Floating ideas—An experiment in enhancing hypergames with maps

OMEGA Int. J of Mgmt Sci. Vol. 13, No. 4. pp. 331-34"7'. 1985

0305-0483 $5 83.00 + 0 . 0 0 Copyright ~ 1985 Pergamon Press Ltd

Printed in Great Britain. All rights reserved

Floating Ideas An Experiment in Enhancing Hypergames with Maps CHRIS HUXHAM University of Strathciyde, UK PETER

BENNETT

University of Sussex, UK (Received August 1984: in revised J'orm December 1984) Within the OR community, an increasing emphasis is being placed on developing approaches to tackle complex, 'messy' decision problems. The work described in this paper arose out of the premise that it would be desirable to integrate ideas from a number of different approaches of this type. Specifically, the paper describes one experimental attempt to link methods for modelling conflict situations (the analysis of options and hypergames) with the cognitive mapping approach to eliciting subjective data. Taking a personally-owned decision problem, mapping was used to enrich the game-based approaches by providing a way of documenting the argumentation underlying the models used. Though difficult to generalise from, the experiment not only suggested that such an extension is likely to be an improvement, but also highlighted some deficiencies in the existing versions of the game-based approaches themselves.

INTRODUCTION IN OPERATIONAL RESEARCH (OR), as elsewhere, researchers often tend to devote their efforts to one particular line of interest, developing a fairly specialised set of ideas as far as possible. However, it also seems important that effort should go into linking the various sets of ideas. Cross fertilisation can aid the development of each individual approach and may also lead to integrative work. In practical terms, the maxim "problems do not come in packages" provides a further justification for having a variety of ideas available. For some years, our own main research interest has been in developing hypergame analysis as a way of structuring and analysing situations involving several decision-makers with conflicting aims. We remain interested in the further development of hypergames p e r se. However, much of our recent effort has gone into trying to integrate insights gained from this work with those gained from other approaches toward 'messy" decision-problems [4]. This 331

paper stems from a joint project involving ourselves and researchers at the University of Bath. Its main purpose has been to investigate ways of combining decision-aiding using cognitive mapping with methods using hypergames and related forms of analysis--e.g, analysis of options. As hypergames are intended to take into account the subjective world of decision-makers-precisely what is captured by cognitive mapping--it seemed plausible that the two could usefully be brought together. (Quite independently, the relationship between them is explored more theoretically by Bryant [9].) A first idea was that one could first build up a map or maps, then extract perceived parties. options, preferences etc--i.e, the 'raw material' for hypergame modelling. Experience on 'trial' problems showed that such a process could be far from straightforward. Current work entails the further exploration both of this and other possibilities. This paper reports one such exploration; in this case, the idea was to structure a perceived problem in game/hypergame terms first, then use piecemeal maps to explore partic-

332

Huxham, Bennett--Enhancing Hypergames ~ith Maps

ular outcomes, thus identifying reasons for assigning perceived preferences to them. This paper describes a first attempt to apply this approach to a real life problem, and to draw some tentative conclusions: the process of doing this also led us to identify some areas for development within the hypergame methdology itself. A PARTIAL OVERVIEW OF THE APPROACHES Our description of the ideas brought together in this study can be no more than a rough overview. It must be emphasised that this is a partial account, largely restricted to those aspects of each approach that turned out to be relevant in this case. To appreciate each approach as a whole, readers not already familiar with the material should refer to the original works cited. Cogniti~'e mapping: the Bath approach This work, pioneered by Eden et al. at the University of Bath, rests on fundamental premises to do with the subjective nature of problems (especially on ideas from 'personal construct' psychology). In practice, their work has been primarily concerned with managing the process of group decision making (see e.g. [11, 12]). A guiding principle is that in many situations, problem-aiding is best done with the consultant acting as a "facilitator' rather than as an "expert" problem-solver. To aid this process, they have developed methods based around cognitive mapping. A 'map', essentially a means of expressing subjective reasoning, is made up of concepts and the links between them. To illustrate, consider the (italicised) 'guiding principle' in the paragraph above. The reasoning could be mapped. as: c o n s u l t a n t as facilitator & "good' p r o b l e m - a i d i n g . . . c. as expert problem-solver. where t h e 2 * m a y be read as "leads to'.

Here the first concept has a clearly-defined opposite, namely 'consultant as "'expert'" problem-solver'. Exploring such 'polar' opposites can help to clarify the concept. Had the opposite been 'no consultant' (whether stated or implied), the original meaning would have been quite different. The opposite 'consultant as a

hindrance" would have implied something different again! The opposite to "good problem-aiding" remains to be specified. Even in this very simple case, there would have been other ways of mapping the argument, differing in detail. What is important is that the map should represent the issue as seen by the problem owners----each must be able to 'own" the maps produced. Since the aim of mapping in this context is to aid thinking and discussion, 'accuracy' in the sense of ensuring that two or more analysts will produce the same map from the same data (so-called 'inter-coder reliability') is seen as irrelevant, as would be any demand that the maps be 'logical' to an outside observer. (In this respect, this approach differs from the mapping techniques used by Axelrod et al. [1]). Within the process-oriented methodology developed at Bath, mapping is used both to capture and explore the subjective reasoning used by individuals, and as a tool for negotiating problem issues--between clients and between client and consultant. In this work, we have focused mainly on the former role, using the tool in a way that largely ignores the perspectives on organisational problem-solving within which it was developed. Options analysis and hypergames Both of these approaches are concerned with modelling situations involving conflicts of interest. Conceptually, both are developments from game theory. Hence, fundamental elements of the model are the relevant players ('actors', 'parties', 'participants'), the actions open to each, and their preferences for the outcomes that can result. The analysis of options approach (see e.g. [15]) categorises the actions available in terms of simple 'yes/no' options, which can be expressed in a tableau format. Analysis proceeds by comparing different possible outcomes ('scenarios'), consisting of feasible combinations of options. One looks for improvements for individuals, sanctions against any such improvements, and so on, with the aim of showing which outcomes are stable--i.e, likely eventual resolutions of the conflict. Hypergame analysis, originally a separate development, started from the premise that different players would perceive different 'games' [2]. One thus needs to consider the actions, preferences, etc seen by each side. This

Omega. Vol. 13. No. 4

can be done using the original game-theoretic format, or by carrying out options analysis, from the point of view of each party. The latter is the format used here. In earlier papers, we have stressed a role for the hypergame approach as an aid to problem-structuring, rather than as a prescriptor of precise courses of action [6]. Specifically, we have suggested that analysis should begin with a 'preliminary problemstructuring' phase, in which one tries to identify sets of issues--which may be linked--and important participants involved in each. To facilitate this, we have developed a notation for modelling the issues and participants, known as a preliminary problem-structuring (PPS) diagram. One function of this is to encourage consideration of relevant factors outside the immediate situation. More specific hypergame or options-analysis models can then be introduced.

A form of linkage Encapsulated in any hypergame-type model, there is a wealth of assumptions about how the parties involved may see the world, and why they may thus be expected to act in particular ways. On their own, however, the game-based approaches lack any procedure for eliciting and representing the argumentation behind the assumptions. Consequently, the former has tended to be done in an ad hoc way, and the latter--if done at all--in plain writing. There thus appeared an obvious role for cognitive mapping in helping to capture the relevant reasoning. Would doing this provide anything additional to the hypergame approach? M E T H O D OF S T U D Y

Choosing a problem Research using post hoc case-studies to try out particular techniques or methodologies has frequently been criticised. Such studies have some role to play, however, partly because of the ethical problems of using untried ideas on a 'real' problem-owner, and also because cases can be chosen with specific features that will illustrate, and aid the development of, given aspects of the approach. Even so, the limitations of post hoc studies done by 'outside' observers are considerable. Here, for example, we were anxious to look at a problem without the benefit of too much hindsight. Even more, we felt that

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it should be done in conjunction with a t least one 'real" participant in the problem. We might then have some basis for judging whether our ideas would be useful as a practical form of decision-aiding. The concept of a "co-operating client' who has a real problem, but is also aware that the study is 'experimental" is one useful way around this dilemma [8], but even then, the researcher needs to maintain a high degree of commitment if the gains are not to be one-sided. Moreover, setting up such a project is a nontrivial task: the aim here was a 'quick and dirty' experiment rather than a prolonged research project. As a compromise, we thus chose to analyse a problem with which one of the present authors was involved. The case was particularly attractive since it appeared to have elements 'obviously' amenable to hypergame analysis, as well as factors that could be well-expressed using the mapping format. In some respects, such a choice obviously makes the study artificial. Choosing a "suitable' problem is a debatable approach (though one that seems justifiable in the context of developing a set of ideas). More importantly, it is certainly unusual for a problem-owner also to be one of the analysts. Does this 'invalidate' the study? We should certainly be very wary of generalising too much from such a case. The interaction between 'client' and analyst was obviously affected not just by the dual role of one participant as such, but by a pre-existing similarity between the 'client's' perceptual frame work and the ideas introduced in analysis. In this respect, conditions were very far from 'typical'. On the other hand, it can be argued that a decision-aiding methodology ought to be useful for one's own decisions, at least from time to time. Otherwise one is in the position of the bald-headed man selling hair-restorer. Moreover, there are positive advantages to be gained from applying ideas to a problem about which one already has intimate knowledge. Though 'success' may prove little, it is a good position from which to observe that the theory does not quite fit! In this case, as noted below, the exercise led us to reconsider the concepts used in hypergame 'problem structuring', as well as some aspects of the formal analysis.

Procedure As the exercise was largely experimental, we feel it important to describe what we actually

Huxham. Bennett--Enhanclng ttypergames with Maps

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did, rather than--as is more usual--providing a tidied-up retrospective description. Our rough initial plan was as follows. First, the problem 'owner' would provide a description of the problem from which to work. We would then structure it in hypergame terms, by producing a PPS diagram and by starting to list available options and possible outcomes. The mapping approach would then be used to explore argumentation around these options and outcomes relevant to perceived preferences. In this particular experiment, we were more concerned with the ability to map a given actor's perception of

a problem in a way that fitted with a game-type structure, than with a differing perceptions that might be held by other parties. (Ordinarily, the hypergame approach places great importance on the latter.) Not suprisingly, the actual procedure was much more cyclical. Each stage of the process could be used to inform and modify each other stage. An outline of how this worked out in practice, including the main feedback loops, is shown in Fig. 1. The next section will describe the various stages (and 'loops') in more detail. We will then summarise both what was learnt

,I (i) description of the problem

(~) elaboration of ) " PPS diac~ram

~,~

identification of parties & players

(iii) identification of options (c) / 7"'Central"

possJble outcomes

in the issue

....

"-,,

some infeasibilities

("good" or "bad")

(iv}

moppin 9

.... of argumentation around various outcomes

(el

.... for various players( " ~ v

J_ I

(v) more thorough analysis of options with preferences [some alternative models exptored) stability anaiysis

Fig. 1. Problem exploration and process of analysis. (Main feedback loops--(a) PPS "forces" further elaboration of the problem. (b) Mapping suggests interactions ignored in "first shot" PPS: hence re-working of (i) and (ii). (c) Considering outcomes allows more concise description of options. (d) Consideration of options, outcomes, infeasibilities again "forces" problem elaboration. (e) More thorough analysis leads to revision of initial "'possible" outcomes.)

Omega, Vol. 13, No. 4 a b o u t the p r o b l e m itself by using the m e t h o d s described, a n d what was learnt a b o u t the methods by trying to apply them. In reality, o u r learning took place as the exercise proceeded, and via s u b s e q u e n t reflection on it. In order to provide a c o n t i n u o u s n a r r a t i v e however, this c o m m e n t a r y has been kept separate from our description o f the study. It is hoped that this will also help readers form their own o p i n i o n s a b o u t the exercise, which can then be c o m p a r e d with ours. THE STUDY (i) The problem The p r o b l e m chosen as a vehicle for exploring our ideas was one that had been giving one o f the writers a good deal of worry. It concerns the affairs of a sporting organisation. The following a c c o u n t p a r a p h r a s e s the description taken as the s t a r t i n g - p o i n t for analysis: here, as elsewhere, proper n a m e s have been o m i t t e d or changed.

335

decisions now rested on the championship issue. (For example, a special Southern Area championship had been arranged on the assumption of the major championship in Wales. If the latter were to be moved to England, it would be better to leave out the area event. The dates of two open meetings depended in turn on that decision.) All this involved negotiation--sometimes delicate---with the clubs concerned. The possibility of a clash of championship dates with the Swedes was increasing all the time, since they were under pressure to fix their date. A clash had happened once before, resulting in a last-minute cancellation amid much bitterness. Finally, another danger now loomed. If Llados were not to run the event, it might be too late to find any other venue. In short, someone had to do something, and quickly--but what?" We deliberately set ourselves the task of a n a l y s i n g the s i t u a t i o n as described above, t h o u g h by the time the study was carried out events had moved o n a little. Decisions to resolve the i m m e d i a t e crisis had been made. The analysis was still o f practical importance, however, not least because a roughly similar problem was s h a p i n g up over the following year's c h a m p i o n s h i p . The t i m i n g also allowed only m i n i m a l hindsight in that i m p o r t a n t aspects of the original situation had still to be played out. It was certainly too early to tell whether the decisions m a d e had t u r n e d out 'right' or 'wrong'.

"The Albatross is a class of sailing dinghy, much used for racing. The class's affairs are organised nationally by the English Albatross Association. This has an elected committee, of which I am currently chairman. There are similar associations in other countries where the Albatross is sailed, notably in Wales, Sweden and Australia. But the English Association has by far the largest mem- (ii) S o m e problem-structuring bership. Internationally, activities are (loosely) coordinated through a class Federation. T h e first step towards analysis was to work "'The story starts in the Summer of 1982: the problem toward a d i a g r a m s h o w i n g the relevant parties, concerned the 1983 World Championship. The annual i n t e r a c t i o n s a n d issues as initially perceived by (summer) event is run in rough rotation between the four main countries, and 1983 was a 'Welsh' year. Normal the p r o b l e m owner. This was d o n e in an iterprocedure was for their association to make arrangements ative way, with the pen passing frequently bewith some suitable sailing club to run the event: preliminary arrangements had been made with a club at tween the two participants. After a few atLlados. English class members were showing some reluc- tempts, the basic structure s h o w n in Fig. 2 tance to go to Wales (for various reasons including emerged. This shows a set o f interactions at the distance). But our committee was committed to proi n t e r - o r g a n i s a t i o n level: moting the event as hard as possible, and a good turnout was felt to be vital. "As time passed, we had become increasingly anxious to have the championship venue confirmed, and date fixed. (a) between the English Association, the Welsh This was needed both to enable people to book their A s s o c i a t i o n a n d the Llados Sailing Club, holidays, and to help us organise the rest of our 1983 specifically over the issue o f when a n d fixtures. Furthermore, the Swedes were organising their own National Championship: a clash of dates here would where the c h a m p i o n s h i p would be held, have been disastrous. However, no firm answers were (b) between the English, Welsh a n d Swedish forthcoming from Wales. Associations, a t t e m p t i n g to avoid a clash of "Out of the blue, in October, came a startling call from the Welsh Association chairman. He reported great c h a m p i o n s h i p s (this issue did n o t involve difficulties with Llados, putting the whole event in doubt. the A u s t r a l i a n s , whose championship No agreement had been reached with the club, which would a n y w a y be held in ' o u r ' winter itself seemed divided into factions for and against running the event. These were giving quite different stories regardmonths), ing facilities, cost, and so on. (c) between the English Association and the 'Time was now t'ery short, for several reasons. Apart from various English clubs, over the 'domestic' week-long championships, the class had an "open meeting' most weekends, each at a different club. Chains of fixture list.

Huxham. Bennett--Enhancing Hypergames with ),laps

336

SA,L,NO CLU [ n tero.ci'lons :

Over main decision

!

I

on

"Worlds"

Over co-ordination

I I

with Swedixh championship

WELSH ASSOCIATION

_ Over domestic I

....

English fixtures Bergen factions within Llados Within each national association

! ENGLISH ASSOCIATION

(Each Association shown with unspecified "infernQl" interac Hans, with potentially many players)

SWEDISH ASSOCIATION

% %

I / (Many) English Clubs

/

• ~----.-,~

[

" l

Fig. 2. PPS diagram: the problem as initially perceived.

Additionally, various seemed relevant:

'internal'

interactions

(d) most significantly, between factions within Llados Sailing Club, ' p r o ' and 'anti' staging the championship there, (e) within each of the Association committees. For example, though the English committee seemed to share a roughly similar view of the problem, some members of it were less sympathetic to the Welsh than others.

It should be stressed that this was not intended as a 'complete' view of the problem as seen by the problem owner, let alone in an 'objective' sense, and could have been elaborated and added to in various ways. Some other interactions were explored at this stage; e.g. those between key individuals within the organisations. As will be seen, however, more were identified at later stages of the exercise, thus leading to an expansion of this initial view.

Omega, Vol. 13, No. 4

(iii)

337

Though we did so later, no attempt to examine the feasible and infeasible outcomes exhausHaving arrived at a reasonably broad overall tively was made at this stage. Instead, the picture, the next step was to consider the "cenoptions were used to generate a few particularly tral' issue exercising the 'problem owner'--that 'important' outcomes--as judged by the probof the championship venue. The aim was to lem o w n e r - - a r o u n d which further arguexamine the interaction between the English and mentation could be based, and to explore some Welsh Associations and the Llados Sailing infeasibilities felt to be significant. The result Club. Other interactions would be considered to was the tableau shown in Fig. 3. Outcomes are the extent that they affected preferences or represented by columns of ls and 0s, which constrained actions. We started by considering show options taken up and not taken up. For the main actions that seemed open to each side, example, the first column represents the status as seen from the viewpoint of the English comquo, in which--reading downwards--Llados mittee, and looking at some possible outcomes. The process of doing this was cyclic. We began had not made a definite proposal, the Welsh by thinking about options for the key par- Association had taken no positive action, while ticipants and these defined some possible out- the English Association was supporting the comes. Discussion of these led us to redefine World Championship's being held in Wales and some options and consider new ones, and so on. not attempting to stage a championship in A working definition of possible options for England. Six different outcomes, together with the choices that would bring them about, were each participant was eventually arrived at: considered now, which seemed conveniently to cover most possibilities differing radically from each other. Rough notes about each were added Llados Sailing Club (1) Propose definite to the tableau, as shown. championship To the right of Fig. 3 are shown some inarrangement feasible combinations of options, with reasons Welsh Association (2) Agree to Llados's noted for their perceived infeasibility. The first proposal (if one three of these columns represent 'logical' infeasibilities. For example, we assumed that the is made) (3) Withdraw from Welsh could not both agree to Llados's proposal and withdraw, and that the Welsh AssociLlados ation could not agree unless a proposal was (4) Seek alternative made by Llados. The other infeasibilities noted Welsh venue reflect some 'non-obvious' features of the situ(5) Take offence ation. A possibility actively under consideration at English by the English committee (option 8) was to run (6) Support event English Association the world championship in England. Constiin Wales tutionally however, such a change could not be (7) Stage an English made except by mutual consent, i.e. unless (at National least) the Welsh decided to withdraw from Championship Llados and not seek another Welsh venue. Thus (8) Stage World (8) is incompatible both with (4) and with Championshp in not-(3). England The next column concerns the option of holding an English National Championship. In this model, the options are broadly Such events, also lasting a full week, had been defined: a more detailed 'tactical' analysis would held in previous years, though this would not have entailed splitting most into several sub- normally be done with a World championship cases. Some of the less 'obvious' options are in the UK. In principle, the English could explained below. Since each of the eight options unilaterally decide to have such a chamcould be taken up or not, the model contains 28 pionship. The infeasibility points to a significant potential outcomes (combinations of options): twist in the story. Llados had previously agreed to consider hosting the World event only ~fthis however not all were taken to be feasible. Options and outcomes

Huxham. Bennett--Enhancing Hypergames with Maps

338

S I GNIr-[ CANT OUTCOMES PERCEIVED

SOME INFEASIBLE COMBINATIONS

Llados Sailing Club 1.

Propose . . . .

0

I

0

0

(0)

-

0

-

.

,

.

Welsh Association 2.

Agree

0

1

0

0

(0)

111

3.

Withdraw . . . . . .

0

0

1

0

(01

I -

-

/..

Alternative ......

0

0

0

1

(0)

-

I

5.

Offence ....

0

0

-

0

{0)

Encjlish

...

-

1

Association

6.

Support . . . . .

1

1

7.

"National s"

0

0

0

0

1

8.

"Wortds"

0

0

0

0

(0)

1

1 1 I

I

I

rc:

I

o

m

N._~o championship

- Worst outcome Status not

Qua

~8

tiked

by us

Next

.<

=-

o

best

for Welsh ?

t~

.% c~

tn

"Original L l a d o s plan" - us n o t t h a t

3

happy wifhj bufbest for the Welsh . . . . . .

g~

o

Best f o r us!

Improvement f o r us from

status

deterred ..taking

/

--

g,

qua-

by Welsh offence?

Fig. 3. Some options and outcomes in the championship issue.

was to be the sole major championship in the UK. One effect of deciding to run a National Championship would be to pull the rug from under the feet of the Welsh, ending their chances of reaching agreement with Llados (see outcome (5)). In some ways, this would be an improvement from the status qua for the English: at least the current uncertainty would be ended,

and the existence of a major championship assured. But what of longer-term relations with the Welsh? They seemed to have a sanction against such a m o v e - - i f only vaguely defined--that of 'taking offence'. Although the probJem-owner felt unable to specify more concretely what this 'option' might entail on the part of the Welsh, it was nevertheless a real cause for

Omega. Vol. 13, ,Vo. 4

concern. ~A natural resistance to causing offence was one reason for this, but there was also another. The Albatross class is, by international standards, a small one involving only four nationalities. Of these, the Australians are, by virtue of their physical location, not very active internationally, so if 'taking-offence' might, in any way, lead to apathy amongst Welsh Albatross sailors, the class would be left with only two active nations. This would call into question the international standing of the class. The last column indicates an area of uncertainty. Would it be possible to run a National championship and support a World event in Wales (necessarily, at an alternative venue)? That might provide a way out of the dilemma, by avoiding offence to the Welsh. Unfortunately, the belief was that if a championship were held in England too, veO' few English boats would make the trip to Wales. This would almost certainly be interpreted by the Welsh, at least, as 'lack of support' for them, whatever the English committee might say to the contraryt Finally, the question marks against options (7) and (8) are meant as a reminder that their feasibility was becoming increasingly doubtful: time was running out for finding a venue. (iv) Mapping around outcomes As the rough notes to Fig. 3 already show, some of the outcomes identified were seen as much more desirable than others by the problem-owner. To make explicit the argumentation underlying such evaluations, we made use of maps showing the perceived consequences of particular outcomes, Taking this idea a step further, we also started to explore the problem-owner's reasoning about other parties' preferences--i.e, the argumentation being attributed to them. Apart from providing an explicit rationale for assigning preferences, this might also provide insights into aspects of the problem not so far considered.

~It might be doubted whether 'Take o f f e n c e . , . " is a proper 'option" in the sense of a more or less deliberate act. Philosophically, this can be argued either way. However, there is no formal objection to treating this--which reflected a real c o n c e r n - - a s an option. If preferred, there are equivalent ways of bringing this into the model---e.g, treating "offence" as a likely consequence of certain outcomes.

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The maps produced are shown in Figs 4--6. Only the positive pole of each concept was identified in most cases--a reflection of our inexperience with the method at the time. The first map resulted from exploring the issue of why the English committee saw the status quo as undesirable, in terms of the effects of failing to fix a venue quickly. Figure 5 has to do with the problems associated with having a championship in Wales, again from an English point of view (as represented by the problem-owner). Note the perceived vicious circle (an unstable feedback loop) between expectation of poor turnout and members' reluctance to go to the event. The more it was expected that few would go, the less attractive the event would be, and vice-versa. To try to overcome, this, the English committee could mount a propaganda effort. But that in turn was being inhibited by the failure to reach a quick decision (see negative link). Here, as elsewhere, the maps could obviously be cross-linked but we were wary of merging them together into a single map. Although similar concepts appeared in each, each map was 'valid' only in the context of the particular outcome being explored: both concept definitions and links between them were contingent on this assumed background. Finally, the map in Fig. 6 was an attempt to consider some likely reasoning on the part of the Welsh committee, again around the desirability of having a championship in Wales. (v) Some formal modelling and analysis So far, we had essentially introduced a series of problem-structuring devices, rather than attempting any sort of thorough analysis. As explained in the next section, the process of doing so did reveal some novel insights into the problem. However, the question remained as to what might b e achieved by building and analysing some more 'complete' formal models. Two final pieces of analysis were therefore carried out. The first involved a more thorough examination of options and outcomes, In the second, preferences were assigned for the main actors, thus defining a perceived game: this was then analysed for stability. Rather than attempting to arrive at a single, 'correct' model, various alternatives were explored regarding both outcomes available and preferences, reflecting different sets of assumptions about the situation---especially where areas of uncertainty

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ence.r tc~int y

inability to fix

(of members)

i n a b i l i t y to c o - o r d i n a t e with Swedes

holidays

~ "

~

FAILURE TO REACH

A

DECISION

~÷ no decision

NO

finot~sation

of Engtish

~

u

t

h

e

r

n

on

Area championship

fixtures

difficulties

with

clubs Fig. 4. Problem owner's map for outcome (I): 'why continuing status qua is undesirable'.

had already been identified. The results of this stage are documented more fully elsewhere [3], but can be summarised quite briefly here. Starting from the options identified in (iii), the first aim was to look exhaustively at possible and infeasible outcomes, given a 'full' set of constraints felt to be realistic. One version of this is shown in Fig. 7. It can be shown that this model contains 25 distinct outcomes. With one notable exception--discussed in the following section--all of these represent variations on the six originally identified in (iii). Preparatory to the final stage, however, it proved possible to simplify the model. Given

Llados's limited role--essentially that of making an option open to the Welsh or n o t - - a n equivalent 2-player system could be constructed. This contained outcomes corresponding to all those in the 3-player model: furthermore the limited information available as to Llados's preferences could be captured implicitly in the infeasibilities and uncertainties considered. Within this simpler framework, the maps in Figs 4-6 were now used to suggest likely preference orderings for the English and Welsh Associations. One version of the resulting game is shown in Fig. 8. This was analysed using a modified version of the microcomputer program

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Omega, Vol. 13, ,'Vo. 4 failure

to reoch a

deci sion quickly (on venue etc.}

propaganda effort by (English) co~mmittee ~

-

_~ ex pectetion

of

poor turnout

reluctance of (English) membership to Wales to

liked

~ove[

÷

by

some 9

..<" dislike of Wales as a venue

at last year's "'Worlds " few Welsh

/

long distance to t rovel

poor turnout at championship

/

DESIRABILI TY OF

~ need

good ret

I~'~HAMPIONSHIP IN WALES

x<

to keep with Welsh

desire

for

"'international" image

+~ N , , . , ~

need t o ' k e e p f Welsh in system

Fig. 5. Problem owner's map around outcomes (2) and (4): 'problems with championship in Wales'. (_.v. should be read as ' .. leads to n o t . . . ').

devised by Fraser and Hipel [13]. The analysis pointed to two stable outcomes (i.e. those in which neither side would gain by changing its behaviour, given the likely response of the other). One involved the Welsh abandoning the attempt to find a venue, leaving the English free to mount the World Championship, the other (~f it was feasible) was the original Llados plan. This implied that unless the Welsh succeeded in reaching agreement with Llados and so held the

O,:~IE IJ 4 - - G

English to the original plan, the latter should have been able to obtain--if necessary, force-their desired result of the World Championship transferred to England. This conclusion was surprisingly 'robust'holding true over the several preference variants considered. What was much less certain, however, was whether the Welsh would in fact take offence in the latter case. In the game of Fig. 8, they are predicted not to do so: however, rather

Huxham, Bennett--Enhancing Hypergames aith Maps

342

better morale of Welsh membership

/

Wetsh should be o fully fledged Assoc. (not "appendage"of E")

short7

of time

/

chance of finding another venue in Wales good pubticity~

l

DESIRABILITY OF CHANPIONSHIP/_IN WA~

/

chanceof ÷ / financial [ o s s ~ possible ~ poor (overall) ....,__ turnout +

popularityof Welsh venuewith English(as opposed to Englishchomp)

* ~

\

.

with Uodos

effort, support

fromEnglishAssoc

*

Fig. 6. Argumentation attributed to Welsh by the problem owner (primarily around outcomes (2) and

(4)).

optimistic assumptions have been made here as to the Welsh preferences. LEARNING ABOUT THE PROBLEM Taking each of the stages of the study in turn, let us now consider what was learnt about the problem at each point. In doing so, we shall also

offer some comments about how the methods used worked in this particular case: a more general commentary is given in the final section as to the use, and further development, of the methods themselves. At the preliminary problem-structuring stage, the exercise was most obviously coloured by the problem-owner's already having visualised the

343

Omega, Vol. 13, ,Vo, 4

Llados Sailing Club 1. Make proposal Welsh Association 2. Agree to L. proposal 3. Withdraw from Llados 4. Seek alternative venue 5. Take offence English Association 6. Support Welsh event 7. Stage National Champ. 8, Stage World Champ.

0

I

I

1

--

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(a)

(b)

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-1 1 (e)

(d) ?

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1 1

(f)

(g)

1 --

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(h)

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(i)

(j)

Infeasible combinations shown are generated by the f o l l o w i n g assumptions (a) Welsh Assoc. cannot "agree" to a non-existent proposal (b) Welsh Assoc. cannot both agree and withdraw from Llados (c) Welsh cannot agree and seek alternative venue (d) English Assoc. cannot support Welsh and stage National Championship (?) (e) English Assoc. cannot hold both a National and Worlo Championship in England (f) English committed to supporting event at Llados (g) English cannot support event in Wales if none is planned (h) English can only stage World event if the Welsh withdraw from Llados and do not seek alternative (i) Llados will only make a proposal if no other championship in U.K. (i) Welsh will not take offence if English support event in Wales, but will do so if support is withdrawn while they're seeking an alternative venue.

Fig. 7. "Full" set of infeasibilities: tableau format.

problem of which the problem-owner had been aware, but which had not been mentioned explicitly in the initial description. (For example-referring back to Fig. 2, it is significant that the English Association did not interact directly with the club at Llados, but only t, ia the Welsh Association. Similarly, the Welsh and Swedish Association interacted only eia the English--the only one of the three not supposed to be holding a championship.) These features were not new to the problem-owner, though the notation did

situation in rough hypergame terms (though without having previously written any of this down). One might therefore expect a satisfactory structure to be easily produced, but to reveal little new. In practice, however, neither part of that assertion seemed true. For reasons explored in the next section, it proved difficult to arrive at a 'satisfactory' picture. On the positive side, however, the structuring process did help to elicit various significant points. Many of these were indeed peculiarities of the

WELSH ASSOCIA TION

1/2. Stage event at Llados 3. Seek alternative venue 4. Take offence

INFEA SlBIL I TIES

FEASIBLE OUTCOMES

Assuming agreement with Llados is possible

(ListedinorderofpreferenceforEnglish)

1 1 0 1 1 . . . . 1 - 0 - - - 1 . . . . . . . 1

1 0

0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 1 1 0 1

ENGLISH A S S O C I A T I O N

5. Support Welsh event 6. Stage National Champ. 7. Stage World Champ

01 -

-

. . . .

10 -

1

1

PREFERENCES

1

-

1

1

0

-

English Welsh

0 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 5

2 9

STABILITY

U

ANALYSIS

U E ×

3 1

4 6

5 8

6 2

7 3

8 9 10 11 12 4 10 7 11 12

U

•

U

•

U U

U E x

x

U ×

×

×

×

•

U U

U

U U

x

×

(1 = most preferred, 12 = least preferred, for each party) (U=Welshw°uld gain by moving) ( U = English would gain by moving)

×

(E = Equilibrium (stable) outcome: neither side would gain by initiating a move away)

Fig. 8. Stability analysis for simplified model.

3.14

Huxharn. Bennett--Enhancing Hyper~ames with ).laps

provide an effective way of communicating them to the analyst, and for the latter to ask pertinent questions. All the above were reflected in the initial PPS diagram of Fig. 2. One can, of course, question the adequacy of the perceptions underlying that picture. In fact, a major aim achieved by the exercise was to raise questions leading to modifications of the existing view. For example, at least one issue was brought to light of which the problem-owner had m~t been aware (at least, in this context). To the analyst, there was something increasingly "odd" about the picture that emerged. Why was the championship issue a problem for the English Association? 'Logically', it seemed to be the responsibility of the Federation, which had not even emerged as a participant. The immediate answer was that in practice, all normal business was dealt with at a national level. Over the years, the Federation had come to have almost no independent existence. As the largest National Association, the English Association had tended de facto to play the Federation's role too. While this might matter little in terms of the everyday running of the class--where it was anyway probably inevitable--it was suddenly realised that this confusion of roles might matter very much indeed in a problem such as this. Particularly, one might expect the other associations to resent any apparent assumption of English 'superiority'. This was something that had been largely overlooked. While there was little that could be done with regard to handling the immediate problem, it seemed worthwhile to look seriously at the Federation in the longer term. Otherwise, it would only be a matter of time before similar difficulties recurred. The next two stages--options attd outcomes and mapping around outcomes--similarly resulted largely in a codification of existing thought. The notation used in both cases seemed to provide an economical way of expressing the relevant structure, and also a helpful base from which to start further exploration. Thus, for example, examining options and outcomes helped one to start thinking more systematically about what could happen. Similarly, by making explicit the reasoning by which outcomes were judged to be "good' or 'bad', the maps both clarified the problem and, in some cases, led one to question assumptions that had hitherto been taken for granted.

In one case, however, this process did lead to something substantially new. The concepts on the first map (Fig. 4) to do with "poor opinion of class organisation" led us to consider a set of interactions that had not been identified at the PPS stage--those between each class committee and its constituency of class members. Furthermore, these interactions were highly relevant to the championship issue, since they affected both the preferences for each committee and the actions they could realistically take. Thus a factor identified at a fairly late stage in the exercise could be fed back to modify and enrich the initially-perceived problem structure. Lastly, what of the final, more formal analysis? To the extent that the newly-identified outcomes represented variants on those already considered, the new models added detail while allowing us to check that the original view was not too wide of the mark. The one substantially new possibility brought up at this stage concerned the outcome in which there would be both a World Championship in Wales and an English National Championship. The possibility of the English holding a National Championship as well had been considered in passing in our initial discussion of infeasibilities. However, it had not been seriously considered as a possible final result: given the near certainty of the Welsh taking violent offence, it was felt that the English Association would always have a better choice available. Nevertheless, this outcome did still appear in the 'full' model. This result came as something of a surprise to the problem owner, and was felt, on further consideration, to reflect a factor that had previously been overlooked. Though the previous argument seemed to exclude the "two championships' as a deliberate choice, this might also happen unintentionally, as a result of both associations becoming committed to their own plans. Given the rather poor ability of the parties to co-ordinate their actions, it was felt that this was an all-too-real possibilty. As to the conclusions derived from stability analysis, it is worth recording that this did 'predict' what actually happened in reality. The Welsh were, in fact, dissuaded from seeking an alternative venue, and shortly thereafter abandoned their negotiations with Llados. This followed a statement by the English that unless agreement were reached by a certain date, the decision to stage a National Championship

Omega. Vol. I3, No. -I

would be taken unilaterally. The World Championship was transferred to England following the Welsh withdrawal. It remains uncertain whether the Welsh were offended. Though not the main point of the exercise, the fact that "what actually happened' fell out of the model as a stable outcome (without, it should be stressed, any "tuning" of the assumptions used) can be regarded as encouraging. For the purposes of this experiment, however, we were concerned not so much with the correctness of any models of the situation, but with whether the models adequately reflected the problem as perceived by one particular participant. With this in mind, let us now consider what conclusions may be drawn from the exercise.

CONCLUSIONS: F U R T H E R D E V E L O P M E N T OF T H E APPROACHES We have stressed that this exercise cannot be regarded as a "typical' form of application. Furthermore, its restricted experimental purpose--that of exploring the combined use of modelling methods relative to the viewpoint of one participant in a problem--heavily influenced the procedure. Consequently, some features that we would 'normally' regard as vital were omitted or only sketched in. This applies particularly to the formal modelling of other parties' possible perceptions (hence our use of 'simple' analysis of options rather than hypergame models). Nevertheless, we believe that two sets of conclusions can be drawn. The first, and more definite, have to do with current modelling methods. Particularly, attempting to apply hypergame structuring and analysis of options to a personally-owned problem showed up the need for some improvements. The other, more tentative, conclusions concern the potential usefulness in general of combining the approaches in this way.

Reflections on game-based modelling The issue that concerns us here is that of whether the models could easily be made to reflect the problem-owner's views and concerns, rather than that of the adequacy of those views them-

345

selves. The fact that one of the researchers was also the problem owner, makes the experiment particuarly well equipped to examine this. In this case, though adequate in most respects, the game-based representations were found to be in need of improvement in response to two difficulties encountered. The first of these concerns the PPS formulation. Regardless of its adequacy in any "objective" sense, Fig. 2 does not give a 'rich" representation of the problem as seen at that point. Attempts at further elaboration, however (e.g. by including key individual actors) only reinforced an impression that we were "forcing' several different types of relationship into a single notation. This problem reflects an ambiguity in the concepts underlying the notation. Especially, there is a need to distinguish two senses of "interaction': (a) in which parties' actions on some issue affect each other (they are 'players' in some given area) and (b) in which there exist lines of communication of particular types. These are conceptually distinct, though interrelated in practice. For example, the English Association and Llados Sailing Club were "interacting' in sense (a), but not in sense (b). (Our use of the term 'direct interaction' only served to mask the difficulty.) Two ways forward exist. One is to develop a richer notation within a single diagram. For example Bowen's problem formulation diagrams which distinguish 'conflict', 'communication', "distorted communication' and so forth, might well be appropriate, though they are not directly based on game-type theories. A second possibility (examined by the writers in [7] is to develop separate representations of different aspects, in parallel. For example, one could use a PPS diagram to represent 'interactions' strictly in 'sense (a)', while examining lines of communication and contact using a 'social network' model. A second difficulty encountered was that of adequately modelling the dynamic aspects of a decision problem. In this particular case, a crucial question for the English committee was perceived to be that of whether to move first--i.e, to decide unilaterally on a National event before time ran out. This dilemma proved difficult to capture using the analysis of options format, though there are, in principle, ways of doing so. Some further discussion of this issue appears in [3].

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Huxham. Bennett--Enhancing H)pergarnes ~tth .I,l~tps

On combining the approaches In this exercise, mapping was used in a limited way, to enrich the methodology of applying hypergame analysis (such enrichment is one of the several possible relationships discussed in [4]). Before outlining our conclusions as to the utility of the approach, let us state clearly what we would hope that a hypergame analysis might achieve. Given that we view hypergames as an aid to problem structuring, we would certainly hope that the approach would leave the problem owner with a clearer view of the nature of the problem than before the analysis. Additionally, the hypergame model leads one to ask specific questions about the situation. If this model is an adequate representation of a relevant part of the world, and if, as we believe, it highlights important aspects of conflict situations which people tend not to be natural O, aware of, then the questions it suggests should occasionally generate some quite new perspective on the problem. Conclusions about the ability of the combined approach to achieve these aims are more likely to be affected by the untypical nature of the study than those of the previous section. Rather than generalising directly from this experience, we have therefore attempted to reflect on why the study turned out as it did, and to relate this to experience of other projects. Doing so leads us to a set of working hypotheses, as follows. The first four specifically concern the linking of maps with a hypergame approach.

(i)

Mapping around outcomes can provide a convenient medium for analyst and problem-owner to explore argumentation relevant to perceived preferences. Additionally, the fact that this argumentation is put on record facilitates experimentation with alternative preference structures, by varying the assumptions on which they are based.

Here, ease of communication was probably much enhanced by the problem-owner's prior knowledge of the approaches used. However, as Eden et al. have stressed, mapping provides a representation making use of constructs already owned by a client. We therefore suggest that: (ii)

The addition of maps as a way of explaining the argumentation behind a hy-

pergame model should be helpful to the "uninitiated" client. Since the argumentation can be expressed in his own terms, he is less likely to be daunted by the apparent technicalities involved in hypergame analysis. Although this study concentrated on using (iii) maps to explore likely preferences, a similar approach could be used to capture other relevant argumentation. For example, maps could be used to express the reasoning behind the assumed feasibility or infeasibility of outcomes (we have looked at this possibility using some of the examples above). (iv) However, the mapping format is particularly suited to the expression of'preference' arguments, in the form of perceived consequences flowing from particular decisions made or outcomes reached. By contrast, reasoning involving precisely-stated combinations of events, as in feasibility arguments ('ifa and b but not c, then x is incompatible with y') is relatively difficult to map directly. In addition to these specific suggestions, some more general points are also worth making. (v)

The study reinforced our belief in the value of a o'clical, rather than linear process in examining and analysing a problem. The process that 'naturally' emerged here was cyclical not only within the stages outlined (as when considering outcomes led to redefinition of options), but also between them. Thus, features identified at the mapping stage modified the original problem structure, and so on. Powerful arguments have been advanced for encouraging such a process in the context of other approaches--particularly that of strategic choice [14]. Further evidence is provided by this study, particularly by the observation that the significance of new "angles' on the problem revealed at a given stage (e.g. the importance of the Federation) was often appreciated only after work on other stages, followed by 'cycling back'. (vi) Clearly, one would expect the most appropriate pattern of cycles to vary with circumstances, In particular, the startingpoint should be chosen so as to prot,ide a

Omega. Vol. 13, No. 4

representation of the problem close to the problem-owner's "natural" way of cisualising it. (Here, the problem-owner was already thinking in "hypergame" terms.) (vii) In this case, the exercise proved effective in generating new insights into the problem. Gradually, the emphasis changed from representing the problem-owner's perceptions to helping to elaborate or even alter them. Given that he had already given considerable thought to the problem, and had done so within a 'hypergame view of the world', .we were surprised that the study elicited so much that was new. This encourages a belief that questions generated by the approach are relevant and likely to be missed without this structure or something similar, though this is somewhat qualified by a final observation.., (viii) In general, it is difficult to distinguish ideas generated by using a particular approach from those generated simply by' having an analyst (or any outsider?) with whom to discuss the problem in hand. In other words, the role of the analyst as a questioner of assumptions may be the vital factor. Indeed, it can be argued that the way in which the process of decisionaiding is managed outweighs all other considerations [12]. These last points raise a complex set of issues. For example, does initial problem-structuring in terms of a specific theoretical format such as that provided by the hypergame approach tend to help decision-aiding (e.g. by leading the analyst to ask pertinent questions) or to hinder it (e.g. by 'losing' the client or focusing on irrelevant issues)? The peculiarities of this exercise prevent its being a good test of questions such as these. Nevertheless, these issues are being addressed in the light of a number of exercises [10]. This forms part of a larger research effort exploring the relationships--both at a practical and theoretical level--between not only mapping and hypergame analysis but also other decision-aiding methodologies--most notably that of Strategic Choice. Overall, the study seemed to show that combining hypergames with maps in the form tried could work. There are other possible combinations That of attempting hypergame analysis as

347

a follow-up to mapping has already been noted. Using maps in parallel with hypergame structuring, and then integrating the models has also been tried, with promising results [5]. Nevertheless, this experiment was successful enough to suggest 'mapping around outcomes" as a method worth trying further, on other types of problems. A C K N O W L E D G E M ENTS The work described in this paper was stimulated by continuing collaborative research involving Colin Eden. We therefore wish to express our thanks to him, as well as to others earlier involved, notably Tim Smithin and the late Robin Bussell. While we hope we have not misrepresented Colin's views when explicitly referring to these, it should be stressed that all opinions expressed here are those of the current authors only. Our thanks are also due to the good offices of Jonathan Klein. Dr P Bennett's work is supported by The Leverhulme Trust.

REFERENCES 1. Axelrod R (1976) (Ed.) Structure of Decision. Princeton University Press, Princeton. 2. Bennett PG (1980) Hypergames: developing a model of conflict. Futures 12, 41-50. 3. Bennett PG (1984) Futher analysis of the Albatross problem. University of Sussex Operational Research group. 4. Bennett PG (1985) On linking approaches to decision aiding. J. Opl Res. Soc. In press. 5. Bennett PG and Cropper SA (1984) Town hall maps, games and things in between. OR Society National Conference at Lancaster University, September 1984. 6. Bennett PG and Huxham CS (1982) Hypergames and what they do: a "'soft" approach. J. Opl Res. Soc, 33(1), 41-50. 7. Bennett PG and Huxham CS (1985) Clarifying the concept of interaction. In preparation. 8. Bowen KC (1983) An experiment in problem formulation. J. Opl Res. Soc. 34(8), 685-694. 9. Bryant JW (1983) Hypermaps: a representation of perceptions in conflicts. Omega 11(6). 575--586. 10. Eden C, Bennett P and Huxham C (1985) Two hundred and twenty three actors in search of a role. In preparation. 11. Eden C and Jones S (1980) Publish or perish?: a case study. J. Opl Res. Soc. 31(2), 131-140. 12. Eden C, Jones S and Sims D (1983) Messing About in Problems. Pergamon Press, Oxford. 13. Fraser NM and Hipel KW (1979) Solving complex conflicts. IEEE Transactions, SMC-9, 12, 805-815. 14. Hickling A (1982) Beyond a linear iterative process? In Changing Design (Edited by Evans B, Powell JA and Talbot RJ). Wiley, Chichester. 15. Radford KJ (1976) Complex Decision Problems. Reston. Massachusetts.

Dr CS Huxharn. Department of Operational Research, Unit'ersity of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G l I XH.

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