from game theory to drama theory...rational” aspects of decision-making (e.g., crisis, emotion,...

From Game Theory to Drama Theory

Jim Bryant

ContentsIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Games and Hypergames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Metagames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6The Analysis of Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9The Problem of Inducement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Emotional Decision-Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14The Concept of Drama Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Drama Theory: Early Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Abstract

Not all group decision and negotiation agreements are right solutions. In order totake a right decision and find a right solution to a problem, one has to first of alldefine the right problem. This chapter presents the evolution of a dynamicproblem – restructuring for definition of right problem/solution in group decisionand negotiation and its manifestation in communication. It starts with a summaryof the framework for Evolutionary Systems Design and the ConnectednessDecision Paradigm Validation Test and then goes through seven ways in whichcommunication, as a cognitive semiotic process, produces connectedness with theOther, namely, shift of attention, common ground, redefinition of communication,empathy, interactive alignment, theory -of -mind reasoning, and reciprocal adap-tation. The presented analysis of authentic interaction data finds that connected-ness with the Other, as a high-level surrogate for connectedness with One, candefine right problem/solution in group decision and negotiation.

J. Bryant (*)Sheffield Business School, Sheffield Hallam University, Sheffield, UKe-mail: [email protected]

© Springer Nature Switzerland AG 2020D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation,https://doi.org/10.1007/978-3-030-12051-1_14-1

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Introduction

Drama Theory provides an analytical framework that a party can use to inform itschoices when dealing with others, either in a negotiation or in a confrontation. Itoffers a ready means of summarizing within a coherent structure the hopes anddemands of those involved and pays due attention to such practically importantmatters as the credibility of claims, threats and promises, and the emotional tone ofan engagement. The approach has evolved from its origins in game theory, devel-oping, as it has diverged, a special focus upon the management of the apparentlyirreconcilable dilemmas that parties inevitably encounter as they attempt to persuadeor are persuaded by others.

Drama Theory today is the outcome of an intellectual process as convoluted asmany of the other pathways that have characterized technological development. Andalong this track lies the debris of theoretical structures as impressive – even heroic –in their way as those of pre-Copernican astronomy or of phlogiston theory: theoriesthat met a contemporary scientific need but which, in time, had to be overturned orradically refashioned to meet more exacting requirements. This Chapter outlines thedevelopment of the intellectual structures that stemmed from Nigel Howard’ssearching critique of game theory in the late 1960s and led to a family of analyticalapproaches to negotiation; while its principal focus in the latter is upon drama theory,other techniques covered in the present volume are also encountered.

In a self-conscious echo of Marinetti’s Futurist Manifesto, drama theory waslaunched with a rhetorical flourish in a manifesto (Howard et al. 1992) that suggesteda wish to analyze the emotional and political aspects of choice and so embrace “non-rational” aspects of decision-making (e.g., crisis, emotion, self-realization) ratherthan restrict itself to the rational choice paradigm on which game theory rests. Inretrospect, this aspiration can be seen as a natural progression from Howard’sinnovation of metagame theory developed while he was working on a project forthe US Arms Control and Development Agency (ACDA) and so the presentnarrative must provide the background to that work and track its ramificationsthrough the following half century.

Games and Hypergames

Famously, the philosopher David Hume (1888) argued that “reason is, and oughtonly to be the slave of the passions,” implying that while our motivating aims areestablished by the passions, it is reason that guides us in achieving these ends. Gametheory is the preeminent analytical tool for implementing this doctrine of instrumen-tal rationality. It does so by treating real human interactions as if they were moves byplayers in the artificial, rule-based world of games, where strategy dependscompletely upon means-end rationality. Game-theoretic analysis deals with individ-ual choice in situations where the information base of each party is shaped by thedeclared intentions and choices of every other participant. Typically, it involves a

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search for ways of achieving outcomes that are best for the individual – “best” istaken in the limited sense of most-preferred, rather than in the wider sense ofsatisfying Humean passions – and it emphasizes personal rather than collectiveutility. A flavor of such analysis can be gained from the chapter▶ “Non-cooperativeGame Theory and Negotiation”.

While the modern formalization of game theory can be precisely dated to thepublication of the Theory of Games and Economic Behaviour by John von Neumannand Oskar Morgenstern in 1944, game theoretic thinking is evident in Classical writers;indeed some problems posed by Classical philosophers are best addressed throughgame theory. One example of the latter, given by Plato is his elder brother Glaucon’sargument (Bloom 1991) that it is only for instrumental reasons that a system of humanjustice has emerged. The argument starts from a view that while people might like totake advantage of others and act unjustly, the harm that they would themselves suffer ifin return they were treated unjustly cautions them against exploiting others; theconsequence is an unwritten agreement neither to do injustice nor to suffer it.

A simple, illustrative game theoretic formulation of this situation involving twoparties (call them Alf and Bet) assumes each as having the choice between being justor unjust. According to Glaucon, from Alf’s perspective the worst outcome wouldresult from acting justly whilst Bet acts unjustly; the best to be unjust while Bet isjust. Mutual justice and mutual injustice are intermediate in worth, with the formerbeing preferred to the latter (Glaucon said that those who cannot choose but haveexperienced injustice would prefer to agree that both should be just). Then theencounter can be summarized as a Normal form game as shown in Table 1.

It can be seen that in this game whichever option the other player takes, a party isbest off being unjust: the equilibrium state – the state from which no player has anincentive to move – is mutual injustice. According to Glaucon, people intuitivelyrecognize these payoffs and so reluctantly resign themselves to conforming to asystem of justice since otherwise they will sink with everyone else into the moredisagreeable world of mutual injustice: but given half a chance (Glaucon’s exampleis the ring of Gyges, which confers invisibility on the perpetrator of evil deeds),people would otherwise act unilaterally in their own selfish interests. Among gametheorists, this is immediately recognized as an example of the Prisoner’s Dilemma, aclassic game to which, to the chagrin of the game theorists themselves, a rationalsolution does not exist (unless the game is repeated).

To demonstrate the exploration of strategy that game theory facilitates, it is worthbriefly examining a variation of the assumptions made in the game above. Suppose

Table 1 Glaucon’s argument: “natural” injustice

Cells show assessments by Alf,Bet.Equilibria are shaded.

Bet’s choice

Just UnjustAlf’ tsuJeciohcs Good, Good Worst, Best

tsujnU Best, Worst Bad, Bad

From Game Theory to Drama Theory 3

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that (as Plato proposes) a society be created in which justice is a core value: that is,all accept mutual justice as the very best outcome. Then the game transforms to thegame shown in Table 2.

Note that idealism has not totally triumphed here and if the cultural aim ofcollective justice were to collapse people are assumed still to seek personal advantage.Mutual justice is a stable outcome from which neither party can improve. However,the malign presence of mutual injustice persists as an alternative, though collectivelyundesired equilibrium. This game is well-known to game theorists and describes manysituations in which parties seek assurance; for instance, it corresponds to Rousseau’sdescription of the social contract. It also exemplifies the situation of the oligarchs ofAncient Greece (Simonton 2017) who needed to maintain solidarity in the face ofpotential democratic uprising: at any time one or more oligarchs might break awayfrom the ruling elite and seek to take control with the wider support of the demos (theFour Hundred oligarchs manifestly failed to achieve this solidarity in 411 BC).

One condition normally required in game theory is that of Common Knowledge(CK)(Vanderschraaf and Sillari 2014). This goes beyond the notion of completeinformation (where each player knows the rules of the game and the preferences ofthe other parties) by requiring that each player is aware that each other player hascomplete information; and each player is aware that each other is aware; and so on.However, a moment’s reflection shows that it is far from clear that in everyday lifepeople have CK of situations that they share together: indeed, misperceptions are notuncommon. Essentially, players can be attempting to play different games.

To see the mischief that arises from such misperceptions, consider the “justicegame” introduced above but this time with two players Col and Dee who perceivedifferent games (Table 3).

On the left in Table 3 is shown the game that Col might perceive. Here it isassumed that Col ranks the outcomes as in the “just society” game (Table 2) earlier.

Table 2 Glaucon’s argument: a just society

Cells show assessments by Alf,Bet.Equilibria are shaded.

Bet’s choice

Just UnjustAlf’ tsuJeciohcs Best, Best Worst, Good

tsujnU Good, Worst Bad, Bad

Table 3 Glaucon’s argument: misperceptions

Col's Perception Dee’s choice

Cells showassessments byCol,Dee

Just Unjust

Col’s choice

Just Best, Good Worst, Best

Unjust Good, Worst Bad, Bad

Dee’s Perception Dee’s choice

Cells showassessments byCol,Dee

Just Unjust

Col’s choice

Just Good, Best Worst, Good

Unjust Best, Worst Bad, Bad

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However, it is further assumed that Col suspects that Dee is a reluctant adherent tojustice (as in Table 1). This gives the game as seen by Col. On the right is shown thegame that, for the sake of illustration, Dee perceives. Making the assumption thatDee’s beliefs about Col, mirror those that Col holds about Dee, then Dee’s perceivedgame is as on the right.

Taking these two games together it can be seen that from Col’s perspective (i.e., inCol’s perceived game) acting unjustly would be Dee’s preferred strategy (in thatgame, for both Col’s choices, Dee does better by acting unjustly); correspondingly,in Dee’s perceived game, Col always does better acting unjustly. The result is aworld of mutual injustice that neither wants. Furthermore, by acting in this way, eachconfirms the other’s suspicions that they would be wrong to place trust in the other.This is just one way – clearly not the only one – in which mutual mistrust can arisefrom misperceptions. More complex misunderstandings can arise when one partyhas options that the other does not even see: thereby “strategic surprise” can occur inmilitary confrontations.

The theory of hypergames was developed (Bennett 1980a) to extend game theoryinto such situations where players’ perceptions of the game they are playing maydiffer. In this framework an n-person game ǖAA; has n associated hypergamesǖAA;k (for k= 1 to n), each representing the perception of the corresponding player.In principle, each such hypergame has, in turn, n associated hypergames ǖAA;jk (forj, k = 1 to n) representing j’s perception of k’s perception. An infinite tree ofhypergames could be envisaged but to date this is only of theoretical interest andthe focus in applications has remained on the first-order hypergames.

In retrospective applications of hypergame, analysis to actual conflict situationsuseful insights have been gained into various aspects of the interactions. An earlystudy (Bennett and Dando 1979) of the Fall of France in World War 2 clearlydemonstrated the disastrous significance that an Allied perception, bounded by ablinkered theoretical model, had upon the outcome of the Axis offensive. In anothercase study (Giesen and Bennett 1979), hypergame analysis showed that a decisionthat was apparently irrational, even stupid, in terms of a conventional game-theoreticformulation was arrived at quite rationally once perceptual limitations and informa-tion conditions were considered. Other uses of the hypergame framework haveincluded such contrasting examples as an investigation of football hooliganism(Bennett et al. 1980) and a study of nations “bidding” to attract a major investmentby multinational organization (Bennett 1980b). This body of work demonstratedhow one shortcoming of game theory can be overcome. More specifically, thehypergame approach offered an effective means of systematically exploring andtesting alternative hypotheses about perceptions in conflict and often threw unex-pected insights upon the motives underlying observed behavior. For obvious rea-sons, it proved particularly relevant to situations where the parties misperceived eachother and consequently helped to explain the importance and value of communicatedinformation; and by implication, the importance and value of sometimes preventingsuch communication to occur.


Metagames

In his ground-breaking book Paradoxes of Rationality: theory of metagames andpolitical behavior, Nigel Howard (1971) used three generic games – “Co-ordina-tion,” “Prisoner’s Dilemma,” and “Chicken” – successively to demonstrate disablingparadoxes that lie in wait for rational agents. In certain games of coordination – forinstance the so-called Battle of the Sexes where a couple wish to spend time togetherbut each argue for using this time differently – there is no single equilibrium: it isimpossible for both parties to be objectively rational. In “Prisoner’s Dilemma”(illustrated above) there are pressures to act irrationally: superficially a rationalchoice may offer a better outcome than an irrational one but when taken with theother party’s response, two rational players fare worse than two irrational ones.Finally, in “Chicken” (e.g., the “Cold War” standoff) both parties must be willing torisk annihilation (to act irrationally) if they are to achieve stability: this is exploredmore fully below. A theoretical discourse, but nevertheless firmly based in the worldof practice through the author’s concurrent work on nuclear proliferation, theVietnam and Arab-Israeli conflicts and issues of social discord (Bain et al. 1971),Howard’s book directly attacked the dominant concept of instrumental rationality. Itwas no surprise that the text attracted both favorable (Thrall 1974; Lutz 1974) andstrongly critical (Harsanyi 1974a) reviews, the latter leading to a heated debate(Harsanyi 1974b, c; Howard 1974a, b) and subtly but steadily to schism frommainstream work in game theory. This breach is only now being healed through afresh recognition of the complementary roles that drama theory – the lineal successorof Howard’s earliest work – and game theory can play in modelling strategic conflict.The early history is still relevant because it established a position which carriesthrough to present-day work in drama theory; that the making of unreasonableassumptions about human rationality should be avoided.

Undaunted by the impossibility of finding a rational solution to such tricky yetcommonplace problems as those introduced above, most game theorists persist in theassumption of strict rationality in their analyses and so are forced to contriveartificially complex definitions of rationality to account for people’s behavior.Howard resisted this temptation to revise the common-sense view of rationalityand instead embraced irrationality by building upon the concepts of majorant andminorant games originally floated by von Neumann and Morgenstern. These aredefined as follows. For a game ǖAA; between Player A and Player B, the gameǖAA;A in which A makes his choice before B and B makes his choice in fullknowledge of A’s decision is called the minorant game of ǖAA;, and the gameǖAA;B in which B makes his choice before A and A makes his choice in fullknowledge of B’s decision is called the majorant game of ǖAA;. Extending theseideas, Howard’s concept of a “metagame” (Howard 1966a, b) is the game that wouldexist if one player chose his strategy after the others and in knowledge of theirchoices: an n-person game ǖAA; has n associated metagames ǖAA;k (for k= 1 to n).However, each such metagame has, in turn, n associated metagames ǖAA;jk (for j,k = 1 to n); and so on, creating an infinite tree of metagames. The assumption is thatbehavior in ǖAA; can be interpreted as behavior in the infinite tree of metagames,

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since for a player to attempt to be objectively rational it must take account of others’subjective games and choose a “metastrategy” – a strategy for selecting a strategy –in the light of the overall metagame tree. Incidentally, this means that players aretreated as being as fully aware of the recursive structure as is any game theorist; thereis no privileged “higher” view that is not theoretically accessible to the participants.

To demonstrate how the metagame concept “solves” games like “PrisonersDilemma” return to the Glaucon’s original argument (Table 1 above). For clarityof exposition, the labels “Fair” and “Unfair” will be used to signify “Just” and“Unjust” behavior on Bet’s part (acknowledging the linguistic inexactitude intro-duced if these were to be interpreted literally). Then the corresponding Alf-meta-game (Table 4) and Bet-metagame (Table 5) are as shown.

The row labels in the Alf-metagame are Alf’s policies: before the forward slashwhat Alf would do if Bet chooses “Fair”; after the forward slash, Alf’s action if Betchooses “Unfair.” The column headings in the Bet-metagame have a correspondinginterpretation. In metagame analysis it is assumed that each player’s choice is basedupon what it anticipates the other player will choose: that is, these metagames aresimulated “in the heads” of the two players prior to any actual game play. Theequilibrium concept used is also built upon this idea: “an outcome . . .. is ‘stable’precisely when all players do in fact succeed in predicting it.” Stable outcomes of theoriginal game which are yielded by equilibria of a metagame are termed meta-equilibria and these are shaded above. Here the two metagames suggest the sameoutcome as in the original game but this is not invariably the case.

As indicated earlier the metagame concept takes strategic reflection to higherlevels: after all, would not each player make its choice taking account of the otherplayer’s predictions of the decision it might take? Such second-level responses canbe given for the preceding example: the Alf-Bet-metagame is shown in Table 6.

Table 4 Glaucon’s argument: Alf-metagame

Bet riafnUriaFJust/Just tseB,tsroWdooG,dooG

daB,daBtsroW,tseBAlf Unjust/UnjustJust/Unjust daB,daBdooG,dooGUnjust/Just tseB,tsroWtsroW,tseB

Table 5 Glaucon’s argument: Bet-metagame

BetFair/Fair Unfair/Unfair Fair/Unfair Unfair/Fair

Just Good, Good Worst, Best Good, Good Worst, BestAlf

Unjust Best, Worst Bad, Bad Bad, Bad Best, Worst


The second column lists all 16 possible reaction patterns (counter policies) by Alfto Bet’s possible policies. The metaequilibria are shaded: while one corresponds tothe outcome found in the earlier game, there is also one corresponding to thecooperative solution of this original game. A plausible dialogue based on declara-tions of their policies could be imagined between the two parties, leading to thisapparently “irrational” result. Such conversations and results have been observed inexperimental situations, thus supporting this unexpected finding. As to whether oneor other of these metaequilibria is more important than the others, metagame analysisremains deliberately agnostic: it is not a theory intended to predict behavior. Whilemany real-life plays of this game of Prisoner’s Dilemma do indeed resolve inCooperation (Payoffs = Good, Good), sometimes joint Defection (Payoffs = Bad,Bad) comes about through mutual mistrust.

Before moving on it is worth observing that there is of course no limit to the levelof recursion that may be used in considering a player’s choices (though there are ofcourse practical limits – even the third order metagame contains more than 4000payoff cells). Luckily Howard proved that all the metaequilibria of a 2-player gameare found at the second stage of the process, and that they persist at higher levels.

It is useful to introduce here the concept of a metarational outcome (ManagementScience Center 1968) since it raises issues that foreshadow subsequent develop-ments of metagame analysis. A metarational outcome is defined in the 2-player caseas an outcome that can be made attractive for one player by some policy chosen bythe other player. That is, such outcomes are outcomes in the normal-form game thatalso correspond to rational outcomes for a particular player in a metagame. So in theBet-metagame (Table 5), Bet’s Fair/Unfair policy makes the outcome (Just, Fair)

Table 6 Glaucon’s argument: Alf-Bet-metagame

BetFair/Fair Unfair/Unfair Fair/Unfair Unfair/Fair

J/J/J/J Good, Good Worst, Best Good, Good Worst, BestU/U/U/U Best, Worst Bad, Bad Bad, Bad Best, WorstU/U/U/J Best, Worst Bad, Bad Bad, Bad Worst, BestU/U/J/UU/U/J/J Best, Worst Bad, Bad Good, Good Worst, BestU/J/U/U Best, Worst Worst, Best Bad, Bad Best, WorstU/J/U/J Best, Worst Worst, Best Bad, Bad Worst, Best

Best, Worst Worst, Best Good, Good Best, WorstBest, Worst Worst, Best Good, Good Worst, Best

J/U/U/U Good, Good Bad, Bad Bad, Bad Best, WorstJ/U/U/J Good, Good Bad, Bad Bad, Bad Worst, BestJ/U/J/U Good, Good Bad, Bad Good, Good Best, WorstJ/U/J/J Good, Good Worst, Best Good, Good Worst, BestJ/J/U/U Good, Good Worst, Best Bad, Bad Best, WorstJ/J/U/J Good, Good Worst, Best Bad, Bad Worst, Best

Alf U/J/J/UU/J/J/J

J/J/J/U Good, Good Worst, Best Good, Good Best, Worst

Best, Worst Bad, Bad Good, Good Best, Worst

8 J. Bryant

metarational for Alf in this metagame, while in the Alf-Bet-metagame (Table 6),Alf’s Unjust/Unjust/Just/Unjust policy makes Fair/Unfair metarational for Bet.Identifying which outcomes are metarational for a given player in a given metagameshows what conclusions that player can deduce from a process of thought leading tothat particular metagame: for example, the considerations that lead Alf to the Bet-metagame may lead him to think that (Just, Fair) is his best outcome. Of course, thisalso depends upon the policy that the player believes the other player is following inthat metagame; if an outcome is not metarational for both players, then it is not ametaequilibrium from that metagame.

The above discussion has demonstrated the significance that must be attached tothe credibility of players’ policies. For the cooperative outcome (Just, Fair) to be anequilibrium Bet must make credible a “Tit-for-tat” policy (i.e., Fair/Unfair) of beingcooperative if the Alf is Just, but uncooperative otherwise. If Alf reacts with thecounter-policy U/U/J/U (which is perfectly “rational” since it involves choosing hisbest response to each of Bet’s policies) then (Just, Fair) will be the optimal outcomefor both players. This means that the crucial issue is finding a way of making credibleappropriate conditional policies. The challenge is underscored by noting that(Unjust, Fair), Bet’s worst outcome is still metarational for Alf in the Alf-Bet-metagame of Table 6. Were Alf to believe that Bet’s policy is always to be fair (i.e., Fair/Fair) then (Unjust, Fair) is the best outcome that Alf can obtain: Alf wouldsee unconditional cooperation as being Bet’s de facto policy if he thought that hemight covertly prepare unjust measures. The difficulty here is that (Just, Fair) is notrational for either player but is only metarational, so it needs to be bolstered bycredible conditional policies to render it stable.

Howard asserted that any specific game is better understood through an analysisof its metagame tree and he demonstrated this through its earliest application. Thiswas a study (Management Science Center 1969a) of the “Bay of Pigs” debacle whichprecipitated the Cuban Missile Crisis of 1961 and led to a heart-stopping standoffbetween the major nuclear powers. More telling than the actual models used todepict the evolving crisis was the fact that the historical process was represented andtracked using the approach: that is, there was a focus on the dynamics of conflict andon the movement from one phase of the narrative to the next. Interestingly, themodels also appeared to achieve some predictive ability (although this was not theirintention), a property found in subsequent case studies. What was most impressiveabout this work was the quality of the insights generated despite the parsimoniousnature of the models. It suggested that working with the players’ subjective gameswas a valid approach.

The Analysis of Options

Metagame analysis provided the theoretical foundation for a facilitated group pro-cess devised by Howard which he called the Analysis of Options (ManagementScience Center 1969b). This was a structured means of enabling an “audience” ofexperts with varied knowledge of a conflict domain to build and subsequently


analyze their own model of the situation: software support for this process was alsodeveloped. The intention was not to “solve” the conflict but to improve decision-making by gaining a better understanding of the strategic structure of the interactions(Howard 1986).

Typically the process commences with the surfacing and listing of the majorissues involved in a situation: these might be critical actions, strategic balances, or“bones of contention.” The parties “owning” these issues and the choices that theyhave available to them – their “options” – are next made explicit: such options areexpressed in binary form (they might or might not be done). These options providethe elements using which the possible strategies of each individual player can bestated (as sets of “yes”/“no” choices about the taking of its options) and the potentialoutcomes of the situation can be described (as sets of players’ strategies). Attentionthen turns to these outcomes, the stability properties of which are examined from theperspective of a specific player (or a coalition of players): this uncovers successivelyunilateral improvements, sanctions against such improvements and inescapableimprovements. These improvements provide an indication of places where leverageupon the situation might be exerted.

Howard’s initial experimental analysis was carried out with members of the USACDA in May 1968 as they explored the possibilities for the Paris peace talks aboutthe Vietnam War. The issues and players chosen for inclusion in the model (Howard1969) are shown in the leftmost column of the Table 7.

Two practically significant outcomes are shown in the second and third columnsof the table, headed descriptively “Cease-fire” and “Negotiated Settlement.” Wherean option is “taken” by the player concerned this is shown by a tick in the

Table 7 Vietnam War: metagame analysis

10 J. Bryant

corresponding cell; an option not taken is indicated by a cross. The outcome is thecombination of potential actions taken/not-taken by the players in its column.

Howard recommended a sequential process of analysis. This is computationallyeconomical and involves establishing the minimum assumptions needed to answerspecific questions that might be asked about the game. To show how such a processmight commence consider the stability of the “Negotiated Settlement.” This needs toviewed in turn from the perspective of each player: for the sake of illustration,suppose it is first considered it from the perspective of the North Vietnamese (NVN).Initially unilateral improvements for NVNwould be considered. Suppose the expertssay that these are as shown in the column headed “Preferred by NVN” whichcorresponds to a set of two outcomes (N.B. the tilde “~” symbol represents“either/or”): then in the absence of credible sanctions NVN will not keep to theNegotiated Settlement. However, even though the outcome is not rational for NVN,it can still be stable if credible sanctions can be used against NVN to prevent themmoving the situation to their preferred outcome(s). The next stage of analysis istherefore to find what sanctions exist against NVN in such circumstances. Thismulti-step process is too long to include here but might result in the following list ofpossible sanctions: USA and SVN resume fighting; USA not withdraw and NLFcease-fire; SVN continue fighting and NLF cease-fire. Whether or not each of thesesanctions would be credible is a matter for expert judgment. For instance, the firsttwo sanctions would hardly be credible if US troops had already been withdrawnfrom South Vietnam! In a rounded examination of an issue using metagames, thissequential probing of one outcome, seen from the perspective of one player would berepeated for other players and other outcomes: Howard likened the overall process toexamining a large, dark warehouse with a small flashlight! However, in practice thesearch and assessment would be greatly accelerated and rendered manageable by thedomain expertise of the client group.

The use of a table to depict multi-player situations as in the Analysis of Optionshas proven a versatile presentational device and has been more widely adopted inlater work. The scale of the analysis that it potentially requires (e.g., in the Vietnamcase with nine options there are potentially 29 = 512 possible outcomes) has alsoencouraged the development of dedicated software tools to support comprehensiveinvestigation, and in turn this has led to the possibility of testing for other, morecomplex, stability properties. For instance, Fraser and Hipel (1980) introduced andinvestigated sequential stability in their approach to conflict analysis. This wassubsequently incorporated in the generalized formulation due to Kilgour et al.(1987), which represented players’ choices, preferences, and sanctions as movesbetween outcomes within a directed graph (the so-called Graph Model, covered inthe chapter ▶ “Conflict Resolution Using the Graph Model: Individuals and Coali-tions”). The historical retrospective provided by Hipel in the chapter ▶ “LookingBack on Decision Making Under Decisions of Conflict” provides an account of thesedevelopments.


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The Problem of Inducement

Unfortunately, the shortcomings of rational behavior are not fully overcome by themetagame concept. This was acknowledged by Howard (1971) who set out the casefor developing what he called a theory of Inducement. Essentially, inducement isinvolved in situations where a player, knowing other’s preferences and relying upontheir propensity to act rationally (in a metagame, if not in the original game), can soact as to achieve an outcome he prefers. What happens then when different playersare seeking to induce different outcomes?

To take a practical example, suppose that two countries – call them Blue and Red– threaten each other with weapons of mass destruction (WMD) over some geopo-litical issue, as summarized in Table 8.

This is a game with two equilibria, at each of which one side but not the other“gives in.” The temptation for each player is to be the one to “stick to its guns” and soachieve its favored equilibrium, but if both sides refuse to step down then they willbring about mutual annihilation. In this game neither Blue nor Red have a “surething” strategy (a strategy that is best for itself regardless of what the other playerdecides).

Consider now ǖAA;Red one of the two first-order metagames that can be gener-ated from the standoff in the basic game: this metagame is shown in Table 9.

Table 9 Geopolitical Conflict: Red metagame

Cells show assessmentsby Blue, Red Equilibriaare circled.

Red’s policy

Red’s Policy “X/Y”means “Do X whenBlue choosesConcede and Do Ywhen Blue choosesResist”

Withdraw/Withdraw

Threaten/Threaten

Withdraw/Threaten

Threaten/Withdraw

Blue’s strategy Concede Good,Good

Bad, Best Good,Good

Bad, Best

Resist Best, Bad Worst,Worst

Worst,Worst

Best, Bad

Table 8 Geopolitical Conflict: basic game

Cells show assessments by Blue, Red.Equilibria are shaded.

Red’s choice

Withdraw ThreatenBlue’ edecnoCeciohcs Good, Good Bad, Best

tsiseR Best, Bad Worst, Worst

12 J. Bryant

Table 9 shows policies rather than simple choices for Red (as Red is decidingwhat to do after Blue has chosen): there are now three equilibria. Reviewing Red’schoices, it can be seen that the rightmost column represents a sure-thing policy, sinceonly in this column is it the case that irrespective of whether Blue decides to concedeor resist, Red’s payoff cannot be improved. However, this sure-thing policy handsvictory to Blue! If ǖAA;Blue were to be constructed and analyzed a correspondingresult would be found: a sure-thing strategy for Blue which allows Red to prevail.However, this paradoxical result does not end there. Any metagame has, in turn, nassociated higher-order metagames (e.g., second-order ones are ǖAA;jk,for j, k = 1to n) and, for the present example, the finding that a sure-thing policy gives victory tothe other side is promulgated throughout the infinite tree of such metagames.

In general, metagame analysis arguably solves descriptively (not normatively) theparadoxes of coordination and cooperation (like “Prisoner’s Dilemma”) but fails tohandle this third breakdown of rationality: the inducement problem as exemplifiedby “Chicken” in the confrontation above. This is because while in the basic game,ǖAA;, of “Chicken” neither side has a “sure-thing” strategy (a “sure-thing” strategyis a strategy that is best for a player regardless of what the other player decides) in themetagame ǖAA;A A has a sure-thing strategy that induces victory for B; and inǖAA;B B has a sure-thing strategy that ensures victory for A; and this pattern ispropagated through the metagame tree. Choosing a “sure-thing” guarantees the bestoutcome for the other side! Being “sure-thing” rational is clearly a bad idea.

It seems reasonable to assume that rational behavior by a player in any gameactually means behaving rationally in the infinite tree of metagames; since for a playerto attempt to be objectively rational it must take account of others’ subjective gamesand choose a “metastrategy” – a strategy for selecting a strategy – in the light of theoverall metagame tree, not just the immediate game. However, as the example abovehas illustrated, choosing a “sure-thing” may guarantee the best outcome for the otherside! A clue to handling this inducement breakdown came from empirical studies ofgame players facing the sort of impasse often encountered at conflict points. Peoplewere seen to become irritated with each other, sometimes verbalizing this throughabusive cliches: “I’ll see you in hell first,” “over my dead body,” etc. Such utterancesseemed to drive or to justify sudden changes in preference – Howard termed thechanges that occur through players’ frustration at a “sticking point” in the interaction,“preference deterioration.” The consequence of one or more players changing theirpreferences is that the game they are playing changes – and, for instance, previouslyunattractive outcomes may became favored, thus unsettling the other party’s preferredequilibrium. Subsequently Howard elaborated these ideas about preference change,first by making more explicit the role of emotions in decision-making and then byproposing “soft game theory” as a theoretical foundation for the rounded schema of“drama theory” (which is examined shortly below and then in a separate chapter of thisvolume ▶ “Using Drama Theory to Model Negotiation”).


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Emotional Decision-Making

Experimental evidence had shown (Management Science Center 1967) that deci-sion-makers are not rational in the narrow sense of the word (e.g., in Prisoner’sDilemma they often chose to co-operate) and (as noted above) that in the “heat” of aconfrontation their preferences may change. Specifically, emotions such as anger andfrustration appear to be concomitants of genuine preference change (whereas peopleare likely to view as dishonest a party which alters its preferences in a coldlycalculated manner or which issues apparently “willing” threats and promises).These emotions are hypothesized to “loosen” parties’ beliefs and values in such away as to allow them to rationalize their redefinition of the interaction. Suchredefinition of the “game” is not envisaged in game theory which takes the players’options and preferences as fixed. Nor was it part of Fraser and Hipel’s modificationof metagame analysis which turned its back upon “unwilling” threats and promises(i.e., “irrational” threats and promises which players are tempted to make credible forstrategic advantage).

In a wide-ranging assessment of progress made in metagame analysis since thepublication of Paradoxes of Rationality Howard (1986) highlighted a number ofdirections for future development. Arguably the most significant of these was whathe termed the “theory of loving preference change”: a formulation of the dilemmasof cooperation illustrated by “Chicken” above. Howard proposed that the challengesof cooperation and conflict which parties face create pressures upon them andprompt emotion of two kinds: positive emotion (love, goodwill) to make promisescredible, so eliminating dilemmas of agreement; and negative emotion (anger,resentment) to make threats credible, so eliminating dilemmas of disagreement.While the role of such sentiments as a means of solving the commitment problemhad been previously acknowledged (e.g., Frank’s work (1988) on altruism), theirexplicit role in a coherent analytical framework for modelling confrontations wasnew. The wider role of emotion in group decision and negotiation is explored morefully in the chapter ▶ “Role of Emotion in Group Decision and Negotiation”.

Promises are the most mystical of speech acts: that the verbal issuing of apromissory obligation can (like a magical incantation) change what occurs in thephysical world is decidedly mysterious. Voluntarily made, once uttered they imposean immediate obligation upon the utterer. Significantly, the mere fact that a personfeels it necessary to issue a promise implies that the promised act is one over whichthere is a temptation to renege: like Odysseus tied to the mast, the promise binds thespeaker to ensure that this likelihood is minimized. Furthermore for promises to bebelieved, a person must be trustworthy and so be someone who is known –who has areputation, from past actions – to carry out such “irrational,” “unwilling” acts.Identical arguments about the credibility of assertions made and about speakercredibility can be made for threats as for promises; and indeed, the two speechacts (Searle 1969) are generally seen as having similar status. Promises and threatstherefore provide a conceptual bridge between the worlds of rationality and irratio-nality. They also have a second, equally important property: promises and threatshighlight the common interests of the parties involved. A promise raises the prospect

14 J. Bryant

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of an outcome that is better for both players; a threat, the prospect of one that isworse. The corollary is that there must be some commonality of interest involved. Itis upon an appeal to this joint interest (through the citing of evidence and the use ofrational arguments) that credibility is built.

From what has been said here there is an important distinction to be made whenanalyzing strategic interactions between “willing” and “unwilling” threats andpromises: appropriate emotions are required to make the latter credible. Correspond-ingly, when emotional responses are encountered during the course of an interactionthey can be interpreted as symptoms of players’ personal struggles with the chal-lenges of making credible assertions. Howard recommended (Howard 1993) theconstruction of a “strategic map” to help identify promises and threats whosecredibility might need enhancing. Such a diagram depicts the improvements thatplayers can make in moving the situation from one outcome (scenario) to anotherand the sanctions that can be bought to bear to counter such improvements.

The Concept of Drama Theory

By 1991 the foundational elements were present for the construction of a new theoryof multi-party decision-making based upon the preceding ideas. What was lackingand was supplied at that point in time was a motivating metaphor around which theseideas might cohere: the metaphor was that of drama. Key aspects of what wasdeclared as a new paradigm were: moving beyond game theoretic rationalityassumptions; taking the game to be subjective (i.e., it is what the players see); and,assuming that the game is “soft” (i.e., it changes as players communicate about it).The new theory was intended to show how parties who attempt to act rationallywithin a fixed game are driven by emotion to act irrationally and change the game,consolidating the transformation by appeals to common interests. These partiesstrive, not for an ideal solution but for self-realization, and it is through this creativesearch that they achieve emotional and logical closure of the confrontation. Themetaphor of drama with its connotations of an open-ended, emotionally-ladenprocess driven forward through crises by dialogue and prompting fresh awareness,represented far better than the rigid, rule-based concept of games the nature of theexchanges that were to be understood. The adoption of this metaphor was very muchin sympathy with wider changes. For instance, in the military domain the Cold Warhad ended and attention was shifting from “war-fighting” to “operations other thanwar.” At the same time, attempts to find technical solutions to complex problemswere being supplanted by problem structuring methodologies intended to stimulateand inform debate and decision-making (Howard 1989): “soft game theory” (How-ard 1990) was one such emerging approach.

“The aim of drama theory is to explain how characters interact to resolve a givenset of issues and how in doing so they are transformed” (Howard 1994). In dramatheory, this evolution is seen as taking place through successive episodes, each ofwhich requires the parties – now called characters – involved to declare andsubsequently make choices that create the starting conditions for following episodes.


A “tree” of episodes is conceived; this includes episodes that might occur, but do not,as well as those that are actually realized. The “interactions” that are modelled indrama theory are the dialogic exchanges between parties as opposed to any physicalinteractions (except insofar as the latter convey messages). The personal transfor-mations concerned include characters’ aspirations, positions, doubts, and percep-tions and involve a shift from their first recognition of the disputed issues throughtheir suggestions for solutions to their eventual attempts at resolution. For analyticalpurposes, this process has been represented as involving a five-phase process: scene-setting, buildup, climax, resolution, and denouement.

Drama involves exchanges between the dramatic personae. Correspondinglydrama theory represents these exchanges between characters (which may be indi-viduals or groups of individuals, organized or otherwise). Drama theory modelsframes. A frame holds an analogous role in drama theory to that of a game in gametheory: it is a representation of a situation as seen by a particular character at aparticular point in time. A character’s framing of a situation includes its understand-ing of what the other characters might do (their options), the outcomes that couldtherefore be co-created by the cast, and its own views about these outcomes.Through dialogue, characters share their frames with each other; initial appreciationsmay thereby be refined or radically modified until a shared appreciation of theircollective predicament is reached. This common reference frame (CRF) may revealagreement (or at least compatibility) or alternatively might show up apparentlyirreconcilable differences. In the former case, the characters may simply need toreassure each other of their good intentions, but in the latter, frustration at theimpasse may prompt them to issue harsh words or else, placably, to moderate theirdemands. This is the point at which the emotional temperature of the interaction mayrise as the characters attempt to convince others of the sincerity of their promises andthreats. The pressures at this Moment of truth (MoT) can cause characters to changethe CRF (for instance by pointing out new actions) thereby moving the whole castinto another episode: or they might modify their personal frames and so trigger freshnegotiations towards a revised CRF. At some point, however, all pressure to makefurther transformations of the final CRF is exhausted. The talking has to cease andactions, whether co-operative or conflictual, are determined by each party. It is at thisstage, as they independently face the outcome that together they have helped toshape, that the mental assessments of the characters might be modelled by gametheory: the game has been “fixed” through the earlier exchanges and each charactercan think rationally about what its best course of action would be. Whether or not ittakes the prescriptions suggested by game theory as a guide depends, of course, onother moral and ethical considerations, but this lies outside the scope of the presentexposition.

Before moving on briefly to describe the development of drama theory, it isapposite to suggest that the reader contrasts the process of dramatic resolutiondescribed here with the models of negotiation processes, both cooperative (see thechapters ▶Negotiation as a Cooperative Game) and ▶ “Non-cooperative GameTheory and Negotiation”).

16 J. Bryant

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Drama Theory: Early Development

The early 1990s saw the consolidation of the model of the process of dramaticresolution, depicting the movement within an episode from “scene setting,” in whichthe CRF is established, through to the denouement, where the practical implicationsof enacted choices are faced by the characters. A unique feature of this process wasthe role attributed to emotion (Bennett 1996) in supporting a character’s “unfreez-ing” from one position and shifting to another. Much as Frank (1988) had argued thatemotion offers a means for people to solve problems of “commitment” (handlingthose unwilling threats and promises which drama theory was explicitly embracing),so the new theory postulated (Bennett and Howard 1996) that emotion accompaniespreference change. Importantly, emotion on the part of one character has the strategicfunction of altering other characters’ views about a situation, as well as its own.

The transformation of the frame which was clearly a central issue for dramatheorists was first expressed mathematically in unpublished papers as early as 1993,but it was much later (Howard and Murray-Jones 2002) that it was explored inpublications. Essentially, this work considered the formal ways in which a framecould expand or contract (through the addition or removal of characters or theiroptions) and how this might occur to shape transformations in the episodic tree.

The paradoxes of rationality are, in drama theory, the triggers for emotions.Initially, the three paradoxes of Howard’s original work (Howard 1971) stillremained central to understanding the pressures that characters experienced at the“moment of truth” when they realize that they do not share a single position.However, early applications prompted reconsideration that led to a formulationincluding five (later six) paradoxes (later called dilemmas). These were definedmathematically by Howard (1998) in a paper that used them to specify conditionsfor a strong resolution of a situation.

A simplification that was to prove important for later work was also made: therealization that for the analysis of a situation it was unnecessary to investigate everyscenario: rather it was sufficient to focus on a “confrontation” – that set of scenariosrepresenting the “position” of each character together with the “conflict point” (thefuture that would occur if each character carried out its sanction). Furthermore, it wasrealized that the corresponding strategic map only needed to include improvementsfrom these scenarios since the sanctions were included in the conflict point itself.Both simplifications arose from practical work with client organizations, but weresubsequently given theoretical justification in the context of the growing body oftheory. They created further distance from other approaches such as the Theory ofMoves (Brams 1994) and the Graph Model (Kilgour et al. 1987) also developing atthat time.

A final conceptual development that was part of this developmental phase ofdrama theory was the use of “general” positions implying that there could beelements of a frame on which a character might be undecided. This extension wasprompted by analysis of confrontations in Bosnia and the need to better representand understand compatibility between the various scenarios that characters mightcocreate (Murray-Jones and Howard 2001) but it has proved to be of far wider value.


By the beginning of the twenty-first century therefore, there had been a fulldecade during which drama theory had evolved from its origins in metagameanalysis into a rounder conceptual framework with its own distinct features. Whilesome theoretical development continued, the field entered a period of consolidationin which practical applications came to the fore. Perhaps inevitably, these applica-tions prompted practitioners working in different domains and with clients havingdifferent requirements to create “local” versions of the framework and this has led tothe situation today where several well-established variants exist. However, despitesuch differences (some of which are described in chapter▶ “Using Drama Theory toModel Negotiation”), the core notion remains that it is productive to think of aninteraction as a drama that transforms under the internal pressures which characterscreate by their stated positions, fallbacks, preferences, and doubts.

moderate

Gov

G R

Rad

call election ?

t

moderate

Gov

G R

Rad

call election Gov Rej(t) with Rad

Gov Per(p) with Rad

?

t

18 J. Bryant

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moderate

Gov

G R

Rad

adopt

call election

Rad Tru with Gov?

t

Intentions

Swerve

Swervemum

Alf Bet

Cross-References

▶Conflict Resolution Using the Graph Model: Individuals and Coalitions▶Looking Back on Decision Making Under Decisions of Conflict▶Negotiation as a Cooperative Game▶Non-Cooperative Game Theory and Negotiation▶Role of Emotion in Group Decision and Negotiation▶Using Drama Theory to Model Negotiation

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Bennett PG (1980a) Hypergames: developing a model of conflict. Futures 12:489–507


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From Game Theory to Drama TheoryIntroductionGames and HypergamesMetagamesThe Analysis of OptionsThe Problem of InducementEmotional Decision-MakingThe Concept of Drama TheoryDrama Theory: Early DevelopmentCross-References

from game theory to drama theory...rational” aspects of decision-making (e.g., crisis, emotion,...

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