Encyclopedia of Sociology Vol

planning, to identify the possible technological futures and their environmental and social impact.

As regards the actual discipline, in addition to futures studies—a very broad term that contains all the different ways of looking at the future, from projection to utopia—there is the term futurology, which was defined by Ossip Flechtheim (1966) as the search for the logic of the future in parallel to the search for the logic of the past in history. Unfortunately, this concept has lost its correct meaning and is now used casually to refer to any fantasy about the future.

Futuristics is another term that is often used, especially in North America. Its meaning is similar to that of futures studies.

A BRIEF HISTORY OF FUTURES STUDIES

It is hard to establish a definite date for the beginning of futures studies. Many indicate the period immediately after World War II with the development in the United States of what was called technological forecasting at RAND (Research and Development) Corporation. According to Wendell Bell (1997), this can be linked to the operational research conducted in the United Kingdom to predict and project the moves of the German bombers.

More or less in the same period, the Europeans also contributed to what may be considered the ‘‘beginnings’’ of futures studies—in France, Bertrand de Jouvenel with futuribles and Gaston Berger with prospective, followed by Pierre Massé and many others; Pater in the Netherlands, Fred Polak with his important books The Image of the Future and Prognosis: A Science in the Making.

The three major organizations dealing with futures studies were established at the end of the 1960s: the World Futures Studies Federation, which started in embryo in Oslo in 1967 and was formally founded in Paris at UNESCO in 1973; the World Future Society, essentially a North American organization founded by Edward Cornish in 1967; and the Club of Rome, founded in Rome by Aurelio Peccei and Alexander King in 1968. The latter in particular had a major impact on decision making with the project ‘‘The Limits to Growth,’’ which is still relevant both in relation to the limits

of the earth and of the need to look at the future in the long term, and in relation to a cluster of human and social issues (the global problematic).

The 1970s posed a serious challenge to futures studies. The severe economic crisis of that period showed that in looking at the future it is necessary to address many aspects and paces of change, given that economic and technological changes are much more rapid than social and cultural changes, for example. The 1970s also challenged the concept of the future as being linear development of the present and the past. There was a reappraisal of futures studies in the 1980s, especially in Europe. In countries such as the Netherlands, Sweden, and Finland, futures studies acquired political importance. In the 1990s developing countries also started to make use of futures studies; with the exception of India, China, and certain Latin American countries, most developing countries had had little interest in futures studies up until then. In the same period, futures studies reemerged very strongly in the United States with the launching of such major projects as the Millennium Project, supported by the United Nations University and the Smithsonian Institute. The Millenium Project, directed by Jerome C. Glenn and Theodore J. Gordon, studies the major threats and challenges of the future and produces the ‘‘state of the future’’ report. The debate on methodologies was also revived, sparking the publication of many basic texts that became prominent in the world debate. Schools of futures studies emerged in Finland and Hungary, and there was increased interest in Australia.

Numerous sociologists have made important contributions to futures studies: William F. Ogburn was appointed by President Herbert Hoover to chair the Research Committee on Social Trends as early as 1929. Harold Lasswell, who laid the foundations for the science of political choices also wrote many less well-known articles on futures perspectives. Daniel Bell wrote the famous report of the Commission Toward the Year 2000 for the American Academy of Arts and Sciences in 1967. John McHale wrote many books and contributed to the founding of the World Futures Studies Federation in the 1960s and 1970s. Elise Boulding greatly contributed with her work on peace in the future and the role of women in the future. One

could mention many more names. The main point to stress is that futures studies and sociology have not always been considered two separate and distinct disciplines.

CHARACTERISTICS OF FUTURES STUDIES

Many characteristics of futures studies relate to the linking of present action with future results. Barbieri Masini (1993) identifies seven characteristics in particular:

1.Transdisciplinary. Futures studies go beyond the interdisciplinary nature of social science. Futures studies needs the parallel approaches of different disciplines as well as the combined effort of many approaches in addressing the complexity of present problems in a rapidly changing society. It needs disciplinary approaches that identify common assumptions and use common methodologies. In terms of methodologies, examples of such approaches are the Delphi and the scenario-build- ing methods, which function with the support of mathematics, statistics, economics, sociology, history, and psychology. To quote Fred Polak: ‘‘all kinds of separate, fragmented portions of the jigsaw puzzle are of little avail, unless they are fitted together in the best possible way, to form an image of the future depicting a number of main areas of development’’ (1971, p. 261).

2.Complex. This represents the other side of the transdisciplinary nature of futures studies. As a concept, complexity was much debated in futures studies, even before it became a clear issue in social sciences, because it is related to uncertainty: The greater the complexity of a given situation, the greater the level of uncertainty; the greater the number of variables needed to describe a social situation, the greater the uncertainty. Because the future is so uncertain, futures studies has to devise methods for lowering the level of uncertainty: One such method is alternative scenario building.

3.Global. Its global nature is probably the bestknown characteristic of futures studies. It is now generally accepted that the future is determined by a continuous interplay between local issues and global issues. Some issues emerge as local and then become global, such as an economic crisis in a given country or part of the world. Some issues are

born global and subsequently affect the local level such as the greenhouse effect.

4.Normative. The impact of the normative is much greater in futures studies than is usually the case in social sciences. Frameworks of values and systems of values can never be completely eliminated in futures studies. Many methods try to lower the level of impact of the normative, but it is always present: Thinking about the future, making decisions about the future, is always related to some hope or fear.

5.Scientific. This is the most debated characteristic of futures studies, precisely because the normative is always present. Great effort has been made to invent devices and methods for increasing the scientific level of futures studies. If it is not possible to define futures studies as scientific, then it must be absolutely rigorous in terms of application and methods. It must be used according to strict scientific rules. Yehezkel Dror (1974) stresses the importance of combining a clinical and a human approach.

6.Dynamic. Futures studies is very dynamic: It is constantly in search of stronger foundations, of better approaches, and of more effective methods for facing the rapidity of change.

7.Participatory. There is less consensus on this characteristic of futures studies than on the previous ones. It is obvious that futures studies methods should be developed with the participation of those who are responsible for choosing the future, that is, decision makers at every level. This may not be possible at every step in the application of methods, but it is certainly something to strive for. Participation is definitely an essential characteristic of scenario-building and Delphi applications.

LIMITS OF FUTURES STUDIES

Like all disciplines futures studies has limits. Barbieri Masini (1993) has singled out six such limits.

1. Self-altering. The moment a forecast, or the result of a futures study, becomes public, it produces consequences that alter the reality in which it operates. In other words, a self-realizing or a selfdefeating effect may invalidate the value of the forecast. This danger was underlined long ago by Robert Merton ([1938] 1973) and is still valid today.

2.Psychological aspects. These are crucial in futures studies, as inevitably in looking ahead one is influenced by hopes and fears. Fear of the unknown is ever present and can have a negative impact on the need to think in alternative terms as the future requires. It is also easy to underestimate the changes that will occur in the future.

3.Irrational aspects. In future processes and events there is always an irrational element that cannot be quantified or evaluated; for example, the whims of a given head of state or the religious reaction of a given population.

4.Implicit hypotheses. These are present in any futures exercise. This aspect is of course related to the normative characteristic mentioned earlier, however, in using futures studies, it is essential to detect the implicit hypotheses.

5.A posteriori verification. A definite limit of futures studies is that it is only possible to verify the validity of a given study after the events forecast have occurred. This is often done and is an extremely useful way of learning more about the application of methods.

6.Availability of reliable data. This clearly is a crucial aspect: Any future-oriented study must be able to rely on good quantitative and qualitative data. There may, for example, be a lack of historical data on which to base a forecast or a lack of relevant ad hoc surveys. This is one of the most important limits of futures studies, for if forecasts are to be reliable, data must be rigorously evaluated.

METHODS

Before entering the debate on methods, it is important to underline the accepted typology of futures studies methods. Futures studies can be extrapolative (opportunity-oriented) or normative (mission-oriented). The definitions in parenthesis are those of Eric Jantsch (1967). In other words, to extrapolate from the past to the present and into the future constitutes one group of methods, of which projections are one. Another is to start from what is needed in the future—an image, a goal, an objective—and work backward, searching in the present for possible and probable ways of realizing it. Nowadays futures studies are never wholly

extrapolative or normative; they usually emphasize one or the other aspect, given the normative characteristic of futures studies.

SCENARIOS

The term and method were introduced by Herman Kahn during the 1960s. Nowadays scenario is a general term that is used to refer to different approaches: those of the Stanford Research Institute (SRI), of the Battelle Institute, of the studies by Michel Godet and others. A scenario can be defined as an ensemble created to describe a future situation and the sequence of events leading from the present situation to a future one.

Theoretically speaking, scenarios are a synthesis of several different hypothetical routes (events, actors, strategies) that lead to different possible futures. Practically speaking, scenarios often describe specific sets of events and variables that have been put together with the aim of focusing on causal processes and related decision-making. According to Herman Kahn (1967), scenarios answer the following basic questions: How does a situation evolve step by step from the present to the future? What are the possible alternatives that different actors in the different moments of decision making can use in order to anticipate, change, or facilitate the process?

From an epistemological point of view, scenarios are analytical and empirical constructions. They are hypotheses that do not ‘‘predict’’ the future but rather indicate a series of options and probable situations. No scenario will ever precisely anticipate the occurrence of a given event; rather it will suggest alternatives with the aim of sensitizing decision makers to what might happen. Hypotheses are never invented but are founded on a rational, consistent diagnosis of the forces that may model events. According to Michel Godet (1995), the scenario hypothesis should respond to the following five conditions. They must be: pertinent, coherent, realistic, important, and transparent.

Scenarios are instruments for better decision making. Their aim is to lower the level of uncertainty and increase the level of understanding of the consequences of actions in the present.

In looking at scenarios, one presumes an awareness on the part of the author of the rapidity and

interrelatedness of change, which will affect both decisions and the understanding of consequences, which can change a preexistent situation, either completely or in part. Scenarios are both synoptic and simultaneous: They can be used to analyze many variables at once and identify the respective turning points in terms of decision-making in steps of five, ten, or twenty years. Timing depends on the area of interest. For example, in the economic area the time span considered will be much shorter than in the educational area.

In recent years, use of the scenario technique has increased greatly, as have its applications. The scenario method seems to be particularly useful in the following situations: (1) to detect long-term trends that can help to formulate alternative within a given context; (2)to identify potential discontinuities and situations and alert organizations, countries, or regions to foresee them and thus prepare contingency plans; (3) to alert organizations, regions, or countries of possible interrelated changes as a reference for planning; (4) to provide a basis for analyzing risks as interactions between socioeconomic areas that may lead to risks and are not understandable if seen only in a specific and isolated area; (5) to evaluate the results of different strategies in different areas that may not have been developed in the awareness of interrelations.

In the public sector the best-known applications include the following. In the 1960s, Herman Kahn used scenarios connected to military and strategic studies that were developed at the RAND corporation. In the 1960s and 1970s, territorial planning by DATAR was used in France. Scenarios derived from systems analysis and global models, such as The Limits to Growth by Meadows and Meadows (1972), analyzed the global consequences of the interrelated growth of population, agricultural production, industrial development, environmental pollution, and use of natural resources. Finally, Jacques Lesourne directed an important exercise of Interfutures for the Organization for Economic Cooperation and development (OECD), which identified the alternatives of the relationships between the North and the South regions of the world.

In scenario building the private sector intervened, perhaps late, but in a sophisticated manner. Shell International Petroleum Company (Royal

Dutch/Shell Group) used scenarios before the energy crises of 1973 and before the debacle of the Soviet Union, its major competitor in the petroleum area. Other large oil companies followed Shell’s example and made extensive use of scenarios— ARGO in the late 1970s and, more recently, Pacific Gas and Electric.

In the private sector scenarios are used by enterprises in many sectors. Financial services have used scenarios to understand competitors and regulate uncertainty. Insurance companies, such as the Allied Irish Bank, have used scenarios to support strategic planning within a constantly changing context.

REFERENCES

Barbieri Masini, Eleonora 1993 Why Futures Studies?

London: Grey Seal.

———, and Javier Medina Vasquez 2000 ‘‘Scenarios as Seen From a Human and Social Perspective.’’ In

Technological Forecasting and Social Change. Amsterdam: Elsevier.

Bell, Wendell 1997 Foundations of Futures Studies 2 vols. News Brunswick, N.J.: Transaction Publishers.

Berger, Gaston 1958 L’Attitude. Paris: Presses Universitaires

de France.

Dror, Yehezkel 1974 ‘‘Futures Studies—Quo Vadis?’’ In

Human Futures, Needs—Societies—Technologies. London: IPC Science and Technology Press.

Flechteim, Ossip 1966 History and Futurology Verlag Anton Main Meisenheim, Arn Glam.

Fuchs, Josef 1977 ‘‘Morale come progettazione del futuro del’uomo’’ [Ethics as Building the Human Future]. In P. C. Beltrao, ed., Pensare il futuro (Thinking the Future). Rome: Edizioni Paoline.

Glenn, Jerome C., Gordon Theodore, Jr. 1999 State of the Future, Challenges We Face at the Millenium. American Council of United Nations Universes.

Godet, Michel 1995 ‘‘From Anticipation to Action.’’ A Book of Strategic Prospectice, Future Oriented Studies. Paris: UNESCO Publishing.

———1995 ‘‘Global Scenarios: Morphological and Probability Analysis.’’ In Scenario Building, Convergence, and Differences Profutures Workshop, Institute for Prospective Technological Studies (IPTS). European Commission Joint Research Council, 17–30.

———1995 ‘‘From Anticipation to Action: A Book of Strategic Prospective.’’ Paris: UNESCO Publishing.

———1979 The Crisis in Forecasting and the Emergence of the Prospective Approach, UNITAR. New York: Pergamon.

Hatem, Fabrice 1993 ‘‘Introduction à la prospective.’’ Paris: Gestion-Economica. 86–89.

——— 1996 ‘‘La prospective. Pratiques et méthodes.’’

Gestion-Economica. 222–232.

Irvin, J., and B. Martin, B. 1984 Foresight in Science, Picking the Winners. London: Pinter Publishers.

Jantsch, Eric 1967 Technological Forecasting in Perspective.

Paris: Ocse.

Jouvenel, Bertrand de 1967 The Art of Conjecture. New York: Basic Books.

Kahn, Herman, and Anthony Wiener 1967 The Year 2000—A Framework for Speculation in the Next 33 Years. London: Macmillan.

Malaska, Pentti 1995 ‘‘Survey of the Use of the Multiple Scenario Approach in Big European Companies Since 1973.’’ In Scenario Building, Convergence, and Differences. Profutures Workshop, Institute for Prospective Technological Studies (IPTS), European Commission Joint Research Council, 42–46.

McHale, John 1969 The Future of the Future. New York: George Braziller.

Merton, Robert K. (1938) 1973 The Sociology of Science. Chicago: University of Chicago Press.

Norse, David 1979 ‘‘Scenario Analysis in Interfutures.’’ Futures. (October):412–428.

Ozbekahn, Hasan 1970 ‘‘Verso una teoria generale della pianificazione.’’ (Towards a General Theory of Planning). Futuribili (October):25–128.

Polak, Fred 1971 Prognosis: A Science in the Making. Amsterdam: Elsevier.

——— 1973 The Image of the Future. (ed. and abridged by Elise Boulding). New York: Elsevier.

Schwartz, Peter 1996 ‘‘The Art of the Long View.’’

Planning for the Future in an Uncertain World. New York: Doubleday.

———, and Kees Van der Heijden 1996 ‘‘Culture d’entreprise et planification par scénarios: une relation de coévolution.’’ In Jacques Lesourne and Christian Stoffaes, eds., La prospective stratégique d’entreprise. Paris: Intereditions.

Wack, Peter 1985 ‘‘Scenarios: Shooting the Rapids.’’

Harvard Business Review (November/ December):139–150.

——— 1985 ‘‘Scenarios: Uncharted Waters Ahead.’’ Harvard Business Review (September/October):73–89.

Wilson, Ian 1995 ‘‘Linking Intuition and Structure: an Integrated Approach to Scenario Development.’’ In

Scenario Building, Convergence, and Differences, Profutures Workshop, Institute for Prosepctive Technological Studies (IPTS), European Commission, Joint Research Council, 31–41.

——— 1978 ‘‘Scenarios.’’ In Jib Fowles, ed., Handbook of Futures Research. Westport, Conn.: Greenwood Press.

ELEONORA BARBIERI MASINI

GAME THEORY AND STRATEGIC INTERACTION

A game is a situation that involves two or more decision makers (called players), where (1) each player faces a choice between at least two behavioral options, (2) each player strives to maximize utility (i.e., to achieve the greatest payoff possible), and (3) the payoff obtained by a given player depends not only on the option that he or she chooses but also on the option(s) chosen by the other player(s). In virtually all games, some or all of the players have fully or partially opposing interests; this causes the behavior of players to be proactive and strategic.

The theory of games is a branch of applied mathematics that rigorously treats the topic of optimal behavior in two-person and n-person games. Its origins go back at least to 1710, when the German mathematician-philosopher Leibniz foresaw the need for a theory of games of strategy. Soon afterward, James Waldegrave (in Montmort 1713; 1980) formulated the concept of maximin, a decision criterion important to game theory. In his book Mathematical Psychics, Edgeworth (1881; 1995) made explicit the similarity between economic processes and games of strategy. Later, theorists such as Zermelo (1913) stated specialized propositions for certain games (e.g., chess). Not until the work of Borel ([1921–1927] 1953) and von Neumann (1928), however, did the foundations of a true theory of games appear. A landmark of the modern era, von Neumann and Morgenstern’s

Theory of Games and Economic Behavior (1944), extended game theory to problems involving more

than two players. Luce and Raiffa (1957) published the first widely used textbook in game theory. For more details regarding the early history of game theory, see Dimand and Dimand (1996) and Weintraub (1992).

Game theory has continued to develop substantially in recent years. Many introductory presentations of the modern mathematical theory are available. Among these are Friedman (1990), Jones (1980), Myerson (1991), Owen (1982), Romp (1997), and Szep and Forgo (1985).

Beyond its status as a branch of applied mathematics, game theory serves social scientists as a tool for studying situations and institutions with multiple decision makers. Some of these investigations are empirical, while others are primarily analytic in character. The dependent variables of central concern in games include allocation of payoffs (i.e., who receives what rewards or bears what costs) and formation of coalitions (i.e., which of various possible alliances among players occur in a game.) Other concerns include whether outcomes of a game are stable or not, whether outcomes are collectively efficient or not, and whether outcomes are fair or not in some specific sense.

GAME-THEORETIC CONCEPTS

Mathematical game theory provides three main tools that assist in the analysis of multiperson decision problems. These include a descriptive framework, a typology of games, and a variety of solution concepts.

Descriptive Framework. At base, a description of any game requires a list of all players, the strategies available to each player, the logically possible outcomes in the game, and the payoff of each outcome to each player. In some instances, a game’s description also includes a specification of the dynamic sequence of play and of the (possibly limited or incomplete) information sets available to players. Payoffs in a game are expressed in terms of utility; this provides a standard means of comparing otherwise diverse outcomes.

An analyst can model or represent a game in various forms. Extensive form depicts all possible strategies of players in a tree format. It is especially useful for modeling games in which play occurs in stages or over time. Strategic form (also called normal form or a ‘‘payoff matrix’’) shows payoffs to players as a function of all strategy combinations.

Characteristic function form lists the minimum payoffs assured for each of the coalitions in a game. Whereas extensive and normal forms pertain to virtually all types of games, characteristic function form pertains only to cooperative games (i.e., games that permit coalitions).

Typology of Games. The second tool from game theory is a general typology of games. This provides a means of codifying or classifying games vis-à-vis one another. At base, there are four major types of games. Games can be either static (i.e., single time period) or dynamic (multiple time periods), and they can involve either complete information (all relevant information is shared and held in common) or incomplete information (some information is private and held only by some players). Much of classic game theory was formulated with reference to static games involving complete information; more recent developments have extended the theory to dynamic games and also to games involving incomplete information.

Games can be two-person or n-person (more than two players), and they can be further classified as cooperative or noncooperative. Cooperative games permit players to communicate before reaching decisions and include some mechanism that enables players to make binding agreements regarding coordination of strategies. Noncooperative games do not permit players to communicate or to form binding agreements prior to play. In other words, cooperative games enable players to form coalitions whereas noncooperative games do not.

Among cooperative games, some are sidepayment games while others are nonsidepayment games. Sidepayment games permit players to transfer payoffs (utility) within coalitions; nonsidepayment games do not. A further distinction applicable to cooperative sidepayment games is that between simple games and nonsimple games. Simple games are those in which the characteristic function assumes only two values, whereas nonsimple games are those in which the characteristic function has more than two values. Analysts use simple games primarily to model social processes with binary outcomes (e.g., win–lose, succeed–fail, etc.)

Solution Concepts. The third set of tools provided by game theory is a variety of solution concepts. A solution concept is theory of equilibrium that predicts (behaviorally) or prescribes (normatively) the allocation of payoffs to players in games. In other words, a solution concept specifies how a game will turn out when played. For this reason, solution concepts are among the most important contributions of game theory.

Game theorists have developed numerous solution concepts. These differ not only in the underlying assumptions but also in the predictions they make. For static noncooperative games, the most prominent solution is the Nash equilibrium (Nash 1951); there are many extensions of this concept (summarized in van Damme 1987). Other approaches to the solution of noncooperative games are those of Harsanyi and Selten (1988) and Fraser and Hipel (1984).

For static cooperative games, there are several classes of solution concepts. One prominent class consists of solutions that predict outcomes which are collectively rational (i.e., imputations). Included in this class are the core (Aumann 1961; Gillies 1959), the Shapley value (Shapley 1953), and the nucleolus (Schmeidler 1969). Other solutions in this class are the disruption nucleolus (Gately 1974; Littlechild and Vaidya 1976), the disruption value (Charnes et al. 1978), the p-center solution (Spinetto 1974), and the aspiration solution (Bennett 1983). Another class of solutions for cooperative games includes concepts that make payoff predictions contingent upon the coalition structures that form during play; these payoff allocations are usually coalitionally rational. Included are the M1(i) bargaining set (Aumann and Dreze 1974; Aumann and Maschler 1964), the competitive bargaining

set (Horowitz 1973), the kernel (Davis and Maschler 1965), the Myerson–Shapley solution (Aumann and Myerson 1988; Myerson 1977), the equal division kernel (Crott and Albers 1981), and the alphapower solution (Rapoport and Kahan 1982). Recently, a third class of solutions has emerged for cooperative games. Solutions in this class attempt not only to determine endogenously which coalition structure(s) will emerge but also to specify the associated payoffs to players. One solution in this class is the central-union theory (Michener and Au 1994; Michener and Myers 1998), which predicts coalition formation probabilistically. Another solution in this class is the viable proposals theory (Sengupta and Sengupta 1994).

EXPERIMENTAL STUDIES OF GAMES

Laboratory experimentation on two-person and n- person games commenced in the early 1950s (e.g., Flood 1952) and it continues to the present. Some gaming studies are primarily descriptive in nature, whereas others investigate the predictive accuracy of various solution concepts.

Experiments of Two-Person Games. Investigators have conducted literally thousands of experiments on two-person games. Most of these treat noncooperative games, although some do treat cooperative games in various forms. Some studies investigate constant-sum games, whereas others treat non-constant-sum games (primarily such archetypal games as the prisoner’s dilemma, chicken, battle of the sexes, etc.).

The major dependent variables in the twoperson studies are the strategies used by players (particularly the frequency of cooperative choices) and the payoffs received by players. Independent variables include the type of game, strategy of the confederate, information set, interpersonal attitudes of players, sex of players, motivational orientation of players, and magnitude and form of payoffs.

Some of this research seeks to understand how differences in game matrices affect play (Harris 1972; Rapoport et al. 1976). Another portion describes how players’ strategies vary as a function of the confederate’s strategy (i.e., partner’s history of play over time); this is reviewed in Oskamp (1971). Another portion of this work investigates

the extent to which predictions from the minimax theorem approximate observed payoffs in con- stant-sum games; Colman (1982, ch. 5) reviewed these findings. Still other work covers cooperative bargaining models; Roth (1995) reviewed research on bargaining experiments. Some experimentation on two-person games has addressed the impact of players’ value orientation on cooperation (McClintock and Liebrand 1988; Van Lange and Liebrand 1991). General reviews of experimental research on two-person games appear in Colman (1982), Komorita and Parks (1995), and Pruitt and Kimmel (1977).

Experiments of n-Person Noncooperative Games. There are several lines of experimentation on n-person noncooperative games. One line investigates multiperson compound games derived from 2 × 2 matrices (e.g., n-person chicken, n- person battle of the sexes, etc.). Important among these is the n-person dilemma (NPD) game, wherein individually rational strategies produce outcomes that are not collectively rational. The NPD serves as an abstract model of many phenomena, including conservation of scarce natural resources, voluntary wage restraint, and situations involving the tragedy of the commons (Hardin 1968; Hartwick and Yeung 1997; Moulin and Watts 1997). The literature contains many experimental studies of the NPD and other social dilemmas (e.g., Liebrand et al. 1992; Rapoport 1988). In addition to varying the payoff matrix itself, studies of this type investigate the effects of such factors as group identity, self-efficacy, perceptions of other players, value orientation, uncertainty, and players’ expectations of cooperation. Reviews of research on NPDs and similar games appear in Dawes (1980), Kollock (1998), Komorita and Parks (1999), Liebrand and colleagues (1992), Liebrand and Messick (1996), and Messick and Brewer (1983).

A related line of research is that by experimental economists on markets and auctions (Smith 1982). This work investigates market structures (such as competitive exchange, oligopoly, and auction bidding) in laboratory settings (Friedman and Hoggatt 1980; Plott and Sunder 1982). Many of these structures can be viewed as noncooperative games. Plott (1982) provides a review of studies investigating equilibrium solutions of markets— the competitive equilibrium, the Cournot model, and the monopoly (joint maximization) model.

There is an increasingly large experimental literature on auctions, some of which is gametheoretic in character. Since auctions usually entail incomplete information (buyers have private information about their willingness to pay and ability to pay), these studies investigate the effects on bidding behavior of such variables as differential information, asymmetric beliefs, and risk aversion. They also investigate different institutional forms, such as English auctions, Dutch auctions, double auctions, and sealed bid–offer auctions (e.g., Cox et al. 1984; Smith et al. 1982). Reviews of the theoretical literature on auctions appear in Engelbrecht-Wiggans (1980), Laffont (1997), and McAfee and McMillan (1987). Kagel (1995) provides a survey of experimental research on auctions.

Experiments of n-Person Weighted Majority Games. Weighted majority games are an important subclass of cooperative, sidepayment, simple games. They serve as models of legislative or voting systems. Theorists have developed many special solution concepts for these games. Early theories applicable to weighted majority games are the minimum power theory and minimum resource theory (Gamson 1961). Riker’s size principle predicts the formation of minimal winning coalitions in these games. Other theories for weighted majority games include the bargaining theory (Komorita and Chertkoff 1973; Kravitz 1986) and the equal excess model (Komorita 1979). The bargaining theory posits that players in a coalition will divide payoffs in a manner midway between equality and proportionality to resources (votes) contributed. The equal excess model is similar but uses the equal excess norm instead of proportionality.

Numerous experiments on coalition bargaining in weighted majority games have tested these and related theories (e.g., Cole et al. 1995; Komorita et al. 1989; Miller and Komorita 1986). Results of these studies generally support the bargaining theory and the equal excess model over the others, although all have deficiencies. Reviews of some experiments in this line appear in Komorita (1984) and Komorita and Kravitz (1983).

Experiments of Other n-Person Cooperative Games. Beyond NPD and weighted majority games, investigators have studied a wide variety of n- person cooperative games in other forms. The primary objective of the work is to discover which

game-theoretic solution concepts predict most accurately the outcomes of these games.

Numerous studies have investigated cooperative sidepayment games in characteristic function form (e.g., Michener et al. 1986; Murnighan and Roth 1980; Rappaport 1990). Other studies have investigated similar games in strategic form. This work shows that in games with empty core, solution concepts such as the nucleolus and the kernel predict fairly well; in games with a nonempty core, however, the Shapley value is often more accurate. Reviews of parts of this research appear in Kahan and Rapoport (1984), Michener and Potter (1981), and Murnighan (1978).

Other studies have investigated cooperative nonsidepayment games. Some of this research pertains to bargaining models in sequential games of status (Friend et al. 1977). Other research tests various solution concepts (such as the core and the lambda transfer value) in nonsidepayment games in strategic form (McKelvey and Ordeshook 1982; Michener et al. 1985; Michener and Salzer 1989).

Another line of experimentation on cooperative nonsidepayment games is that conducted by political scientists interested in committee games or spatial voting games. These are n-person voting games in which policies are represented as positions in multidimensional space. For the most part, this research attempts to test predictions from alternative solution concepts (Ferejohn et al. 1980; Ordeshook and Winer 1980). Some of this work has led to new theories, such as the competitive solution (McKelvey and Ordeshook 1983; McKelvey et al. 1978), and to further developments regarding established ones, such as methods for computing the Copeland winner (Grofman et al. 1987). Experimental research on spatial games is reviewed in McKelvey and Ordeshook (1990).

DYNAMIC GAMES

Although early developments in game theory centered primarily on static games (i.e., games in which interaction among players is single-period or single-play in nature), many subsequent developments have addressed dynamic games occurring over time. In a dynamic game, time (or stage) is an important consideration in strategy, and the choices and actions of players at any stage are conditional on the history of prior choices in the game. There

is a growing theoretical literature on various classes of dynamic games, including repeated games, differential games, and evolutionary games. Introductions to the topic of dynamic games appear in Friedman (1990), Fudenberg and Tirole (1991), Owen (1982), and Thomas (1984). The empirical literature on dynamic games is still small relative to that on static games, although experimental studies of repeated games appear increasingly often.

The term supergame refers to a sequence of (ordinary) games played by a fixed set of players. One important type of supergame is the repeated game, wherein the same constituent game is played at each stage in the sequence. For instance, if some players play a prisoner’s dilemma game again and again, they are engaging in a repeated game. At this point in historical time, the dominant paradigm for the study of dynamic strategic behavior is that of repeated games. Certain repeated games are of interest because they allow collectively rational outcomes to result from noncooperative equilibrium strategies. Axelrod (1984) has analyzed the development of cooperation in repeated games. Selten and Stoecker (1983) have used a learning theory approach to model end-game behavior of players in repeated prisoner’s dilemma games. Aumann and Maschler (1995) have studied repeated games with incomplete information. A survey of literature on repeated games appears in Mertens and colleagues (1994a,b,c).

Theorists have developed various solution concepts applicable to repeated games and multistage games. Among these are the backward induction process, the subgame perfect equilibrium (Selten 1975), and the Pareto perfect equilibrium (Bernheim et al. 1987). Cronshaw (1997) describes computational techniques for finding all equilibria in infinitely repeated games with discounting and perfect monitoring.

Another class of dynamic games is the differential game, played in continuous time. Much of the literature on differential games focuses on the two-person zero-sum case. Some applications of differential games are military, such as pursuit games, where the goal of, say, a pursing aircraft is to minimize time or distance required to catch an evading aircraft (Hajek 1975). The classic works on differential games include Friedman (1971) and Isaacs (1965). Models of differential games with more than two players are discussed in Leitman

(1974). Other useful works on differential games include Basar and Bernard (1989) and Lewin (1994). The vector-valued maximin for these games is discussed in Zhukovskiy and Salukvadze (1994).

Biologists and economists have used game theoretic concepts to study evolutionary games, which are dynamic models of social evolution that explain why certain inherited traits (i.e., behavioral patterns) arise in a human or animal population and remain stable over time. In some evolutionary games (especially those with animal populations), the individuals are modeled as having neither rationality, nor conscience, nor expectations, so strategy selection and equilibrium derive from behavioral phenotypes rather than from rational thought processes. Models of this type often incorporate such phenomena as mutation, acquisition (learning), and the consequences of random perturbations. Theorists have advanced various concepts of evolutionary stability and evolutionarily stable strategies (Amir and Berninghaus 1998; Bomze and Potscher 1989; Gardner et al. 1987; Maynard Smith 1982). Summaries and extensions of work on evolutionary games appear in Bomze (1996), Friedman (1991, 1998), Samuelson (1997), and Weibull (1995).

INSTITUTIONAL ANALYSIS VIA GAME

THEORY

Economists and political scientists have long used game theory in the analysis of social institutions. In work of this type, an analyst specifies an institution (such as a Cournot oligopoly or an approval voting system) in hypothetical or ideal-typical terms and then applies game-theoretic solution concepts to see which payoff allocation(s) may result at equilibrium. Through this approach, an analyst can compare the outcomes of alternative institutional forms with respect to stability, efficiency, and fairness. Broad discussions and reviews of this literature appear in Schotter (1981, 1994), Schotter and Schwodiauer (1980), and Shubik (1982, 1984).

Economic Institutions. Von Neumann and Morgenstern (1944) were among the first to explore the role of n-person game theory in economic analysis. Since that time, economists have analyzed a variety of institutions in game-theoretic terms, including oligopoly and other imperfect markets. Markets in which there are only a few sellers