there	may	be	numerous	modes	of	valid	reasoning	and	an	individual	decision-maker	may	choose	to	endorse any one of them, but none of these modes of reasoning are privileged over others on the basis of instrumental	raAonality.	Instrumental	pracAcal	reasoning	allows	an	agent	to	infer	the	best	means	to	achieve its	goals.	Therefore	instrumental	raAonality	must	presume	both	the	unit	of	decision-making	agency	as	well as its goals and	neither	of these	are amenable to	evaluaAon	by the theory	of raAonality itself.	However, Sugden	discusses	a	number	of	condiAons	that	may	need	to	be	saAsfied	in	order	for	an	individual	to	endorse team reasoning.	He sees team reasoning as cooperaAon for	mutual advantage.	Hence	whether or not a person	team	reasons	will	depend	on	whether	it	is	beneficial	for	that	decision-maker	to	do	so	individually	(in terms	of	his	or	her	individual	preferences	and	goals).4	Further,	team	play	by	a	parAcular	decision-maker	may be	condiAonal	on	the	assurance	that	other	players	are	reasoning	as	members	of	a	team	as	well. Sugden	can	sAll	accept	a	lot	of	what	Bacharach	says	about	the	circumstances	in	which	people	team	reason, as	can	any theory	of team	reasoning (Gold,	2012).	Sugden's	agents sAll	need to conceive of	the	decision problem	as	a	problem	for	the	team,	rather	than	as	a	problem	for	them	as	individuals,	before	they	can	team 4 To	understand	the	idea	of	mutual	benefit	it	is	important	to	note	that	the	payoff	numbers	associated	with	different outcomes	in	games	are	meant	to	represent	the	interacAng	players'	preferences	that,	in	some	sense,	mirror	their goals	and	moAvaAons	in	these	games.	In	this	light,	higher	payoff	values	represent	higher	levels	of	preference saAsfacAon.	This	interpretaAon	of	payoffs,	however,	causes	a	general	difficulty	in	experiments,	in	which	we	need to	assume	that	the	payoffs	presented	to	parAcipants	are	correctly	aligned	with	their	true	moAvaAons	and preferences.	If	games	used	in	experiments	are	incenAvized	using	monetary	payoffs,	for	example,	we	need	to assume	that	the	interacAng	parAcipants'	true	moAvaAons	are	aligned	with	the	maximizaAon	of	personal	monetary payoffs. 5 Team	Reasoning:	Theory	and	Evidence reason (Sugden, 2000, pp .	182-183). The	difference is that, in Sugden's theory, people	make a choice to team	reason	and	assurance	plays	a	part in this,	whereas for	Bacharach, team	reasoning is the	result	of	a psychological	process	and	may	lead	team	reasoners	to	be	worse	off	than	they	would	have	been	if	they	had reasoned	as individuals (for instance they	may cooperate in a	Prisoner's	Dilemma	when the	other	player defects;	for	more	on	how	this	can	happen	see	Gold,	2012). Bacharach	and	Sugden	agree that	all goals	are the	goals	of	agents	and that it is	not	possible to	evaluate those goals	without first specifying the unit of agency. Thus, even though Sugden allows for the unit of agency	to	be	chosen,	it	is	not	a	maXer	of	instrumentally	raAonal	choice.	In	contrast,	Hurley	(2005a,	2005b) suggests	that	there	is	no	need	to	idenAfy	the	unit	of	agency	with	the	source	of	evaluaAon	of	outcomes	and that	we	can	idenAfy	personal	goals	prior	to	idenAfying	the	unit	of	agency.	Hurley	says	that,	"As	an	individual I	can	recognise	that	a	collecAve	unit	of	which	I	am	merely	a	part	can	bring	about	outcomes	that	I	prefer	to any	that	I	could	bring	about	by	acAng	as	an	individual	unit."	(Hurley,	2005a,	p.	203).	Hence,	Hurley	suggests that	principles	of	pracAcal	raAonality	can	govern	the	choice	of	the	unit	of	agency;	one	should	choose	the unit	of	agency	that	best	realizes	one's	personal	goals.	If	that	unit	is	the	team,	then	one	should	team	reason as	a	maXer	of	pracAcal	raAonality.5 The	problem	for	theories	that	allow	raAonal	choice	of	the	unit	of	agency	is	how	to	specify	the	goals	that	we should	be	striving	for,	independent	of	the	unit	of	agency.	Hurley	suggests	that	we	should	privilege	personal goals but, once we recognise that there are other possible units of agency (and evaluaAon), we	might quesAon	why it is the case that the personal level takes priority.	For a decision-maker in	Regan's (1980) theory	of	cooperaAve	uAlitarianism,	for	example,	the	goal	is	always	uAlitarian	and	the	quesAon	is	what	unit of agency	one should	be	adopAng	given this goal.	However, taking	goals as given to	us	by	our theory	of value,	or	moral	theory,	turns	team	reasoning	from	a	theory	of	raAonal	choice	into	a	theory	of	moral	choice, which	is	not	intended	by	many	of	its	proponents. The problem is brought out in recent work by Gauthier (2013). Gauthier has long held that it can be instrumentally raAonal to cooperate in the Prisoner's Dilemma game (Gauthier, 1986). In a recent reworking of his theory, Gauthier (2013) contrasts two opposed concepAons of deliberaAve raAonality: maximizaAon (equivalent to individualisAc	best-response reasoning)	and	Pareto-opAmizaAon.	He	suggests that	Pareto-opAmizaAon	is	a	necessary	condiAon	for	raAonality	in	mulA-player	games.	A	Pareto-opAmizing theory "provides only a single set of direcAves to all the interacAng agents, with the direcAve to each premised	on	the	acceptance	by	the	others	of	the	direcAves	to	them"	(Gauthier	2013,	p.	607).	The	outcome selected	must	be	both	efficient	and	fair	in	how	it	distributes	the	expected	gains	of	cooperaAon.	Although	he does	not	explicitly	use the term	"team reasoning", it is clear that	Gauthier's theory is similar to ideas	of team	reasoning	for	mutual	gain.	His	jusAficaAon	for	team	reasoning	is	that	it	would	pass	a	contractarian	test whereby it is "eligible for inclusion in	an	actual society that	consAtutes	a	cooperaAve	venture for	mutual fulfilment"	(Gauthier,	2013,	p.	618). 5 Hurley	(2005b)	follows	Kacelnick	(2006)	in	disAnguishing	two	concepAons	of	raAonality:	raAonality	as	consistent paXerns	of	behaviour	and	raAonality	as	processes	of	reasoning	that	underlie	that	behaviour.	Hurley	subscribes	to the	first	concepAon,	therefore	the	processes	in	an	agent	that	actually	generate	his	or	her	raAonal	behaviour	need not	be	isomorphic	with	the	theoreAcal	account	of	why	the	behaviour	counts	as	raAonal.	Hence	she	invesAgates local	procedures	and	heurisAcs	from	which	collecAve	units	of	agency	can	emerge.	According	to	her	picture, choices	can	be	instrumentally	raAonal	even	if	they	result	from	a	crude,	low-level	heurisAc. 6 Team	Reasoning:	Theory	and	Evidence As	Gauthier	(2013,	p.	624)	puts it,	his	goal is	to	show	that	"social	morality is	part	of	raAonal	choice,	or	at least, integral to raAonal cooperaAon".	However, whilst he has sketched out what Pareto-opAmizaAon would	involve,	Gauthier	has	not	provided	any	argument	for	its	raAonality;	he	concludes	that	he	has	not	yet been	successful	in	bridging	the	two	and	that	more	needs	to	be	done	regarding	the	connecAon	to	raAonality (in	other	words,	how instrumental raAonality	may	require	us to	cooperate in	social interacAons).	But it is hard to see how	Gauthier could bring Pareto-opAmizaAon	within instrumental raAonality. If he goes the same	route	as	Hurley	and	privileges	the	individual's	perspecAve	and	goals,	then	he	needs	to	explain	why	it is instrumentally	raAonal to	cooperate	when	the individual	could	do	beXer	by	deviaAng in	situaAons	that have	the	double	crossing	feature.	Or,	if	the	idea	is	that	there	is	some	addiAon	to	instrumental	raAonality	for choosing	the	level	of	agency,	then	it	is	hard	to	see	how	to	characterize	such	a	process.	A	reasoning	process already seems to	presume	an	agent	who is doing the reasoning.	As	Bardsley (2001,	p. 185)	puts it, "the quesAon `should I ask	myself "what am I to do?" or "what are	we to do?"?' presupposes a first person singular	point	of	view". 3.	What	Do	Teams	Strive	For? We now turn to reviewing	different proposals about a team's goals. The approaches presented differ in whether they require individual decision-makers to someAmes sacrifice their personal interests for the benefit	of	other	members	of a team	and	whether they rely	on	making interpersonal comparisons	of the interacAng	players'	payoffs.	Bacharach	(2006)	menAons	Pareto	efficiency	as	a	minimal	condiAon,	i.e.,	that	if a	strategy	profile is	superior in	terms	of	Pareto	efficiency,	then	it is	preferred	by	the	team	to	the	strategy profiles	that	it	is	superior	to.	The	exclusion	of	all	Pareto	inefficient	strategy	profiles,	however,	says	nothing about	how	a	team	should	rank	the	remaining	strategy	profiles	where	there	is	a	conflict	of	personal	interests, such	as	presented	by	the	pair	of	outcomes	(C,	D)	and	(D,	C)	in	the	Prisoner's	Dilemma	game. In	some	of	the	early	developments	of	the	theory,	e.g.,	Bacharach	(1999,	2006)	as	well	as	some	of	the	more recent	papers,	e.g.,	Colman	et	al.	(2008,	2014)	and	Smerilli	(2012),	the	maximizaAon	of	the	average	of	the interacAng players' payoffs is used as an example of a team payoff funcAon. This funcAon-that is, a mathemaAcal	representaAon	of	a	team's	goals	in	an	interpersonal	interacAon-is	consistent	with	the	strong interdependence	feature	and	the	related	Pareto	efficiency	criterion	discussed	in	the	previous	secAon,	and	it is	easy	to	see	that	it	selects	the	outcomes	(Hi,	Hi)	and	(C,	C)	as	uniquely	best	for	a	team	in	the	Hi-Lo	and	in the	above	Prisoner's	Dilemma	games	respecAvely.	(Specifically,	maximising	the	average	payoff	will	select	(C, C)	in	any	Prisoner's	Dilemma	game	where	the	average	of	the	payoffs	from	(C,	C)	is	higher	than	the	average from any other outcome.) This funcAon, however, someAmes fails	with respect to the noAon of	mutual advantage. Consider a slight variaAon of the Prisoner's Dilemma game illustrated in Figure 4. Here the maximizaAon of the average of the two players' personal payoffs	would prescribe the aXainment of the outcome	(D,	C).	As	such,	it	would	advocate	a	complete	sacrifice	of	the	column	player's	personal	interests	for the	benefit	of	the	row	player	alone. 7 Team	Reasoning:	Theory	and	Evidence The	averaging	funcAon	also	relies	on	making	interpersonal	comparisons	of	the	interacAng	players'	payoffs, which	suggests, for	example, that the row	player	prefers the	outcome	(D,	C) to (C,	C) to	a	greater	extent than	the	column	player	prefers	the	outcome	(C,	D)	to	(D,	D)	in	Figure	4.	Strictly	speaking,	such	comparisons go	beyond	the	orthodox	assumpAons	of	expected	uAlity	theory,	which	make	numerical	representaAons	of the interacAng players' preferences possible but do not automaAcally grant their interpersonal comparability.	As	such,	a	theory	of	team	reasoning	that	uses	this	funcAon	as	a	representaAon	of	a	team's goals	is	only	applicable	in	contexts	when	such	interpersonal	comparisons	of	payoffs	are	possible.6 Although	not	many	alternaAve	funcAonal	representaAons	of	a	team's	goals	have	been	proposed	(perhaps partly	because	many	works	on	the	theory	of	team	reasoning	have	so	far	considered	examples	where	teamopAmal	outcomes	seem	evident, such	as the	outcomes (Hi,	Hi)	and (C,	C) in the	Hi-Lo	and the	Prisoner's Dilemma	games),	a	number	of	properAes	that	representaAons	of	a	team's	goals	should	saAsfy	have	been put	forward.	One	of	them	is	the	noAon	of	mutual	advantage	discussed	by	Sugden	(2011),	which	suggests that	the	outcome	selected	by	a	team	should	be	mutually	beneficial	from	every	team	member's	perspecAve. Although he does not present an explicit funcAon of a team's goals, in a recent paper Sugden (2015) proposes to	measure	mutual advantage relaAve to a parAcular threshold. The threshold is each player's personal	maximin payoff level in a game-the payoff that he or she can guarantee him or herself independently	of the	other	players'	chosen	strategies. In the	Hi-Lo	game	this is	0 for	both	players. In the Prisoner's	Dilemma	game	of	Figures	2	and	4,	this	is	1,	since	it	is	the	lowest	possible	payoff	that	either	player can aXain by playing	D. A strategy profile is said to be	mutually beneficial if (a) it results in each	player receiving a payoff that is greater than his or her	maximin payoff level in a game, and (b) each player's parAcipaAon	in	team	play	is	necessary	for	the	aXainment	of	those	payoffs.7 Karpus and Radzvilas (2016) propose a formal funcAon of a team's goals that is based on the noAon of mutual advantage similar to the one above	whilst also incorporaAng the Pareto efficiency criterion (in a weak sense of Pareto efficiency, which means that an outcome of a game is efficient if there is no alternaAve	that is	strictly	preferred	to it	by	every	player in	the	game). It	suggests	that	an	outcome	that is opAmal for a team is one that is associated	with the	maximal amount of	mutual benefit. The extent of 6 If	the	numbers	in	game	matrices,	for	example,	represent	monetary	payoffs	and	all	players	value	money	in	the same	way	(that	is,	an	addiAonal	unit	of	currency	is	subjecAvely	worth	just	as	much	to	one	player	as	it	is	to another),	then	interpersonal	comparisons	of	payoffs	are	not	problemaAc.	If,	however,	the	payoff	numbers	in games	represent	players'	personal	moAvaAons	as	von	Neumann-Morgenstern	uAliAes,	then	such	comparisons	are tricky. 7 Note	that	according	to	the	above	definiAon,	both	(Lo,	Lo)	and	(Hi,	Hi)	are	mutually	beneficial	outcomes	in	the	Hi-Lo game,	since	even	(Lo,	Lo)	guarantees	both	players	more	than	their	maximin	payoff.	Hence,	the	definiAon	of	mutual advantage	does	not,	by	itself,	exclude	Pareto	inefficient	outcomes	and,	for	Sugden	(2015),	which	of	the	mutually beneficial	outcomes	will	be	sought	by	a	team	depends	on	which	outcome	each	player	in	a	game	will	have "reciprocal	reason	to	believe"	will	be	sought	by	every	other	player.	See	also	CubiX	and	Sugden	(2003)	for	more details	on	"reason	to	believe",	which	is	based	on	a	reconstrucAon	of	Lewis'	(1969)	game	theory. 8 C D C 2,	2 0,	3 D 5,	0 1,	1 Figure	4:	A	variaAon	of	the	Prisoner's	Dilemma game Team	Reasoning:	Theory	and	Evidence mutual	benefit is	measured	by the	number	of	payoff	units	by	which	an	outcome	advances	every	player's personal	interests	relaAve	to	some	threshold	points,	such	as	the	players'	maximin	payoff	levels	in	games	as suggested	by	Sugden	(2015).	For	example,	if	both	players'	maximin	payoffs	(in	a	two-player	game)	are	0,	an outcome	associated	with	a	payoff	of	3	to	Player	1	and	payoff	of	2	to	Player	2	offers	2	units	of	mutual	benefit (the addiAonal unit of individual benefit to Player 1 is not	mutual).8 As such, the funcAon idenAfies the outcome (Hi,	Hi) as	uniquely	opAmal for a team in the	Hi-Lo	game	and	prescribes the	aXainment	of the outcome	(C,	C)	in	all	the	versions	of	the	Prisoner's	Dilemma	game	discussed	above.9 II.	Evidence 4.	The	Difficul7es	of	Empirical	Tes7ng There is	a	major	difficulty	that	any	empirical test	of team	reasoning	will	unavoidably face: the	fact that	a number of separate hypotheses are being tested at once. The	main hypothesis to be tested is whether people reason as members of a team in a parAcular situaAon. This, however, is intertwined with two addiAonal	auxiliary	hypotheses.	The	first	is	whether	the	parAcular	situaAon	at	hand	is	one	in	which	people might	reason	as	members	of	a	team	in	general,	and	the	second	is	whether	the	experimenter	has	correctly specified the	goals that the	members	of the team try to	achieve. These	may involve	assuming	parAcular answers to the	"when	do	people	reason	as	members	of	a	team?"	and	the	"what	do	people	do	when	they reason	as	members	of	a	team?"	quesAons	that	we	idenAfied	above.	Also,	if	decision-makers	do	not	follow individualisAc best-response reasoning in certain situaAons, we need to be able to disAnguish team reasoning from other possible modes of reasoning that they may choose to endorse, e.g., regret minimizaAon	or	ambiguity	aversion,	or	from	factors	that	influence	decisions,	like	risk	aversion. Despite these difficulAes, a number of relaAvely recent empirical studies have been carried out in an aXempt	to test the	theory	of team	reasoning.	Since	the	aim is to test the	theory	of team	reasoning	tout court,	the	experiments	use	situaAons	where	it	is	naturally	invoked	as	an	explanaAon	of	actual	play. They	can be broadly divided into two groups: those that focus on team reasoning where it resolves a Nash equilibrium selecAon	problem (coordinaAon	problems) and those that focus	on team reasoning	where it selects	outcomes	that	are	not	Nash	equilibria	(as	in	the	Prisoner's	Dilemma).	We	will	review	both	types	of studies in turn. The focus is on piqng team reasoning against other explanaAons of coordinaAon and cooperaAon	in	these	games, so	experimenters	hope	that	the	outcome	that	they	idenAfy	as	the	team	goal	is uncontroversial,	although	we	will	see	that	someAmes	there	is	room	for	dispute. 5.	Tests	Based	on	Nash	Equilibrium	Selec7on 8 In	Karpus	and	Radzvilas'	funcAon	payoffs	are	first	normalized	so	that,	for	each	player,	the	least	and	the	most preferred	outcomes	in	a	game	are	associated	with	payoff	values	0	and	100	respecAvely. 9 There	is	a	connecAon	between	the	noAon	of	mutual	benefit	in	team	play	and	Gauthier's	(2013)	idea	of	raAonal cooperaAon	discussed	earlier.	For	Gauthier,	raAonal	cooperaAon	is	aXained	by	maximizing	the	minimum	level	of personal	gains	across	players	relaAve	to	threshold	points	beyond	which	individuals	would	not	cooperate.	This	is similar	to	the	way	the	maximally	mutually	beneficial	outcomes	are	idenAfied	using	the	funcAon	of	team's	goals presented	by	Karpus	and	Radzvilas	(2016).	Gauthier,	however,	does	not	provide	a	clear	characterizaAon	of	what the	aforemenAoned	threshold	points	are	and	his	jusAficaAon	for	raAonal	cooperaAon	is	based	on	the	idea	of "social	morality"	(see	earlier	discussion	in	SecAon	2)	rather	than	the	interacAng	players	aXempAng	to	resolve games	in	mutually	advantageous	ways. 9 Team	Reasoning:	Theory	and	Evidence The first category of experiments involves games with mulAple Nash equilibria where non-equilibrium outcomes	yield	no	payoffs	to	the	interacAng	players.	As	such,	they	are	Nash	equilibrium	coordinaAon	games in	which	players	try	to	coordinate	their	acAons	on	one	of	the	available	equilibria	in	order	to	aXain	posiAve payoffs. Team reasoning is said to single out one	of the equilibria as uniquely opAmal for a team	and is tested	against	other	possible	modes	of	reasoning	that	may	be	at	play.	The	dominant	alternaAve	explanaAon of behaviour in these experiments (to that of the theory of team reasoning) is	assumed to be cogniAve hierarchy theory,	which	posits the	existence	of individualisAc	best-response reasoners	who	differ in their beliefs about what other players are going to do in games. The level-0 decision-makers are said not to reason	much	at	all	when	playing	games	and	choose	any	of	the	available	opAons	at	random, i.e.	they	play each	available	opAon	with	equal	probability.10	The	level-1	reasoners	assume	everybody	else	to	be	cogniAve level-0	and	best-respond	to	the	level-0	decision-makers'	strategy.	The	level-2	reasoners	assume	everybody else	to	be	cogniAve	level-1	and,	similarly,	best-respond	to	the	expected	strategies	of	a	level-1	player,	and	so on for higher level cogniAve types. Although in principle the cogniAve hierarchy theory allows for any number of cogniAve types (where each type assumes other players to be of one level lesser type than themselves),	in	pracAce	it	is	usually	assumed	that	most	decision-makers	are	level-1	or	level-2	reasoners. Bardsley	et al. (2010) conducted	a similar	experiment	at two separate locaAons-one in	Amsterdam	and one in	Noqngham-using a set of	Nash	equilibrium	coordinaAon	games	described	above.	An	example is given in	Figure	5. In this	game,	the	best	response	to	a	player	who	chooses	any	of the	opAons	with	equal probability is to	pick	one	of the	opAons	associated	with	the	payoff	of	10.	This is	because	somebody	who chooses	at	random	is	expected	to	play	each	of	the	four	available	strategies	with	equal	probability	of	1⁄4.	As such,	the	expected	payoff	from	choosing	A,	B or	C	(when	the	co-player	chooses	at	random)	is	10	x	1⁄4	=	2.5 while	the	expected	payoff	from	choosing	D	is	9	x	1⁄4	=	2.25.	Therefore,	a	level-1	reasoner	would	never	choose D.	From	this	it	follows	that	level-2	reasoners	would	never	choose	D	either,	since	they	are	best-responding	to the	choice	of	level-1	types,	and	would,	hence,	also	pick	one	of	the	opAons	associated	with	the	payoff	of	10. Bardsley	et	al. (2010)	hypothesized	that	team	reasoners	would	choose	opAon	D	due	to	the	uniqueness	of the	outcome	(D,	D)	and	the	indisAnguishability	of	the	outcomes	(A,	A),	(B,	B)	and	(C,	C),	which	allows	players to	easily	coordinate	their	acAons.	In	the	experiment,	games	were	not	presented	to	parAcipants	in	the	form of	a	matrix	as	shown	in	Figure	5	and	there	was	no	way	to	disAnguish	between	the	available	strategies	and 10 This	is	assumed	in	the	most	frequently	occurring	version	of	the	cogniAve	hierarchy	theory.	For	a	sightly	different version,	where	level-0	decision-makers	randomize	between	all	of	the	available	opAons,	but	assign	slightly	higher probability	to	the	play	of	the	strategy	associated	with	the	highest	personal	payoff	or	that	with	the	most	salient label,	see,	for	example,	Crawford	et	al.	(2008). 10 A B C D A 10,	10 0,	0 0,	0 0,	0 B 0,	0 10,	10 0,	0 0,	0 C 0,	0 0,	0 10,	10 0,	0 D 0,	0 0,	0 0,	0 9,	9 Figure	5:	An	example	of	a	game	from	the Amsterdam	experiment	in	the	form	of	a	game matrix Team	Reasoning:	Theory	and	Evidence outcomes other than in terms of payoffs that the players would aXain if they	managed to successfully coordinate	their	choices.	For	example,	the	outcome	(A,	A)	could	not	be	idenAfied	as	being	unique	due	to	its top-leo posiAon in the	matrix or because of being associated	with choice opAons labelled	with the first leXer	of	alphabet.	NoAce	that	(D,	D)	is	not	Pareto	efficient:	it	is	inferior	to	the	outcomes	(A,	A),	(B,	B)	and	(C, C).	The	reasoning	behind	the	suggesAon	that	team-reasoning	decision-makers	would	opt	for	the	outcome (D,	D)	is	that,	in	the	case	of	the	three	indisAnguishable	outcomes	(A,	A),	(B,	B)	and	(C,	C),	a	player	can	only "pick"	one	of	them	and	hope	that	the	other	player	would	"pick"	the	same	one,	whereas	in	the	case	of	the outcome (D,	D), a player is "choosing" the corresponding strategy	D because of the uniqueness of that outcome.	If	both	players	pick	one	of	the	three	indisAnguishable	outcomes,	there	is	a	1⁄3	chance	that	they	will pick	the	same	one,	whereas	if	they	both	choose	strategy	D,	they	can	be	sure	of	aXaining	the	outcome	(D, D).	So	the	expected	payoff	from	trying	to	coordinate	on	one	of	the	outcomes	(A,	A), (B,	B)	or (C,	C) for	a team-reasoning	decision-maker	is	31⁄3	while	the	certain	payoff	from	coordinaAng	on	the	outcome	(D,	D)	is	9. (See	Gold	and	Sugden's introducAon	to	Bacharach	(2006)	for	more	on	this idea.)	To	put	this	differently, it may be said that	ex ante, before the uncertainty about the other player's acAon is resolved and when players	take	into	account	the	likelihood	of	coordinaAng	their	acAons	in	the	computaAon	of	their	expected payoffs, the opAmal outcome in terms of Pareto efficiency is (D,	D). Ex post, once the game has been played,	the	three	outcomes	(A,	A),	(B,	B)	and	(C,	C)	Pareto	dominate	(D,	D).11 The experimental results, though showing a clear deviaAon from individualisAc best-response reasoning (assuming that it would not discriminate among the available Nash equilibria), are different in the Amsterdam	and	the	Noqngham	experiments.	The	results	from	Amsterdam	seem	to	suggest	the	presence	of team reasoning rather than cogniAve hierarchy reasoning,	whereas the results from	Noqngham tend to suggest the opposite. In addiAon to making choices in numerical coordinaAon games, such as the one illustrated	above,	both	experiments	asked the	parAcipants to	complete	other	non-numerical "text" tasks. These	differed	between	the	two	experiments	and	the	authors	speculate	that	there	may	have	been	spillover effects from the text tasks on the modes of reasoning used	in the numerical coordinaAon tasks. In Amsterdam,	text	tasks	involved	picking	the	odd	one	out,	so	parAcipants	may	have	tended	to	pick	strategies that	were	associated	with	outcomes	appearing	as	odd	ones	out	in	the	number	tasks,	while	in	Noqngham text tasks	gave	more	scope for	picking favourites, so	parAcipants	may	have	tended	to	focus	on	outcomes that	were	associated	with	their	favourite	payoffs. Another	pair	of	experiments	that	focus	on	the	Nash	equilibrium	selecAon	problem	was	carried	out	by	Faillo et	al.	(2013,	2016).	Both	experiments	presented	the	parAcipants	with	two-player	games,	in	which	they	had to	pick	one	of	three	opAons	presented	as	segments	of	a	pie.	See	Figure	6	for	an	example.	Upon	successfully coordinaAng	on	one	of	the	three	pie	segments	parAcipants	received	posiAve	payoffs,	though	these	were	not always	the	same	for	the	two	players.	In	the	game	of	Figure	6, if	we	call	the	top	leo	slice	R1,	the	top	right slice	R2,	and	the	boXom	slice	R3,	then	the	outcomes	(R1,	R1),	(R2,	R2)	and	(R3,	R3)	yielded	pairs	of	payoffs (9,	10),	(10,	9)	and	(9,	9)	to	the	two	players	respecAvely.	A	representaAon	of	this	game	using	a	game	matrix is	given	in	Figure	7. 11 Note	that	this	idea	is	based	on	an	implicit	assumpAon	that	decision-makers	are	not	extremely	risk-loving.	If	the interacAng	decision-makers	both	preferred	the	1⁄3	chance	of	receiving	a	payoff	of	10	to	a	certainty	of	the	payoff	of	9 (i.e.,	if	they	both	were	extremely	risk-seeking),	then	the	team-opAmal	choice	may	be	to	pick	one	of	A,	B,	or	C	in the	hope	of	coordinaAng	on	one	of	the	outcomes	(A,	A),	(B,	B)	or	(C,	C)	respecAvely. 11 Team	Reasoning:	Theory	and	Evidence Like	the	experiments	of	Bardsley	et	al.	(2010),	these	experiments	were	designed	to	pit	the	theory	of	team reasoning against cogniAve hierarchy theory. Faillo et al. (2013, 2016) also followed Bardsley et al. in hypothesizing	that	team	reasoners	would	take	into	account	the	probability	of	successful	coordinaAon	when working	out	the	expected	payoffs	associated	with	the	available	opAons.	Pairs	of	Nash	equilibria	counted	as indisAnguishable	from	the	perspecAve	of	team	reasoning	when	they	were	symmetric	in	terms	of	payoffs	to the two players, such as the pair of outcomes (R1,	R1) and (R2,	R2) in the above example. In fact, the outcomes	(R1,	R1)	and	(R2,	R2)	were indisAnguishable in	all	games in	the	two	experiments	and	the	team opAmal	choice	was	always	associated	with	the	aXainment	of	the	outcome	(R3,	R3).	(The labels	R1,	R2	and R3 were hidden from parAcipants and the posiAons of pie slices were varied across three different treatment	groups.	The	staAsAcal	analysis	of	results	showed	no	significant	effects	of	pie	slice	posiAons	on	the choice	of	R3	versus	R1	or	R2.) Table	1	summarizes	the	results	of	Faillo	et	al.	(2013).12	Team	reasoning	is	a	good	predictor	in	7	out	of	the	11 games, where the	modal choice was the opAon	R3. The observed choices in the remaining 4 games (in addiAon	to	3	of	the	games	in	which	the	theory	of	team	reasoning	is	a	good	predictor)	can	be	explained	by cogniAve	hierarchy	theory.13	As	such,	the	results	of	the	experiment	are	somewhat	mixed.	Faillo	et	al.	(2013) conclude	that	team	reasoning	fails	when	it	predicts	the	choice	of	a	slice	that	is	ex	post	Pareto	dominated	by 12 The	type	of	pie	games	used	and	the	conclusions	drawn	in	the	two	experiments	are	quite	similar.	We	here	focus	on the	results	reported	in	the	first	study. 13 For	example,	in	the	game	G3	the	cogniAve	hierarchy	theory	predicts	level-1	reasoners	will	play	the	strategy associated	with	the	highest	personal	payoff.	This	is	the	opAon	R1	for	the	player	who	receives	the	payoff	of	10	from the	outcome	(R1,	R1)	and	the	opAon	R2	for	the	player	who	receives	the	payoff	of	10	from	the	outcome	(R2,	R2). Thus,	the	level-2	reasoners'	best	response	strategies	to	the	choices	of	level-1	types	will	be	a	mixture	of	opAons	R1 and	R2,	depending	on	which	player	they	are.	As	a	result,	the	cogniAve	hierarchy	theory	predicts	a	mixture	of	R1 and	R2	choices	with	no	play	of	R3. 12 R1 R2 R3 R1 9,	10 0,	0 0,	0 R2 0,	0 10,	9 0,	0 R3 0,	0 0,	0 9,	9 Figure	7:	An	example	of	a	3x3	pie	game	in	the form	of	a	game	matrix Figure	6:	An	example	of	a	3x3	pie	game	as	seen	by	two	interacAng	players You get 10, the other gets 9 You get 9, the other gets 9 You get 9, the other gets 10 You get 9, the other gets 10 You get 9, the other gets 9 You get 10, the other gets 9 Team	Reasoning:	Theory	and	Evidence the	other	two	and	this	is	not	compensated	by	greater	equality	(games	G3,	G5,	and	G7)	as	well	as	when	the team-opAmal outcome yields less equal payoffs than the other opAons and this is not compensated by Pareto	superiority	(G10).	They	suggest	that	we	need	a	more	general	theory	of	team	reasoning	and	offer	two ways	in	which	the	theory	could	be	amended	to	explain	their	results.	One	is	to	incorporate	the	circumstances of	group	idenAficaAon	(one	of	the	auxiliary	hypotheses	in	any	test	of	team	reasoning,	as	explained	above). Ex	post	Pareto	dominance	and	equality	may	play	an	important	role	in	group	idenAficaAon,	in	which	case	ex ante	Pareto	dominance	will	not	be	sufficient	to	trigger	team	reasoning	by	itself.	The	other	is	to	accept	that people may not achieve the level of reasoning "sophisAcaAon" that would allow them to idenAfy the opAmality	of	the	ex	ante	Pareto	efficiency.	"Naive"	team	reasoners	may	want	to	pursue	the	group	interest but,	because they	do	not idenAfy the	uniqueness	of the	outcome (R3,	R3), they	only	use	ex	post	Pareto efficiency	and	equality	of	payoffs	(when	it	is	not	dominated	in	terms	of	Pareto	efficiency)	when	determining what	the	group	should	do. Although	the	aim	of	this	experiment	was	not	to	test	the	claim	that	game	harmony	predicts	team	reasoning, it	is	clear	that	the	results	do	not	support	that	idea.	Whilst	there	is	a	high	level	of	team	reasoning	in	game G6,	which has perfect alignment of payoffs,	G5 also has perfect alignment of payoffs but relaAvely liXle team reasoning. In contrast, G4 and G9 have lower levels of payoff alignment but high levels of team reasoning.	So	the	predicAons	that	payoff	alignment leads to team	reasoning	and	payoff	conflicts	miAgate team	reasoning	is	not	supported	by	this	set	of	games. There	is	another	way	to	explain	the	results	of	Faillo	et	al.	(2013),	which	challenges	their	assumpAon	about what	the	team	takes	as its	goals.	Suppose	that	team-reasoning	decision-makers	first	establish	the	opAmal outcomes from the perspecAve of the team by idenAfying those outcomes that	maximize the extent of mutual	advantage	as	suggested	by	Karpus	and	Radzvilas	(2016).	These	outcomes	are	always	efficient	in	the weak	sense	of	Pareto	efficiency.	(Recall	that	an	outcome	of	a	game	is	said	to	be	Pareto	efficient	in	the	weak sense of Pareto efficiency, if there is no alternaAve that is strictly preferred to it by every player in the 13 Game Payoffs Results,	% (R1,	R1) (R2,	R2) (R3,	R3) R1 R2 R3 G1 (9,	10) (10,	9) (9,	9) CH	14%	TR CH	11%	TR CH	74%	TR G2 (9,	10) (10,	9) (11,	11) CH	0%	TR CH	1%	TR CH	99%	TR G3 (9,	10) (10,	9) (9,	8) CH	51%	TR CH	45%	TR CH	4%	TR G4 (9,	10) (10,	9) (11,	10) CH	16%	TR CH	4%	TR CH	80%	TR G5 (10,	10) (10,	10) (9,	9) CH	48%	TR CH	34%	TR CH	18%	TR G6 (10,	10) (10,	10) (11,	11) CH	1%	TR CH	3%	TR CH	96%	TR G7 (10,	10) (10,	10) (9,	8) CH	51%	TR CH	31%	TR CH	18%	TR G8 (10,	10) (10,	10) (11,	10) CH	26%	TR CH	22%	TR CH	52%	TR G9 (9,	12) (12,	9) (10,	11) CH	16%	TR CH	11%	TR CH	73%	TR G10 (10,	10) (10,	10) (11,	9) CH	43%	TR CH	27%	TR CH	30%	TR G11 (9,	11) (11,	9) (10,	10) CH	6%	TR CH	7%	TR CH	86%	TR Table	1:	Summary	of	Faillo	et	al.	(2013)	results,	showing	the	percentage	of	subjects	making	each choice	in	each	game; in	all	games,	team	reasoning	is	assumed	to	predict	the	choice	of	R3 (highlighted	in	grey);	choices	predicted	by	cogniAve	hierarchy	theory	are	indicated	by	CH Team	Reasoning:	Theory	and	Evidence game.)	The	players	then	seek	ways	to	coordinate	their	acAons	on	one	of	the	outcomes	in	the	idenAfied	set using unique features of some outcome (if an outcome with unique features exists) as a possible coordinaAng	device.	This	approach	could	explain	choices	observed	in	games	G3,	G5	and	G7	in	addiAon	to the	7	explained	originally.14	For	example, in the	game	G5, the	outcomes (R1,	R1)	and (R2,	R2)	are	strictly preferred	to	the	outcome	(R3,	R3)	by	both	players	and,	hence,	by	Karpus	and	Radzvilas's	approach,	they	are deemed	opAmal	from	the	perspecAve	of	the	team.	Since	there	is	no	further	way	to	discriminate	between the	laXer	two	outcomes,	team-reasoning	decision-makers,	according	to	this	interpretaAon,	end	up	playing	a mixture	of	the	two.	In	the	game	G1,	on	the	other	hand,	none	of	the	three	equilibria	can	be	excluded	from the set of team-opAmal outcomes, since they all provide the same extent of	mutual benefit to the two players. The outcome (R3, R3), however, is unique in this set and team-reasoning decision-makers, therefore,	opt	for	this	outcome. 6.	Tests	Involving	Non-Nash	Equilibrium	Play We now turn to tests of team reasoning where a team selects outcomes that are not Nash equilibria. Although any empirical study of games in	which team reasoning prescribes non-equilibrium	play can be seen	as	a	test	of	the	theory	(e.g.,	any	test involving	the	Prisoner's	Dilemma	game)	reviewing	all	historical studies	of	games	of	this	type is	beyond	the	scope	of	this	chapter. Instead,	we	will focus	on	two	relaAvely recent	experiments	that	specifically	refer	to	the	theory	of	team	reasoning	in	their	hypotheses. Colman	et	al.	(2008)	conducted	an	experiment	(Experiment	2	in	their	paper)	with	five	one-shot,	3x3,	twoplayer	games	with	symmetric	payoffs	(i.e.,	each	game	was	played	once,	there	were	three	strategies	available to each player and the payoffs to the two players were symmetric). All games had a unique Nash equilibrium	and	a	unique	non-equilibrium	outcome	that	was	opAmal	from	the	perspecAve	of	a	team.	The study assumed team play to be the maximizaAon of the average of players' payoffs. The predicted outcomes,	however,	would	be	the	same	using	any	of	the	accounts	of	a	team's	goals	discussed	in	SecAon	3 above.	An	example	of	one	of their games is given in	Figure	8,	where the	unique	Nash	equilibrium is the outcome	(E,	E)	and	the	opAmal	outcome	for	a	team	is	(C,	C). The	results	of	the	experiment	show	that	in	four	games	(out	of	five)	slightly	more	than	half	of	parAcipants chose	strategies	that	were	associated	with	the	team-opAmal	outcome	and	in	one	of	the	games	this	share was	higher	(86%).	An	important	feature	of	all	games	in	the	experiment	was	that	the	team-opAmal	outcome was superior to the	Nash equilibrium in terms of Pareto efficiency (which	makes these cases somewhat similar to the Prisoner's Dilemma game). This may suggest that in cases of one-shot interacAons with unique	Nash	equilibria	that	are	not	Pareto	efficient	about	half	of	decision-makers	reason	as	members	of	a 14 In	the	game	G10	this	approach	establishes	team-opAmal	outcomes	to	be	(R1,	R1)	and	(R2,	R2),	thus	predicAng	no play	of	(R3,	R3). 14 C D E C 8,	8 5,	9 5,	5 D 9,	5 7,	7 5,	9 E 5,	5 9,	5 6,	6 Figure	8:	An	example	of	a	3x3	game	form Colman	et	al.	(2008) Team	Reasoning:	Theory	and	Evidence team	and	play	accordingly. In	a	different	experiment,	Colman	et	al.	(2014)	used	another	set	of	eight	one-shot,	3x3	and	four	4x4,	twoplayer games where every game (with the excepAon of one) contained a unique Nash equilibrium and disAnct	but	also	unique	non-equilibrium	predicAons	based	on	the	theory	of	team	reasoning	and	cogniAve hierarchy	theory.15	Examples	of	the	games	are	given	in	Figures	9	and	10. The	study	assumed	team	play	to	be	associated	with	the	maximizaAon	of	the	average	of	players'	payoffs	(the corresponding outcomes are indicated in bold in Figures 9 and 10). Sugden's (2015) noAon of mutual benefit (see	SecAon	3	above)	and the funcAon	of team's goals	discussed	by	Karpus	and	Radzvilas (2016) would	yield	different	predicAons	in	some	of	these	games	(for	example,	in	Figure	9	the	opAmal	outcome	for the	team	based	on	the	noAon	of	maximal	mutual	advantage	would	be	the	outcome	(A,	A)).	The	results	of the	experiment	are	mixed,	with	at least two	out	of three	or three	out	of four	available strategies	played quite frequently. This, combined	with uncertainty about	which outcome is the team reasoning soluAon, makes	it	difficult	to	idenAfy	which	mode	of	reasoning	predominates. Furthermore,	many	of these	results	could	be	explained	by	a	combinaAon	of	level-0	and	level-1	reasoning, which	simply	corresponds	to	random	picking	and	best-responding	to	a	random	choice	of	the	other	player (also	see	Sugden,	2008,	who	suggests	that	these	results	would	be	obtained	with	a	populaAon	consisAng	of 50% team-reasoners, 40% level-1 and 10% level-0 types). There is some evidence that increasing the difficulty	of	a task increases the	amount	of randomizing (Bardsley	and	Ule,	2014).16	Since the	games that Colman	et	al.	(2014)	used	had	numerous	strategies	and	non-symmetric	variable	payoffs,	and	appear	to	be quite	complex	and	cogniAvely	demanding	in	the	idenAficaAon	of	raAonal	outcomes,	random	picking	and	the principle of insufficient reason (which	means best-responding to a random choice)	may provide a good explanaAon	of	the	actual	choices. Conclusion	and	Further	Direc7ons In	this	chapter	we	reviewed	some	of	the	recent	developments	of	the	theory	of	team	reasoning	in	games. Since its early developments, which were triggered by orthodox game theory's inability to definiAvely resolve	certain	types	of	games	with	mulAple	Nash	equilibria (such	as	the	Hi-Lo	game)	and	explain	out-of15 The	study	also	refers	to	a	mode	of	reasoning	called	the	strong	Stackelberg	reasoning,	but,	since	the	laXer	always predicts	the	play	of	a	Nash	equilibrium,	in	all	(but	one)	of	the	studied	cases	it	is	indisAnguishable	from individualisAc	best-responding. 16 Bardsley	and	Ule	(2014)	test	for	team	reasoning	vs.	cogniAve	hierarchy	and	the	principle	of	insufficient	reason	in	a 'risky'	coordinaAon	game,	where	players	may	experience	losses	as	well	as	gains.	Their	results	favour	team reasoning.	(We	learned	of	this	paper	too	late	to	review	it	in	detail	in	this	chapter.) 15 A B C A 3,	3 1,	1 0,	2 B 1,	1 1,	4 3,	0 C 0,	0 2,	1 2,	5 Figure	9:	An	example	of	a	3x3	game	from Colman	et	al.	(2014) A B C D A 4,	4 2,	0 3,	2 1,	5 B 2,	2 3,	3 2,	2 2,	0 C 4,	3 2,	4 2,	5 3,	2 D 5,	2 0,	3 0,	0 1,	1 Figure	10:	An	example	of	a	4x4	game	from Colman	et	al.	(2014) Team	Reasoning:	Theory	and	Evidence equilibrium	play	in	others	(such	as	the	Prisoner's	Dilemma	game),	the	theory	has	advanced	in	a	number	of different direcAons. From the theoreAcal point of view, different answers were proposed to the two fundamental	quesAons that the theory	of team reasoning	needs to	address: "when	do	people reason	as members	of	a	team?"	and	"what	is	it	that	they	do	when	they	reason	in	this	way?".	In	response	to	the	first quesAon,	it	has	been	suggested	that	the	mode	of	reasoning	that	an	individual	decision-maker	adopts	may depend on that decision-maker's psychological make-up, it may be endorsed by the decision-maker depending on a number of condiAons that need to be saAsfied, such as the assurance of others' parAcipaAon in	team	play	and	the	noAon	of	mutual	benefit,	or it	may	be	a	result	of	raAonal	deliberaAon about	which	mode of reasoning is instrumentally	most useful in any given situaAon. In response to the second	quesAon,	one	aspect	that	differenAates	the	suggested	answers	is	whether	they	allow	team	play	to advocate	a	potenAal	sacrifice	of	some	members	of	a	team	for	the	benefit	of	others. The	results	of	the	nascent	developments	in	empirical	tesAng	of	the	theory,	a	number	of	which	we	reviewed in the second part of this chapter, are, at best,	mixed and further research in this field is needed. The studies	start	from	the	assumpAon	that	the	games	they	use	are	situaAons	where	people	could	be	expected to team reason. Nevertheless, some of them can be seen as providing indicaAve answers to the first quesAon,	"when	do	people	reason	as	members	of	a	team?",	because	they	arguably	idenAfy	circumstances in	which	people	are likely to team	reason.	One interpretaAon	of	Faillo	et	al. (2013) is that	ex	post	Pareto dominance	and	equality	play	an	important	role	in	group	idenAficaAon.	One	interpretaAon	of	Colman	et	al. (2014) is that the team reasoning outcome needs to be simple and clear, as complex or cogniAvely demanding games lead people to randomise.	However, these are speculaAve hypotheses which were developed	post	hoc	to	explain	the	experimental	results	and	they	sAll	need	to	be	put	to	the	test.	None	of	the experiments	aim	to	test	the	mechanism	by	which	people	adopt	team	reasoning:	whether	it	is	caused	by	a psychological	process	or	a	decision,	and	the	role	of	assurance	and	players'	beliefs	about	what	others	will	do. With	regards	to	the	second	quesAon,	"what	is	it	that	team	reasoning	decision-makers	strive	for?",	in	some of the games that have been studied, the predicAons of the various funcAonal representaAons of team interests	coincide.	This	is	ooen	so	in	Nash	equilibrium	coordinaAon	games.	But	even	then	some	differences are	possible	(recall,	for	example,	the	interpretaAon	of	results	discussed	by	Faillo	et	al.	(2013)	based	on	ex ante	vs.	ex	post	opAmality	of	the	considered	outcomes	and	the	idea	of	coordinaAon	among	outcomes	that are	maximally	mutually	beneficial). In	more	complex	scenarios	studied	by	Colman	et	al. (2008,	2014),	the differences between various predicAons of team play loom larger, which may therefore offer a beXer ground	to	test	the	compeAng	assumpAons	about	team	reasoning	decision-makers'	goals,	keeping in	mind that	if	games	get	too	complex	that	may	miAgate	against	team	reasoning. Any	experimental	test	of	the	theory	of	team	reasoning	is	complicated	by	the	mulAplicity	of	hypotheses	that are	to	be	tested	simultaneously	in	connecAon	with	the	above	quesAons.	It	may	thus	be	necessary	to	apply methods that go beyond mere observaAon of decision-makers' choices in games, e.g., asking the parAcipants to explain the reasons	behind their choices, or encouraging the adopAon	of one	or another mode	of reasoning through the	use	of addiAonal pre-play tasks.	One	possibility for further experimental work is to study how priming group or individualisAc thinking affects people's choices in simple Nash equilibrium	coordinaAon	games	where	the	team-opAmal	outcome	seems	to	be	obvious.	Such	a	test	would accord	with a number of versions of the theory	with respect to	what is assumed to trigger the shio in individuals'	adopted	mode	of	reasoning	as	well	as	a	number	of	suggested	funcAonal	representaAons	of	a 16 Team	Reasoning:	Theory	and	Evidence team's	goals. Acknowledgements We	are	extremely	grateful	to	Nicholas	Bardsley,	Julian	Kiverstein,	Guglielmo	Feis	and	Mantas	Radzvilas	for their	invaluable	suggesAons	which	we	used	to	improve	earlier	versions	of	this	work.	We	are	also	grateful	to James	Thom	for	a large	number	of insighwul	discussions	on the topic	during the	course	of	preparing this chapter.	Our	work	on	this	chapter	was	supported	by	funding	from	the	European	Research	Council	under	the European	Union's	Seventh	Framework	Programme	(FP/2007-2013)	/	ERC	Grant	Agreement	n.	283849. 17 Team	Reasoning:	Theory	and	Evidence References Bacharach,	M.	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