1. Introduction
It is often said that game theory can help managers to gain new insight, or to think better about problems of competition and business strategy [8,14,26,39]; but what does "thinking better" really mean, in contemporary management contexts? If the phrase is simply taken to mean avoiding miscalculation, or identifying an equilibrium point, then game theory and its various extensions (e.g., Supergames, Metagames, Information-dependent games, etc.) provide the appropriate analytic framework. However, if "thinking better" implies an improved understanding of the World as it now really is, or improving creativity when finding and solving important problems, then the role of game theoretic models in business strategy becomes laid open to a rather significant critique. First, the players in games of business strategy are themselves often changing their structures, their boundaries and their identities, as all types of productive entity are re-configuring in novel ways, made possible by the new communications technologies [24,44]. Secondly, while contemporary managers are undoubtedly confronting increased competition in the marketplace, they are also (often reluctantly) having to confront many social and environmental problems. In sum, formal game theory cannot be expected to yield practical solutions to many of the most important problems of contemporary "strategic" business management.
Despite the limitations, research in game theory could still help managers to "think better", especially if the theory is adapted, in ways to be defined shortly. As a first step, it may be noted that formal models in general (e.g., for forecasting, asset-valuation, or strategic-analysis, etc.) have often been observed to function in organizations in unorthodox ways (see Section 2) that is, ways that are disconnected from the mathematical theories that gave birth to them. In particular, the formal models of game theory, as they have become more widely known and understood, have also tended to promulgate quite distinctive assumptions about business goals, competitive behavior and the nature of rationality in management. For this reason, game theoretic models do much more than merely represent or explain strategic behavior, they also affect that behavior and slowly change it. Put differently, the models themselves tire like memes (Dawkins [12]), which are the cultural equivalent of genes. The models, or memes, occupy players' minds (individually and collectively) as they are copied, spread out, or propagated through a community of thinkers, or players.
In Section 3 of the paper, various extensions and adaptations of game theory are briefly described. The "extensions" involve mathematical developments of simple game models, characterised by the fundamental assumption of Rational-Utility-Maximizing (RUM) players. "Adaptations", in contrast, involve extending the players' set of rationalities by including other distinctive forms, some of which are not captured by RUM. (For fuller accounts of but a few of the elusive forms of rationality see [2,10,17,22,35,38, 40].) Examples of adaptations include the operationalized version of Metagames [26] and Hypergames [4], as well as the conceptual model of an Ultragame [45,48,50], elaborated in Section 3. Section 4 of the paper then discusses various ways of comparing and evaluating the extensions and adaptations. Finally, by invoking the conceptual framework of Strategy-as-Rationality [44,49], this meta-theoretic treatment of games and their rationalities is placed at the core of strategic management theory and practice.
2. Roles of mathematical models
Several studies have identified unorthodox roles of formal (quantitative or mathematical) models in organizations [16,18,36]. These roles can be classified (Table 1) as (i) relating to the internal politics of organizations, such as conferring power to individuals based upon their expertise with the model, (ii) soft-OR applications, in which adapted models function as problem-structuring methodologies, and (iii) ideological roles, in which formal models come to symbolize, promulgate, or propagate particular assumptions and beliefs about the organization and its strategic problems. Each of the above "roles" is quite plainly social, as well as analytic and cognitive. Indeed, it has increasingly become recognized by management scientists [ 11,18,27,36] that the building and validating of all formal mathematical models are "not only cognitive activities, but also social activities" [27, p. 162]. The present paper explores this social dimension, in the special case of game theory: its politics, its formulations and its ideologies.
With game theory, the consequences of ignoring the social dimension of model-validation and model-use, whilst attending to the traditional mathematics of optimization, can indeed be rather serious. Fifteen years ago, Davis and Hersh [11] suggested that mathematical modellers often "deliberately force... social aspects of the universe" into the "delightful (mathematical) patterns they have wrought"; implying that they force out the more elusive social, ideological and moral aspects of the system being modelled. Later, Etzioni [17] made a rather similar point, in his book, The Moral Dimension. He noted that formal economic theories, based upon RUM players and agents, often "miseducate" students of business management and tend to co-produce a future society or socialsystem with all the "wrong" characteristics. For example, the students (and the society) become more comfortable with, or de-sensitized to the corresponding language of threat, fear, predation, opportunism and guile (all in the name of fiduciary duty); but they remain relatively impatient, careless or ignorant about words such as fairness, justice, dignity and moralrights.
It is not only neo-classical and evolutionary economics, with their corresponding perspectives on strategic management [44,56], that have successfully propogated the seductive language of Jungle-Warfare, throughout many business and political communities: in his book Darwin's Dangerous Idea, the philosopher Daniel Dennett has specifically warned of the risks associated with "doing good work in Evolutionary Ethics", also based upon game theoretic models, whilst nonetheless remaining "dismayingly heedless of the misuses to which (these models) might be put, by ideologues of one persuasion or another" [ 13, p. 491].
2.1. Models as memes
Formal models quickly "leap from mind to mind", like memes, in effect generating copies of themselves, changing or infecting individual and collective minds and slowly influencing the Zeitgeist. Accordingly, the general characteristics of memes become noteworthy. First, like genes, memes help themselves: once they have been created, they tend to disable any opposing or hostile forces in their environment. This dynamic was clearly illustrated in the success of the Tit-for-Tat algorithm (a meme) in Axelrod's evolutionary competition [1]. In the case of game models (like the Prisoners' Dilemma Game viewed as a meme), this "disabling" capability has historically taken on the form of RUM-capturing: the many attempts (some Nobelprize winning) to disable our more traditional notions of morality and sociality, by capturing them in terms of the players' interests and utilities.
Secondly, successful memes (like genes) are not necessarily advantageous to the society or total system that hosts them. As Darwin himsell' wrote "I cannot persuade myself that a beneficient and omnipotent God would have designedly created the Ichneumonidae (a type of wasp) with the express intention of their feeding within the living bodies of caterpillars". Put differently, some of the genes (or memes) that are generously hosted by a system (or culture) can turn out to be highly destructive. In this sense, there are good memes and bad memes [13].
Is game theory "good" or "bad"? Those who see something distinctive and elusive (i.e., not "captured") in their notions of morality, sociality and ethics; something that cannot be adequately represented or expressed in terms of mere interests, preferences and desires, must also see something correspondingly "bad" about game theory... its ideological overtones, with its potentially corrosive social impact. More constructively, despite the occasional claims, by economists, of the theory's capability for generating "good advice" [7, p. 215] for managers and strategists, it would now seem that it is also capable of improvement. Like other memes, game theoretic models might also be purposefully adapted, or consciously re-designed, by deliberate and persistent human intervention.
3. Adaptations
During their 50 year history, the so-called "simple" game models [26] have been extended, in various ways (Fig. 1 and Table 2). An "extension" of a formal model is a mathematical development which yields a deeper or more comprehensive analysis. Such extensions characteristically retain the implicit assumption of RUM players~. This means, as Von Neumann himself put it, that "the behavior (of each of the players) is (assumed to be) motivated by the same selfish interests as the behavior of the first player" [64, p. 13]. Examples of this types of formal extension include Supergames [1,29,30], Games-with-imperfectinformation [23], Metagames [26] and Psychological, or information-dependent games [19,20]. These are labelled m1 to m5 in Table 2, where some of their more salient properties are listed.
In contrast with extensions, the term "adaptation of a formal model", as used here, refers to developments of the model, or its operationalized methodology, that incorporate, or sweep-in, some other distinctive forms of rationality. These could include the elusive forms [2,10,17,22,35,38,40] that may not necessarily be captured, or reducible to RUM. When a model is adapted, in this sense, its image under the mapping decision-function-rationality [43,47] becomes extended, but not necessarily the pure mathematics of the model itself (Fig. 1). Examples of such "adaptations" of simple games include Metagames in their operational form [26], Hypergames as a "methodique" [4] and Ultragames (described below). These adaptations are labelled m6 to m9 in Table 3.
3.1. The Ultragame model
The conceptual model of an Ultragame [45,48,50] is the result of pursuing the process of adaptation of game models, to its ultimate conclusion. An Ultragame (m5 and m0 in Table 3) simply sweeps in all the distinctive forms of rationality, the entire rationality-set, into a model[2] of strategic interaction amongst multiple types of entity, based upon their plural-rationality. It is implicitly assumed that each player is not only engaged in a competitive battle to further its "selfish interests", or utilities, even when broadly defined; but it is also engaged in a search for success, with reference to plural-rationality. Put differently, all of the players in an Ultragame are assumed to have significant concerns for society, morality, ecology and autonomy that mediate their behavior, but that cannot be fully captured as preferences over a set of well-defined strategic alternatives.
Despite its incomplete formal exposition, the conceptual model of an Ultragame can readily be made operational as a structured inquiry, or framework for strategic thinking [55]. This can be used in practice to support internal strategic analysis, when players direct questions at themselves, or for understanding the behavior of other entities, as in traditional business "competitor" analysis methodologies [55]. Various questions, in ordinary, natural-language, flow directly from each distinctive form of rationality. For example, there are questions rooted in the cognitive and instrumental forms of rationality, but associated with simple-games, such as: "What are the competitors' expectations about our behavior? What are its internal incentive structures?" (e.g., [42]), but there are other questions, based upon the more elusive forms of rationality, such as: "Does the entity... have a history or policy of treating others fairly? ... avoiding or minimising harm? ... preserving traditions? ...contributing to the development of institutions that symbolise a good life with others? ...protecting the rights of others? ... fostering autonomy and positive freedom?
There are many people who think that contemporary corporate managers and network participants should be asking all of these questions, then seeking or designing some answers; not to mention openly discussing the questions whilst encouraging others to do so. Indeed, it is the primary purpose of the Ultragames model to re-direct the players' attention accordingly (cf. Table 2).
3.2. Synergistic design
A further adaptation of game theory, an Ultragame (2) [58] also incorporates the idea of synergies amongst the distinctive forms of rationality[3]. In this adaptation, each strategic-entity is re-conceptualized as being hyper-rational, in the special sense of the word used recently in Sociology (see Glossary). Hyper-rational entities seek to implant synergies amongst their own plural forms of rationality [33, 48]. Additional questions for strategic analysis follow quite naturally from various forms of rationalitysynergy [48,49], for example:
"Does the entity (or player)... ... apply scientific knowledge to increase the utilization of its lower-level practical skills?" (i.e., the theoretical and practical Weberian forms.) ... forge links with benevolent institutions in ways that strengthen its sense of identity?" (i.e., the contextual and expressive forms.) ...creatively seek new ways of producing wealth for exchange, that also promote social justice, further democratic aims and also help to restore vital ecosystems." (i.e., the deliberative and RUM forms.)
There are indeed a great many people who now think that managers should be asking precisely these sorts of questions, then actively seeking or designing some positive answers, much more often [15,24,25, 52]. Yet, neither simple game theory nor its extensions can possibly help to cultivate or propagate this type of strategic thinking.
3.3. Illustration
Despite the prevailing competitive ideology, associated with extended games, some contemporary strategic-entities already behave as if they were players in an Ultragame, but not an extended game. For example, in 1992, the famous clothing company Levi Strauss reportedly broke off its relationship with some of its international garment suppliers, because the suppliers' business practices were deemed to be socially or environmentally unacceptable. The company then documented its "Business-partner terms of engagement" that set out some hard questions to be asked about suppliers, thus encouraging all players to adopt more socially responsible business practices. In this episode, Levi Strauss were not searching for some optimal price-quality vector amongst some given alternatives. Like many other business players, they had committed themselves to a process of persuasion, assistance and co-operative re-design.
In this socially responsible business practice of active "partner engagement", or persuasion (with words as well as money), in which dialogue and morality play a distinctive role in bringing about creative change, can be modelled as an Ultragame. Yet it cannot be fully captured as an extended games, nor the "supplier as a competitor" conceptual model of business strategy (e.g., [42]). The latter models completely fail to capture the spirit and rationale of the more progressive "partner engagement" doctrine.
This contrast between the Simple game model and an Ultragame is amplified in Figs 2 and 3. In the figures, player 1 is a supplier company' (a workshop, or sweatshop) located in a less-developed country. Its owner-managers (not to mention the employees) can perceive an alternative to the status quo: to become a progressive business. However, this would require some further investment, leading to a higher unit cost, at least in the short term'. These costs could be passed on, as a higher supply price. The status quo choice is simply to continue as an oppressive employer, paying very low wages for long hours; but enjoying relatively low unit cost. Player l's preference then depends upon what player 2, the overseas buyer, is expected to do. Player 2 might prefer to renew the contract, or go elsewhere. When the strategic problem is thus formulated, as a Simple game, the rankings for both players are as shown in the matrix (Fig. 2).
With this formulation, the calculated (RUM) solution is to close the deal at the lower price. When implemented in the real world, this solution helps perpetuate and reinforce the habits of oppression. Casual observation of many global sourcing policies readily confirms that this is not such a rare outcome. Indeed... and this is a the major point of the present paper... the outcome is rather inevitable, so long as one persists in formulating strategic business problems as games of interests. Therefore, from a human systems perspective, this formulation is itself a major part of the problem.
The Ultragame model now offers an explicit alternative formulation (Fig. 3). Rather than calculate joint interests, Ultragame players are engaging in inquiry, persuasion, reflection and creative re-design of their strategic possibilities. This process continues until the strategic problem is settled, resolved, or dissolved [47, 51,58]. More specifically, player 1, the supplier, asks some hard questions about player 2 (Q in the figure) and about itself (Q'). Some specific examples are:
Q1. Does this entity (i.e., buyer and self) have a reputation or policy emphasizing fairness in the treatment of stakeholders?
Q2. Are the entity's routine practices in line with its expressed values?
Q3. Does the entity utilize experience at all levels of operation in a process of continual improvement and re-design? etc.
At the same time, player 2 (the buyer) seeks answers to another set of questions as they apply to player 1 (q in Fig. 3) and to itself (q'), as follows:
q 1. Does the entity have programs in place to develop its internal capabilities (e.g., training, education, etc.)?
q2. Is there a pattern over time in this supplier's decisions? (e.g., delays, quality problems, poor treatment of staff, broken agreements, etc.)
q3. Is our own situation (e.g., cashflow problems) unduly influencing our current dealings with the supplier? (e.g., inclining us to overlook the bad working conditions, etc.).
All of these questions flow from considerations of plural rationality and hyper rationality (in the synergyseeking sense). That is, entities ask whether each particular form of rationality and form of synergy is manifest in all of the other entities within the system being modelled. When this type of conceptual modelling occurs amongst multiple players, the outcome in the real world tends towards increased levels of trust and openness, as well as health, or competitive fitness [58]. Put differently, the adapted conceptual model, with the re-formulation of the strategic problem as an Ultragame, is itself a solution [68].
4. Meta-modelling
Despite the likely outcome of choosing Ultragames as a method of strategic analysis, they are not universally preferred. Accordingly, of the various models listed in Tables 2 and 3 one could ask the metamodelling question: "Which model is best?" The column headings of the tables then provide a framework for structuring an evaluation of the alternative models, as follows.
4.1. Rigour-relevance
All of the extensions of simple games (m1 to m5 in Table 1) are mathematically rigourous, but, for various reasons [7] they are hardly ever used to solve real managerial problems. (However, almost 50 years after the original work, applications have been found to problems such as the setting of "fair" user-pays fees for privatised airport runway facilities.) In contrast, the soft-OR adaptations (m6 and m7 in Table 3) have been used in practice to facilitate problemsolving in a variety of organizations [46]. Ultragames (rn8 and m9) now occupy a rather special position on the rigour-relevance spectrum [41]. They are plainly conceptual rather than mathematical, but they are particularly relevant to problems that the players themselves may not even consciously perceive. These include problems associated with the players' integrity, ideology and language, as well as future problems and others' problems.
4.2. The purposes
The mathematical extensions of game theory were developed partly out of intrinsic curiosity [11], but also to yield potentially useful insights into utilitymaximizing behavior. They have been used to prescribe action, accordingly (e.g., find an equilibrium point). In addition, the models have yielded many testable experimental hypotheses [9]. In contrast, the adaptations of game theory were designed in order to function as platforms, tutors and keys (Table 1), to "open doors" [27, p. 163], to explore scenarios, or to prepare for negotiations. The purpose of Ultra-games is much more fundamental: it is to function as a switch (Table 1) that re-directs the players' attention away from their immediate interests and desires, but towards the more elusive forms of rationality and the task of creative re-design.
4.3. The players
In extended games, the players are conceptualized as utility maximizing homo economicus. They have consistent preferences amongst given well-defined objects-of-choice (moves or strategies). In the softer adaptations, however, the players are homo economicus AND homo cogitans. The strategic alternatives are constructed percepts, whilst beliefs are accessed and revised as the game is played (i.e., the belief-oriented, or cognitive forms of rationality are swept into the model). In Ultragames, the players also become homo civicus [15]; that is, they are mindful of the elusive forms of rationality and the importance of remaining open to persuasion by social dialogue and reflective deliberation. The objects-of-choice in the game might be partly defined, partly constructed? or vaguely perceived. For example, they could be hyper-real symbols and signs [21], or prototypes of synergistic designs, envisioned and experienced in virtual worlds. In the latter case, the players have also become homo creans (creator) AND homo designans (designer) [48,52,57].
4.4. Decision-errors
In extensions of games, an error takes the form of a miscalculation, or a player's choice of a dominated strategy. For example, in the one-off, 2-player Prisoners' Dilemma Game, "co-operate" is sometimes called an "error", because it is dominated by "defect". In games of imperfect information, errors are normally associated with miscalculations involving probabilities. (In the metatheory, these are sometimes interpreted in misapplications of players' cognitive heuristics.) In psychological games, errors can also involve the overlooking of some of the outcome-related influences on the psychic-utilities of the players [63]. In metagame and hypergame analysis, the notion of "error" is further expanded to include the overlooking of important possibilities, the mis-construing the other players' perceived games, or even wrongly identifying the other players [26,36].
An error in an Ultragame is much more fundamental: it is a poor choice of rationalities by the players (Fig. 4). In this context, "poor" refers to evaluative meta-rational criteria, such as globality, universalizability and self-support [46,51]. Ultragame players can make errors-of-omission, when they ignore the elusive forms of rationality, or when they fail to design and implant rationality-synergies. It is becoming increasingly apparent that this type of "error", when it becomes widespread in a human system, leads to increased levels of disparity, resentment, frustration and oppression.
5. Implications for managers
The meta-analysis of game models, with their rationalities, can be placed at the heart of Strategic Management theory and practice, simply by invoking the conceptual framework of Strategy-asRationality [44,49]. This framework consists of (i) a strategy-set whose elements are the major concepts and components of theories of Strategic Management, (ii) an entity-set whose elements are the multiple types of player, or strategic-entity (e.g., individual, firm, network, virtual-corporation, etc.), and (iii) the rationality-set. "Strategy-as-Rationality" then sets out an isomorphic correspondence between the strategyset and the rationality-set. The framework extends the "individual metaphor" for the firm, widely employed in the general theory of strategic management [3]. (It is noteworthy that objections to the metaphor have been described elsewhere as "roadblocks in the path of inquiry" [38].)
When the Ultragame model is placed within the framework of Strategy-as-Rationality, it carries some rather fundamental implications for managerial policies and practices. In addition to the methodology of inquiry (set out in the previous section), there are other prescriptions concerning (i) the enrichment of the language of Strategic Management, (ii) the propogation of an augmented ideology, and (iii) the possibility of attaining individual and collective integrity.
5.1. Enriched language
The problem of choosing models, as depicted in Fig. 4, corresponds (via the isomorphism in the framework) to a choice of concepts in strategic-thinking, as well as language for the strategy-discourse (Fig. 5). Thus, for example, the choice of the RUM-captured forms of rationality, with the extended (but not adapted) game models, corresponds with the deployment of the traditional language of economic competition. Words like threat, fear, predation, sanctions, monitoring and control, then become the norm [42]. In comparison, the (meta-rational and meta-modelling) choice of plural and hyper forms of rationality, with the corresponding Ultragame model, leads quickly to an enriched discourse with an augmented vocabulary. This includes words like coexistence (Kyosei in Japanese), sociality, civility, openness, creativity and synergistic design [52,56]. Many people think that such words should be heard much more often, in contemporary business and politics, at all levels.
5.2. Ideological transition
The traditional language of Competitive Strategy is often associated with the relentless pursuit of essentially selfish interests, by the stronger and more powerful players. For many people this has now come to symbolise a negation of freedom: unacceptable levels of subjugation, disempowerment and marginalization. They have slowly become trapped within the "descending iron cage" that Max Weber associated quite directly with instrumental or calculated forms of rationality. Put differently, they have become victims of the economization of society (G. Ritzer calls this "McDonaldization").
It is now possible that new models like Ultragames, with other, similar techniques [47,51,57] could take on the role of keys (cf. Table 1) enabling all types of entity to prise open the doors of this cage. To amplify and communicate this point, the three notions discussed so far: adaptation of models, extensions of the rationality-set, and augmentation of language, can be presented together as a unified schema (Fig. 6). As simple game models are adapted, becoming more like Ultragames, their decision-functionrationalities become extended and the corresponding language of Management becomes augmented and enriched. As the adapted models and the augmented language spread throughout individual and collective minds, the ideology of Strategic Management is slowly transformed, becoming much more like Business Ethics [25,46,53].
5.3. Integrity
The notion of ideological transition (the right hand side of Fig. 6) can also be expressed in much more personal and practical terms, literally closer to home. The ideology of economic competition, competitive strategy and utility maximization (the top of Fig. 6) has encouraged countless individuals to strongly differentiate their work life from their personal or family life. When these people enter an office, or a factory, they become fighters, warriors, or slaves; but when they physically leave the workspace, they quickly transform themselves into discussants, mentors, friends, or lovers. Despite the growth of working at home (and in transit) many continue to defend this way of life, i.e., the principle of role-differentiation.
Strategy-as-rationality fosters an alternative principle: role-integration. The ideology of Ultragames, with plural-rationality and hyper-strategy (bottom of Fig. 6) seeks to trap all entities, including individual managers themselves, into becoming "integrated and balanced persons", at all times [59, p. 100]. This forced re-integration of personal and managerial (or productive) life-roles seems rather timely. It is especially well-suited to the many new forms of production now made possible by technological advance (e.g., the virtual firm or network), not to mention the many new types of family.
6. Conclusion
The idea that game theory can help managers to "think better" about their strategic problems has now been given a much wider interpretation. Traditional game theory and its extensions have certainly yielded many mathematical insights, with some testable hypotheses. The methodologies of metagames and hypergames have helped managers to explore scenarios, or to arm themselves more thoroughly for negotiations; but, when they are re-armed with the concept of an Ultragame, managers quickly become capable of thinking better and talking better about their strategic problems, others' problems and future problems. In this way, the adaptations of game theory could now be used as platforms, for designing, discussing and reflecting upon new strategies and structures for living and working together, for the common good. Put differently [13, p. 510] adapted game theory could become one of "the mind tools we need to design and redesign ourselves, ever searching for better solutions to the problems we create for ourselves and others".
[1] Various distinctive forms of rationality are special cases of RUM, such as the extensive form [5] in which the objects-of-choice are forecasts based upon extrapolated of historical data. Many other forms such as bounded, sympathy, could be captured as RUM.
[2] More formally, we could write: D(mg)=R where D is the mapping decision-function-rationality [53] and ms is an Ultragame model and R is the rationality-set.
[3] If Y is the set of such synergies, we could write: D(m9)=R[NON ASCII CHARACTER]Y.
>Table 1
Some unorthodox roles of formal models
(i) "Political" roles include models as... status-symbols: when the managers who understand and operate the
model acquire status and power based upon this expertise.
pliers: when the need to estimate model parameters enables managers
to extract confessions, or assumptions, from subordinates, or to
squeeze them into line.
batteries: when the participants in a detailed analysis tend to
increase their psychological commitment to any resulting
prescriptions (i.e., the illusion of control).
(ii) "Soft" roles include models as...
platforms: when models become an arena or platform for an organized
discussion, or reflection.
Socratic tutors: when models enable their users to learn, or to
educate themselves, by means of structured inquiry. For example
presentation of the Prisoners' Dilemma Game
sometimes evokes questions about possibilities for cooperation.
keys: when models become like a set of keys [47] which will "open
doors for the actors and allow them to procede" [27, p. 163].
(iii) "Ideological" roles include models as...
rituals: when the process of model-building serves to reinforce a
culture of profit maximization (associated with RUM) in an
organization.
glue: when models bind or unite managers (or team members)
together, behind a common set of goals, concepts and vocabulary.
filters and switches: when a model serves to direct (or re-direct)
attention towards (or away from) particular aspects of a managerial
problem, such as the social and moral
aspects.
memes: when models function as units of cultural transmission. Like
popular tunes, they leap from mind to mind and affect the behaviour
of the "infected" entities.
Table 2
Extensions of games, with some properties
Model Decision-function Objects-of-
m rationality is... choice are...
m1
Simple game RUM
(normal or (strategic)
extensive form)
given
m2 RUM and
Supergame . (evolutionary) probabilistic
m3 RUM (with
Imp-info-game Bayesian revision)
m4 RUM constructed
Metagame (1) (meta-rationality[1]) algorithmically
(1971) from the given
OOCs
m5 RUM given,
Info-dependent or (psychic utility) incorporating
psychological psychological
games states
Type of Rigour- Purpose(s)
prescription relevance
Choose a pure or
mixed or High rigour. Improve understanding,
probabilistic provide insight,
strategy, prescribe, quide and
and/or make side- hypothesise.
agreements.
Choose a Hardly ever used To uncover the
metastrategy or as technique. objectively rational
conditional behaviour in a game.
strategy, etc. To capture hopes,
fears, As in m1-m4.
disappointments,
etc.
Players are Decision
homo... error is to...
Choose a
dominated
strategy, etc.
economicus
miscalculate
Table 3
Adaptations of games, with some properties
Model Decision-function Objects-of-
m rationality is... choice are...
actions (given or
m6 meta-rationality[1] generated)
Metagame with belief-forms perceived as
(1987) means of control
of issues
m7 RUM perceived
Hypergame with belief-forms hypothesised
(assumed)
vaguely perceived,
m8 plural-rationality partially defined
Ultragame (1) constructed,
symbolic,
hyper-real
m9 designed
Ultragame (2) hyper-rationality strategies
Type of Rigour- Purpose(s)
prescription relevance
Inquiry,
incorporating
promises, fears,
hopes, etc. Moderate rigour, Problem-structuring,
used facilitating
as tool and agreements,
As for (meta-) technique. understanding
game but with conflict,
reconsideration of arming oneself,
the identity of exploring senarios.
other players and
their preferences.
Inquiry Low rigour. Redirect attention,
based upon plural- Relevant to propogate ideology,
rationality. problem- re-make players.
owner, other's
problems
Engage in optimal and future As above.
design, with problems. Motivate
synergies synergies
and optimal design.
Players are Decision
homo... error is to...
Overlook
possible
outcome
scenarios.
economicus and
cogitans
Misperceive
other players'
perceived
game.
economicus and Poor choice of
cogitans and rationality as
civicus evaluated by
meta-criteria.
creans and Failure to design
designans synergistic
alternatives.
DIAGRAM: Fig. 1. Extensions vs. adaptations of formal models.
DIAGRAM: Fig. 2. A sourcing decision as a simple game.
DIAGRAM: Fig. 3. Sourcing policy as an Ultragame.
DIAGRAM: Fig. 4. Selecting game-models as choosing rationalities.
DIAGRAM: Fig. 5. Choosing rationalities as choosing strategy-concepts.
DIAGRAM: Fig. 6. Adaptations and transitions.
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