FormalPara Definition

Both words in the term ‘game theory’ are unfortunate descriptors. ‘Game’ implies playfulness; ‘theory’ implies a single organizing idea. Yet game theory addresses matters as weighty as international nuclear strategy (e.g., Poundstone 1992), global environmental concerns and world economic issues. Moreover, it is not a singular theory. Instead, its models consider a variety of structural conflicts, ranging from cooperative to non-cooperative, two- to n-party, complete to incomplete information, and static to dynamic.

The ‘game’ in game theory refers to strategic interactions in which parties’ outcomes are interdependent (Rapoport 1973). Depending on the definition, game theory is the study of (1) the problem of exchange (von Neumann and Morgenstern 1944), (2) decisions in conflict situations (Rapoport 1973), (3) how players make decisions that affect each other (Hamburger 1979), (4) the interaction of rational decision makers (Myerson 1991) or (5) multi-person decision problems (Gibbons 1992). ‘The essence of a “game” … is that it involves decision makers with different goals or objectives whose fates are intertwined,’ writes Shubik (1964: 8).

Since issues of exchange, conflict and interdependence are pervasive in organizational and social life, game theory’s domain might appear universal. Game theory’s potential applicability is indeed farreaching, but it restricts its analytic approach considerably.

Game theory has developed two overlapping domains. Its first, original domain is strictly theoretical. A game theorist makes assumptions, considers their logical consequences and proves theorems which, given the assumptions, are true. Theoretical game theory uses applied mathematics and economic logic to analyse the interplay of informed, calculating actors via formal, analytic theoretical models; it is precise and clean. Like the physical sciences, it investigates human interaction as if in a vacuum, and its greatest successes produce truly beautiful, elegant models.

Game theory’s second domain concerns the application of its principles to actual human behaviour. Here, its theoretical assumptions cannot be completely fulfilled, and its hypotheses and propositions, like those of other social sciences, can only be investigated probabilistically. The messy realities of everyday interactions make this domain (and most other social scientific endeavours) problematic.

The confusion created by game theory’s two domains has often led to inappropriate criticisms. For example, Raiffa (1982: 21) writes, ‘Game theorists examine what ultrasmart, impeccably rational, super-people should do in competitive, interactive situations.’ Although it is true that game theory may not describe the behaviour of the general public, its attention to sophisticated, strategic actors and its attempts to accommodate non-equilibrium behaviour are arguably more informative than the study of mundane actors.

Game theory is a complex, dynamic elaboration of decision theory. It might be called ‘the theory of interdependent decision-making’, as it investigates the interdependent interaction of rational decision makers. And, like decision theory, it can enrich the study of organizations (e.g., Bazerman 1990).

Game theory’s original goals were to analyse interactions by highly strategic parties who are acting in their own best interests. More recently, it has expanded its goals towards the general analysis of potentially conflictual interactions. Applicability was neither its original theoretical intent nor its current state of empirical sophistication. Instead, theoretical game theory restricts its analysis to tractable (quantifiable, economic) interactions among parties who can formulate appropriate and sometimes intricate strategies. We know from a wealth of research on decision-making (e.g., Dawes 1988; Bazerman 1990) that these strategies can be beyond the scope of most human intelligence. But, as Raiffa (1982) and others have persuasively demonstrated, understanding game theory’s intricacies allows researchers to understand when and why people depart from its prescriptions. Its strong theory provides potent tools for advancing our research on and understandings of conflict and power.

Assumptions and Basic Concepts

Game theory expects that people will act in their own best interests. Many game-theoretic models also assume that the parties’ choices of actions and outcomes can be unambiguously defined; that the consequences of their joint choices can be precisely specified; and that choosers have distinct, clear and consistent preferences. Game theory seeks equilibrium outcomes in which none of the parties are motivated to unilaterally change their strategic choices.

Although its assumptions may require a pristine theoretical environment, the realm of game theory sounds much like the domain of organizational politics. Among game theory’s advantages for the study of organizational strategy are its ability to provide a formal structure for analysing competitive interactions via strong theoretical prescriptions.

Pareto optimality (or Pareto efficiency), for example, is an old game-theoretic concept. Decades before game theory existed, an Italian philosopher defined Pareto optimality as the final outcome of an interaction that would not allow one party to improve its outcome without reducing another party’s outcomes. Thus, when two firms negotiate, they should achieve an agreement on the Pareto frontier (see Fig. 1), jointly attaining as much as they can from their interaction. If they fall short of the Pareto frontier, they can both improve by moving towards the frontier.

Game Theory, Fig. 1
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The Pareto frontier. The solid line in this figure depicts the Pareto frontier – a set of outcomes that cannot be improved upon for one player without leading to a loss for the other. Note that player 1 can do better if they move from A to B but this would cost player 2. Player 1 and player 2 can do better if they move from A to C. They can also both do better than A any time player 1 gets more than 1.5 and player 2 gets more than 2.3 – which is not only possible but far more efficient than settling at a non-Pareto outcome, A

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Although this seems to be a simple notion, it’s very powerful. Von Neumann and Morgenstern’s (1944) original formulation of game theory was motivated, at least in part, by the search for optimal (rather than simply satisficing) strategies (e.g., Simon 1947). Early research by Siegel and Fouraker (1960) found that, over time and with feedback, people moved towards Pareto-optimal outcomes in bilateral monopoly negotiations (one seller versus one buyer, with neither having any other options).

A second basic concept in game theory is the Nash equilibrium. If the analysis of an upcoming interaction indicates that two of the many possible strategies are each party’s best response to each other, the combination of these strategies is a Nash equilibrium. For rational players, discovering these strategies completes the game, for neither will be motivated to change. If one party does not discover its predicted Nash equilibrium strategy, then feedback should lead it to change its strategy to increase its outcomes. Thus, even if both parties do not have the mathematical or analytical ability to calculate their Nash equilibrium strategy, they may still discover it over repeated play by seeking to better their own outcomes. This often happens in primitive biological systems (e.g., Smith 1978).

The logic of Pareto optimality and Nash equilibrium strategies can be roughly but easily translated into the language of strategy: (1) get as much as you can out of a deal, and (2) find the best response to your opponent’s action. Pareto optimality and a Nash equilibrium both express these maxims cleanly and clearly, so there can be little confusion about their exact meaning. Herein lies their beauty and their power.

Consider another example, one where a game-theoretic solution may be surprising. In the original ‘Battle of the Sexes’ game, a man and a woman must decide what they will do on their only evening together. They prefer to go out together rather than separately, but each person’s preference as to where to go is the opposite of the other’s.

If these issues are transferred to the case of two competing organizations, the conflict might concern the format of a new product and whether the two companies will standardize to one another’s format or compete not only on products but on format. Among the three most prominent options, Company #1 prefers option A to option B to option C, and Company #2 prefers option C to option B to option A. Both companies know that they can compromise on option B, and, in fact, this would lead to the greatest growth in the product’s overall market. This would also satisfy cooperative social norms and be in the customers’ and maybe even both companies’ shareholders’ best interests.

But if Company #1 is ready to go to market before Company #2, it can make a strong competitive move by selecting option A. Company #2 may have realized that it was behind and, as a result, invested in developing option B or option C. Its best option in terms of profits, however, may be to follow the lead of Company #1, even if this relegates it to second place in terms of market share. Thus, game theory suggests that, in this context, being the first mover can give one company an almost unassailable advantage if it acts individualistically. This choice may not, however, engender future cooperation within this industry.

Limitations

Game theory has suffered a number of spectacular failures in predicting people’s behaviour (even though doing so was never its original intent). For instance, John von Neumann, the father of game theory, advised the leaders of the United States to use the atom bomb as soon as it was developed. According to Poundstone (1992), his recommendation came from his analysis of the prisoner’s dilemma game: since both sides have an incentive to defect that is independent of their expectations of the other side’s actions, it is important to be the first defector, especially when the payoffs are so severe. In essence, he expected that, if the United States did not drop the bomb first, its competitor would. That a nuclear war has not transpired (and that people often cooperate in finite Prisoner’s Dilemma games, experiments and real-world analogues) is one of game theory’s major predictive failures.

Another failure was the early analysis of monopoly and veto games (where one powerful party needs either no partner to make a decision or cannot be excluded from a group’s final decision). Game theory predicts that the monopolist or veto player will reap all of a game’s possible benefits. This rarely happens. As Rapoport (1973) notes, even in the business world, such extremely cold-blooded competitiveness almost never occurs. Experimental research (e.g., Murnighan 1985) has also shown that factors such as meeting face to face severely depress monopolists’ and veto players’ outcomes. But while these predictions failed, subsequent models (e.g., Shapley and Shubik 1954; Roth 1987) made much more accurate predictions (Murnighan and Roth 1980).

Game theorists have recently been incorporating more socially relevant factors, including uncertainty, into their models, such as the unexpected cooperation so frequently observed in Prisoner’s Dilemma games, thus increasing their predictive ability. Kreps and colleagues (1982), for instance, showed that, with some uncertainty about an opponent’s strategy (i.e., he or she may or may not value cooperation) or whether defecting provides an opponent with higher short-run payoffs than cooperation, cooperative choices may be expected theoretically (at least until the endgame). At the same time, it seems clear that a host of social factors, including myopia, altruism and social norms, lead people to choose much more cooperatively than game theory predicts.

In contrast, Camerer’s (1991) argument for the usefulness of game theory in the field of strategic management suggested that most business strategy decisions fit within the broader scope of game theory and that researchers who have derided game theory have not rejected an old version of the beast as long outdated. Dynamics, communication and differential perceptions of the game are now part of game-theoretic investigations, making it much more applicable to research in organizational behaviour and strategy.

Although game theory uses assumptions of rationality to generate equilibrium solutions to conflictual interactions, many models do not require much rationality. Even when they do, communication, adaptation and/or evolutionary processes can lead to equilibria; rational decision-making is not the only path to ‘rational’ actions. Camerer (1991) refers to game-theoretic reasoning ‘as a mathematical shortcut’ that theorists use to determine what intelligent, adaptive players will do.

Game theory’s theoretical domain is neither descriptive nor normative: it neither describes everyday people’s actions nor does it tell them what to do. Instead, it’s analytic: ‘game theorists analyze the formal implications of various levels of mutual rationality in strategic situations’ (Aumann 1991: 6). Theoretical game theory analyses limited problems in specifically bounded domains and solves them mathematically. Its emphasis on the strategic makes game theory a natural choice for testable applications in strategy research.

Finally, game-theoretic models now incorporate the findings and observations reported in recent empirical work, particularly experimental economics. As Rubinstein (1991: 912) suggests, ‘If games exist only in the mind of a player, the minds of players are a useful place for an empiricist to be.’ Thus, reiterating Reger (1992), the combination of game theory and social cognition holds considerable research promise.

See Also