International Journal of Forecasting 18 (2002) 369–374www.elsevier.com/ locate/ ijforecast

F orecasting games: can game theory win?

*Paul GoodwinSchool of Management, University of Bath, Claverton Down, Bath BA2 7AY, UK

Abstract

I present evidence to suggest that studying the use of game theory in prediction is a legitimate area of research and suggestways in which game theory might be used to make or support predictions. Green’s study predominately assesses theaccuracy of predictions by game theorists (whomay have made informal use of game theory concepts) rather thanpredictions obtained from formal game theory models. I argue that the accuracy of predictions derived from such models islikely to be contingent on the characteristics of the conflict and provide a partial taxonomy of these characteristics, togetherwith their hypothesised effects. I also argue that it would be worth investigating the potential use of game theory as an aid toobtaining probabilistic predictions. 2002 International Institute of Forecasters. Published by Elsevier Science B.V. Allrights reserved.

1 . Introduction the study, or game theorists? (iii) To whatextent can we draw practical inferences from

The paper by Green (2002) deals with a the results of the study. (iv) Where should futurefascinating and important area, namely the research effort be directed?prediction of outcomes of conflicts. The paperextends earlier work, reported in Armstrong(2001), which has shown that the use of role 2 . Game theory and predictionplaying to predict the outcomes of conflictsleads to forecasts that are significantly more A key question underlying the paper is:accurate than those obtained through unaidedshould game theory be used for prediction or isexpert judgment. In the current paper, the focus it essentially a prescriptive tool designed to aidis on the relative accuracy of forecasts obtained decision-makers who have to make strategicthrough role-playing and game theory. This choices under conditions of conflict? There arecommentary addresses four questions: (i) Is it close parallels with decision analysis here.legitimate to study the use of game theory for Much evidence suggests thatunaided decision-prediction? (ii) Is game theory being assessed in makers do not make choices consistent with

those suggested by decision analysis (Goodwin& Wright, 1998). Allais’s paradox (Allais,*Tel.: 144-122-532-3594; fax:144-122-582-6473.1953) where people violate the prescriptions ofE-mail address: mnspg@management.bath.ac.uk(P.

Goodwin). utility theory, is a famous example of this.

0169-2070/02/$ – see front matter 2002 International Institute of Forecasters. Published by Elsevier Science B.V. All rights reserved.PI I : S0169-2070( 02 )00022-5

370 P. Goodwin / International Journal of Forecasting 18 (2002) 369–374

Factors like habit, the inability of decision . . . to [inter alia] forecast the outcome ofmakers to process all of the information associ- political events that influence business activi-ated with a decision, and the consequent use of ty.mental heuristics (Goodwin & Wright, 2001;Tversky & Kahneman, 1974), are all likely tolead to discrepancies between what people 3 . Game theory or game theorists?choose and what normative methods say theyshould choose. Indeed, theraison d’ etre of a The second main question about the paper is:prescriptive technique is that the unaided deci- is game theory being assessed or game theor-sion maker would make a different (inferior) ists? To consider this, it may be instructive todecision to that prescribed by the technique. consider the possible approaches a game theor-

However, two factors suggest that the use of ist might adopt when faced with the task ofgame theory in forecastingis a legitimate area prediction. The ‘purest’ approach would involvefor investigation. First, I selected a convenience the exclusive use of a game theory model tosample of six introductory textbooks on game derive the prediction. To achieve this the gametheory and found that two of these suggest that theorist would, ideally, need to obtain infor-the technique does have value as a forecastingmation on factors such as the number of players,method. For example, Dixit and Skeath (1999), the strategies available to the players, and thein their book ‘Games of Strategy’, state: players’ utilities (which are likely to be multiat-

tributed) for all strategy combinations. In addi-The second use (of Game Theory) is in

tion to this, information on the type of gameprediction. When looking ahead to situationswould be required. For example, do the playerswhere multiple decision makers will interactdetermine their moves sequentially or simul-strategically, we can use game theory totaneously; do all the players have full infor-foresee what actions they will take and whatmation or is some information known only tooutcomes will result.certain players; can the rules of the game bemanipulated; are agreements enforceable?Indeed, as Hargreaves, Heap, and VaroufakisWhile modern game theory is capable of hand-(1995) point out, regarding game theory asling a diverse range of game types, much of thismerely a prescriptive technique would: ‘‘greatlyinformation may be difficult to obtain. Forundermine [its] attraction since the arrestingexample, determining players’ multi-attributeclaim of game theory is that it can be used toutilities will be dependent on having knowledgeexplain social interactions’’. Explanation is, ofof their value systems and attitudes to risk.course, a necessary precursor of insightful pre-When this knowledge is not available, approxi-diction.mations or assumptions will be required. ForSecond, game theoryis being used as aexample, a multiattribute utility function mightpredictive technique in practical contexts. Forbe approximated by ranks designed to reflect theexample, Decision Insights Inc. of New York,relative attractiveness of a game’s outcomes to awho claim to work with Fortune 500 companies,given player. Sensitivity analysis may be usefulgovernment institutions and investment banks,in situations like this to determine the robust-amongst others, state on their websiteness of predictions to changing assumptions.(www.diiusa.com) that they:Nevertheless, inadequate models may still lead

. . . develop practical game theory models to erroneous predictions. For example, in ex-

P. Goodwin / International Journal of Forecasting 18 (2002) 369–374 371

perimental studies, the failure of game theory that most of the experts were formulating gamemodels to predict accurately players’ strategies theory models of the situations—either toin simple games involving monetary outcomes produce their forecasts directly, or as a basis forhas been attributed not to game theory per se, subsequent judgmental prediction (an impres-but to the fact that the models did not include sion supported by the five independent ratersthe players’ tendency to reject outcomes which who studied the game theorists’ explanations).were perceived as being grossly unfair to the This suggests that most of their forecasts wereother player (Thaler, 1988; Cameron, 1995). purely judgmental. However, since the game

In view of these difficulties the game theorist theorists were significantly more accurate inmight, instead, use a game theory model to their predictions than unaided judges it appearsclarify his or her thinking, but then make a that either their ‘ingrained game-theoretic think-judgmental adjustment to the model’s prediction ing’ or their experience as students of conflictto try to compensate for the deficiencies of the situations, or both, were acting to their advan-model. In this approach, the game theory model tage. Unfortunately, it is not possible to dis-is being used as a forecasting support system. criminate between these possibilities on theWhile in both approaches the model will reflect basis of the explanations provided.the subjective perceptions and skill of the gametheory expert, in the second approach the judg-mental adjustment is not formally based on 4 . Practical inferences?game theory.

Finally, the game theory expert might not The next question is:to what extent can weemploy game theory explicitly at all, but simply draw inferences from the results of the study formake a judgmental prediction of the outcome of practical forecasting? In the early stages ofa dispute. The rationale for employing a game research in a new area there is always atheorist here would be that being an expert in a temptation to draw unconditional conclusionsdiscipline leads to the concepts associated with from results. Later research often reveals thatthat discipline becoming ingrained in one’s conclusions are contingent upon particular cir-thinking, even when the method is not being cumstances. How might conditions in conflictexplicitly used. Some people argue that this may situations vary, and are there any conditionsbe the case. For example, the Nobel laureate, where the use of game theory might be expectedPaul Samuelson has written ‘‘To know game to lead to accurate predictions?theory is to change your lifetime way of think- Raiffa (1982) has constructed a partial classi-ing’’ (see Dixit & Skeath, 1999). However, if fication of conflict situations (he admitted that itgame theorists do predict in this mode it is was impossible to obtain a complete taxonomyuseful to distinguish between their use of game of all possible disputes). This classification hastheoretic thinking and the possibility that they been used as a starting point for the list ofmay simply be drawing on their experience of characteristics shown in Table 1. Hypothesesstudying a large number of conflict situations. about whether the characteristics will be detri-

Green asked the game theorists in his study mental or favourable to accurate prediction byhow they arrived at their predictions and he has game theory are also given in the table. Thehelpfully provided details of their responses on hypotheses are based mainly on the extent tothe Internet (athttp: / /decision.co.nz/approach. which the conditions mean that outcome of thepdf). There is little evidence in these responses conflict is likely to be predictable or whether the

372 P. Goodwin / International Journal of Forecasting 18 (2002) 369–374

Table 1Characteristics of disputes and their likely effect on game theory forecast accuracy

Characteristic

Favourable:Low uncertainty Good knowledge of payoffs by parties

Option sets clearly defined and known by partiesRules of game known by partiesHonesty and openness in negotiationsThird party intervention possibleMonolithic parties

Reduced complexity Use of decision aid by at least one partyLearning Repetitive negotiationsProfessionalism Skilled experienced negotiators

Unfavourable:Bounded rationality Payoff dependent on more than one attribute

More than two partiesLarge number of optionsLinkage between issuesTime constraints on deal

High uncertainty Negotiators need ratificationCreative/flexible negotiatorsContract not binding

Emotional factors Parties subject to emotional influences

Source: adapted from Raiffa (1982).

conditions are consistent with the three key incomplete information, even when this uncer-tainty relates to the sets of available strategiesassumptions of game theory (Hargreaves et al.,and the rationality, or otherwise, of an opponent1995). These are that parties in the conflict:(Dixit & Skeath, 1999, p. 35).

1. are instrumentally rational; How robust are the key assumptions of game2. have common knowledge of this rationality; theory likely to be across a variety of conflict3. know the rules of the game. situations? Simon’s (1955) concept of bounded

rationality suggests that, as the complexity ofThese assumptions essentially imply that the the game increases, the decision making partiesparties in a conflict will be utility maximisers will lack the mental capacity to process all ofwho also know that the other parties are utility the information needed to maximise utility. Asmaximisers. These parties will also know: (i) all indicated in Table 1, this suggests that gamethe possible actions available to themselves andtheory will be less effective in forecasting theirthe other parties, and (ii) the payoffs that will actions. Departures from utility maximisation asaccrue to each party contingent on combinations a result of emotional factors will have a similarof these actions being chosen (although some ofeffect. For example, in a series of negotiations,this information may be held in probabilistic parties who feel they have behaved badly inform). Despite these core assumptions, it should earlier disputes may be more amenable tobe acknowledged that game theory can embrace yielding concessions in subsequent negotiationssome situations where there is uncertainty and to compensate for their behaviour. Similarly,

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conflicts where the parties have poor quality to anticipate the effect of this on the value ofinformation about the available sets of options, game theory as a predictive tool.or the contingent payoffs, are also likely to leadto outcomes that deviate from the predictions ofgame theory. Indeed, the actions of creative 5 . Suggestions for further researchnegotiators whoinvent mutually attractive op-tions during the negotiating process (Raiffa, Table 1 considers how the characteristics of1982; Goodwin & Wright, 1998) will be par- conflict situations may affect the accuracy ofticularly difficult to predict. game theory predictions. However, it does not

In contrast, there is some experimental evi- consider the accuracy of these predictionsrela-dence that after severalrepetitions of playing tive to those of other methods, like role-playing.relatively simple games, which each have a For example, some of the characteristics that areunique Nash equilibrium, with different oppo- favourable to game theory may also favournents, people do learn to play the Nash equilib- other methods, possibly because they simplyrium strategies predicted by game theory (Davis make the conflict inherently easier to predict.& Holt, 1993). Observations of baseball and Further research will be needed to discovertennis players also suggests that experience of whether there are characteristics that uniquelyplaying games repeatedly can lead to the use of favour prediction by game theory.strategies that are consistent with Nash equilib- It is also worth noting that, in the experimentsria (Dixit & Skeath, 1999, p. 215). Similarly, described by Green, the participants were facedthe Ghemawat and McGahan (1998) study, with a choice from a fixed set of pre-determinedcited by Green, found that repeated games options. In real-time negotiations new optionsbetween electricity generators were forecast and opportunities may emerge and environmen-relatively accurately through game theory, when tal factors and pressures on negotiators maythey involved a small number of players. In change (e.g., an initially supportive public mayaddition, there is some, albeit limited, evidence tire of the disruption caused by a trade union’sfrom experiments that professional negotiators dispute). Clearly, the true test of the relativemay behave more consistently with the predic- power of the methods discussed in the Greentions of game theory than non-professionals do study is whether the outcomes of current,(Potters & Van Winden, 2000). hitherto unresolved, disputes can be accurately

Some of the factors in Table 1 will be more predicted.important than others, depending on the context Finally, it is surely worth investigating prob-of the dispute, and there are also likely to be abilistic prediction (e.g., an estimate that there isinteractions between the factors. For example, a 0.3 probability that the outcome will bex andresearch suggests that repetitive games involv- a 0.7 probability that it will byy)—Brier scores,ing single attribute payoffs may be amenable to or similar approaches, could be used to evaluateaccurate game theory predictions, but repetitive the forecasts. Probabilistic predictions wouldgames, which involve the need for the parties to seem to be a natural way of addressing theuse probabilities, because of uncertainty in uncertainty inherent in the outcomes of con-information, are less amenable (Davis & Holt, flicts. They convey more information than sim-1993). Clearly, other factors could be added to ple predictions of the most likely outcome andTable 1. For example, it also seems likely that they would be a necessary input to somewhether the negotiations are held in public or normative decision models (e.g., decision treeprivate will effect the outcome, but it is difficult models based on expected utility) where a

374 P. Goodwin / International Journal of Forecasting 18 (2002) 369–374

Armstrong, J. S. (2001). Role playing: A method todecision maker needs to take into account theforecast decisions. In Armstrong, J. S. (Ed.),Principlespossible outcomes of a conflict. It should not beof Forecasting: A Handbook for Researchers andforgotten that game theory itself often pre-Practitioners. Norwell, MA: Kluwer Academic, pp. 15–

scribes that parties should select strategies in a 30.probabilistic manner through the device of Cameron, L. (1995). Raising the stakes in the ultimatum

game: Experimental evidence from Indonesia. Princetonmixed strategies. Surprisingly, although prob-University, Industrial Relations Section, Working Paperabilistic prediction was available to the game345.theory experts in the Green study, only one

Davis, D. D., & Holt, C. A. (1993).Experimental Econ-respondent adopted it for just one of the predic- omics. Princeton, NJ: Princeton University Press.tions. Dixit, A., & Skeath, S. (1999). InGames of Strategy. New

York: WW Norton and Company.Ghemawat, P., & McGahan, A. M. (1998). Order backlogs

and strategic pricing: The case of the US large turbine6 . Concluding commentsgenerator industry.Strategic Management Journal,19(3), 255–268.There are a number of ways in which game

Goodwin, P., & Wright, G. (1998).Decision Analysis fortheory might be useful in forecasting the out-Management Judgment, 2nd ed., Chichester: Wiley.

comes of conflicts. Green’s study has predomi- Goodwin, P., & Wright, G. (2001). Enhancing strategynantly investigated the accuracy of the judg- evaluation in scenario planning: A role for decisionmental forecasts by game theory experts and analysis.Journal of Management Studies, 38, 1–16.

Green, K. C. (2002). Forecasting decisions in conflictfound this to be inferior to the accuracy ob-situations: A comparison of game theory, role playingtained through role playing, but superior toand unaided judgement.International Journal of Fore-unaided forecasts produced by students. How-casting, 18, 321–344.

ever, the use of formal game theory models to Hargreaves, Heap, S. P., & Varoufakis, Y. (1995).Gamesupport judgment, and the use of the models in Theory: A Critical Introduction. New York: Routledge.

Potters, J., & Van Winden, F. (2000). Professionals andtheir own right, also appear to be worth inves-students in a lobbying experiment: Professional rules oftigating. In using such models there are likely toconduct and subject surrogacy.Journal of Economicbe two main sources of possible forecast error:Behavior and Organization, 43, 499–522.

incompleteness in the information available to Raiffa, H. (1982).The Art and Science of Negotiation.the modeler and the failure of disputants to Cambridge: Harvard University Press.behave consistently with the assumptions of Simon, H. A. (1955). A behavioral model of rational

choice.Quarterly Journal of Economics, 69, 99–118.game theory. This suggests that some types ofThaler, R. H. (1988). Anomalies: The ultimate game.conflicts may be more amenable to predictions

Journal of Economic Perspectives, 2, 195–206.involving formal models than others. Further Tversky, A., & Kahneman, D. (1974). Judgment underresearch effort could be directed into identifying uncertainty: Heuristics and biases.Science, 185, 1124–these situations, while the use of game theory to 1131.produce probabilistic predictions is also worthinvestigating.

R eferences

Allais, M. (1953). Le comportement de l’homme rationneldevant le risque, critique des postulats et axiomes del’ecole americaine.Econometrica, 21, 503–546.