Group Decision and Negotiation, 6:511–528 (1997) © 1997 Kluwer Academic Publishers
Game-theoretic and Behavioral Negotiation Theory KJELL HAUSKEN The University of Chicago, 1126 E. 59th St., Chicago, IL 60637
Abstract This article evaluates the state of the art and provides an interdisciplinary framework for game-theoretic and behavioral negotiation theory. The former is based on concepts like extensive form, payoff and information structure, and equilibrium concepts. The latter has a foundation in psychology, organization theory, sociology, and related fields. The objectives of the article are to build upon recent advances in both game-theoretic and behavioral negotiation theory, bring the disciplines closer together, and generate a foundation for future research in interdisciplinary negotiation theory. The article develops two interdisciplinary frameworks for game-theoretic and behavioral negotiation theory. Implications of the frameworks are discussed to illustrate their applicability and superiority over earlier frameworks. Key words: negotiation, bargaining, game theory, behavioral theory, strategy, psychology, interdisciplinary framework
1. Introduction This article describes the state of the art of game-theoretic (strategic) and behavioral negotiation theory. Two interdisciplinary frameworks for game-theoretic and behavioral negotiation theory are developed. The objectives are to build upon recent advances in both disciplines, bring them closer together, and generate a foundation for future research in interdisciplinary negotiation theory. Section 2 describes current strategic, or game-theoretic, negotiation theory, to give the reader a general overview of the substance of what is current in the field. Twenty-three representative models are presented, and five classes of suggestions are listed for how strategic negotiation theory can be further developed. Section 3 presents what is possibly the best interdisciplinary framework for behavioral negotiation theory available in today’s literature, developed by Neale and Northcraft (1991). The framework incorporates recent research in behavioral negotiation theory, attempts to incorporate game theory, and is labelled integrative. I present four kinds of critique against Neale and Northcraft’s (1991) model, mainly related to their use of a too old and static conception of game theory. Section 4 incorporates the recent advances in strategic negotiation theory, as described in Section 2, to improve Neale and Northcraft’s (1991) model. Two frameworks are developed, embodying recent advances in both strategic and behavioral negotiation theory. The first framework presents negotiation theory as it might typically be conceptualized by
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an organizational behaviorist. The second framework presents negotiation theory as it might be conceptualized by a game theoretician. Section 5 discusses implications of the frameworks, and illustrates their applicability and superiority over earlier frameworks. The objective is to show how game-theoretic and behavioral ideas mutually reinforce each other and contribute to interdisciplinary research designs, which are more representative and adequate in that they combine explanatory factors from different schools of thought in a greater variety of ways.
2. Current status of strategic negotiation theory The bargaining problem was first presented by Edgeworth (1881), who described the set of individually rational Pareto optimal agreements. Gradually emerging since the late 1920s, an early presentation of game theory was made by von Neumann and Morgenstern (1944). Game theory has since then been used in a variety of disciplines. One of them is strategic negotiation theory, where time-strategic, institutional, informational, and commitment aspects are crucial. Game theory allows for analyzing foundational features that are relatively culture independent, assuming self-interest. Proponents typically argue that it disciplines analytical thinking. Strategic negotiation theory has a combined focus on equilibrium and efficiency. Dating back to the Fundamental Welfare Theorems by Arrow and Debreu (1954) and Debreu (1959), there has been a focus on comparing equilibrium behavior with efficient behavior. Hence while, e.g., Chatterjee and Samuelson (1983) and Cramton (1992) derive equilibrium behavior, Holmstrom and Myerson (1983) among others concentrate more on efficient behavior. Combining the two approaches, Satterthwaite and Williams (1989), e.g., focus on efficient equilibrium behavior. Further developing this combined concept, Gresik (1995) provides a full characterization of efficient equilibria arising from the use of sealed-bid arbitration rules. Given this focus on efficiency in addition to equilibrium, some argue that “the potential welfare gains from improving the efficiency of bargaining outcomes are enormous, perhaps even greater than those that would result from a better understanding of the effects of macroeconomic policy” (Crawford 1982, p. 607). Inspired by von Neumann and Morgenstern (1944), Nash (1950, 1951, 1953) suggested two approaches for solving the bargaining problem: one axiomatic and one strategic. The axiomatic approach poses a number of “beneficial” axioms implying a unique solution, and has been dominant within the bargaining literature until about 1980. The approach is mainly macro-oriented, and is sometimes called cooperative theory since the actors are allowed to make binding agreements with each other. The strategic approach focuses on actors’ choices of strategies in a noncooperative game modeling the bargaining process over time. The breakthrough for strategic theory came with Rubinstein (1982), who analyzed alternating offers by two actors discounting utility over time. Some attempts have been made to combine the strategic and axiomatic approaches. One example is the work of Myerson (1979, 1984, 1985), who presented his revelation principle and developed the term mechanism design or Nash program for the analysis of the set of all bargaining solutions which can be realized as an equilibrium in a strategic bargaining process.
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Much of strategic negotiation theory with incomplete information is based on the Harsanyi (1967/1968) doctrine (his type theory). Harsanyi (1967/1968) assumed that each player appears to his opponent as an unknown type drawn from a known probability distribution of possible types. This has proven to be a somewhat successful way of formalizing games with incomplete information, because it avoids infinite reasoning chains of the kind “if I think that you think that I think that…” Chatterjee and Samuelson (1983) were the first to apply Harsanyi’s (1967/1968) type concept in a static bargaining model, considering seller’s and buyer’s reservation prices as unknown knowledge. One alternative is to consider the opponent’s discount factor as the unknown knowledge (Rubinstein 1985a). In the spirit of Selten’s (1975) perfectness criteria for equilibria of extensive form games, Kreps and Wilson (1982) developed the sequential equilibrium concept for games with incomplete information. Strategic negotiation theory as developed since 1982 rests heavily on the Harsanyi (1967/1968) doctrine and Kreps and Wilson’s (1982) sequential equilibrium concept. As negotiations proceed through time, and each player, engaged in sequential equilibrium behavior, gets to know more about his opponent, the probability distribution he has formulated over his opponent’s type gets updated according to one acknowledged rule of statistical inference, Bayesian updating. The interplay between the strategic and axiomatic theories has contributed to an interesting development. The basic structure of twenty-three of the most representative articles in this development is given in Figure 1.
Figure 1. Strategic negotiation models with incomplete information.
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Generalizing, we can develop the following set of characteristics, pertaining to extensive form, payoff structure, information structure, and equilibrium concepts, generating the kinds of models specified in Figure 1: 1. Regarding offers: If only one actor is allowed to bid, • are all kinds of bids possible? • bids with constant/variable time intervals? • response from opponent instantaneously or after time delay? • new bid possible during waiting time? • can bids be retrieved, revised, or rescinded? • can an actor choose to accept an earlier bid? If both actors are allowed to bid, the following must be specified: • can any player make the first offer? • are the players to bid alternately? • can any player bid/accept at any point in time? 2. Time horizon; e.g., static, two or a finite number of periods, an infinite number of periods, continuous infinite time horizon. 3. One- or two-sided incomplete information. How is this uncertainty formalized (e.g., reservation price, discount factor)? Continuous or discrete probability distributions? Are these common knowledge? 4. Utility function: • cardinal/ordinal? • are interpersonal comparisons of utility possible? Does the utility function say anything about • time preference (e.g., discount factor, constant cost/time)? • attitude towards risk (neutral, averse, seeking)? • interpretation of status quo point? 5. With several buyers/sellers, a high number of additional assumptions are required, e.g., regarding whether any player can change partner at any point in time (matching process?), learning as the game proceeds, reputation transmission, switching costs, etc.
3. Critique of a behavioral framework for negotiation theory Behavioral negotiation theory has a strong root in psychology, organization theory, sociology, and related fields. Within this tradition “box frameworks” seem most amenable for incorporation of or reconciliation with strategic or game-theoretic negotiation theory. One such framework developed by Neale and Northcraft (1991) is presented in Figure 2. Neale and Northcraft (1991, p. 148) find it unfortunate that most negotiation scholars have been bound by a particular discipline and research tradition. They therefore set out “to summarize a series of research perspectives to identify what is known about the nature
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Figure 2. Framework for behavioral negotiation theory.
of two-party bargaining or negotiation and develop a framework for future research in the area.” Their framework categorizes this research into two streams; one concerning contextual characteristics, and the other concerning negotiators’ cognitions and interaction processes. The major part of Neale and Northcraft’s (1991) article involves explaining each concept and parameter in Figure 2. Aside from some considerations of the interaction between static and dynamic factors, and a few suggestions for future research, the reader is given little detail demonstrating the benefits of the framework, how it is superior to earlier frameworks, and how it can be used in empirical research, negotiation experiments, data gathering about negotiations, and hypotheses construction and further theory building. The particular conception of game theory in Figure 2 seems chosen to underline and highlight those specific characteristics of behavioral negotiation theory that represent this latter theory’s strength. More specifically, Figure 2 ignores what has happened within game theory over the last three decades. This section describes Neale and Northcraft’s (1991) framework, and directs four kinds of critique against it. Associated with their static conception of game theory, Neale and Northcraft (1991) consider power (French and Raven 1959; Pfeffer, 1981), deadlines (time pressure reduces levels of demands, aspirations, bluffing), and integrative potential (differential value assessment, nonconstant sum games; Thomas 1976). Neale and Northcraft (1991) also present a static conception of agency theory, as this pertains to constituencies and third parties, rather than drawing upon the dynamic approaches emerging in today’s literature (Tirole 1988; Holmstrom and Milgrom 1987; Holmstrom and Myerson 1983). Regarding negotiator interaction processes, Neale and Northcraft (1991) first consider influence tactics. Examples of these are French and Raven’s (1959) five power bases (rewards, coercion, expertise, legitimacy, charisma) to which we today commonly add information power and connection power, and Kipnis and Schmidt’s (1983) persuasive
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tactics (assertion, rational argument, manipulation). Neale and Northcraft (1991) secondly consider communication tactics, noting for example that successful negotiators make more offers and stick to them, and that the appearance of fairness may be at least as important as being fair. It is occasionally argued that these fluid aspects are more suitably described in psychological than in mathematical language. However, the psychological aspects are of course also incorporated into and thus lie hidden in the mathematical parameters, either in the dynamic structure of the extensive form, in the time discount factors and payoff structure (preferences), or in the subjective probability distributions over reservation prices (beliefs). Neale and Northcraft (1991) consider four classes of negotiator cognitions: planning, information processing, affect, and individual differences. Planning is a major method for identifying systematic mechanisms for developing and identifying negotiation strategies. Thus one studies strategic elements, interactive nature, and the nature of revisions of plans. Information processing may be biased by framing, anchoring and adjustment, availability, overconfidence, reactive devaluation. Affect is a more “hot” cognitive process, influential through need-based illusions or dual concern. Individual differences describe whether negotiators are endowed with such traits as Machiavellianism or perspectivetaking ability. Let me direct four kinds of critique against Neale and Northcraft’s (1991) framework. First, Neale and Northcraft (1991, p. 150) note that “game theory has little to do with observed choice behaviors.” This has to do with choice of research perspective. As Raiffa (1982, p. 21) puts it, game theory chooses a “symmetrically prescriptive” approach. Game theory typically assumes rationality in the sense that behavior is consistent with the maximization of subjective expected von Neumann–Morgenstern (1944) cardinal utility, and intelligent actors, in the sense that every actor understands everything about the structure of the situation, including the fact that others are intelligent rational decision makers. Advantages pertaining to these aspects are that we get a benchmark for how perfect (mythical) players will act. One alternative to “symmetrically prescriptive research” is “symmetrically descriptive research” (Raiffa 1982, p. 20), by describing what negotiators actually do. Thus, secondly, Neale and Northcraft (1991, p. 150), quoting Rapoport (1959), suggest that game theory has been described as “unfit” as a descriptive model of the negotiation process because it is based on what they call “extreme assumptions.” Game theory is in constant development, and assumptions gradually become less extreme. The “recent updates” of game theory referred to by Neale and Northcraft (1991, p. 150), involving relaxed assumptions, are the work by Harsanyi (1967/68) about incomplete information, which over recent years has led to the static and dynamic models in Figure 1, and social-moral utility functions, as presented by Taylor (1987) and Hausken (1996a, 1996b) involving maximizing weighted sums of interest to self and others. Aspects related to these latter developments are not accounted for in Neale and Northcraft’s (1991) framework. We may hypothesize that prescriptive and descriptive research may possibly approach each other asymptotically in future research, because prescriptive models need to present ideals with more rigorous justifications than simplified assumptions and what is furnished by math-
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ematical simplicity, and because descriptive models need to become more optimal to avoid being ignored by practitioners as unfit. Third, Neale and Northcraft (1991, p. 151) write that “game theory as a model of negotiation… ^with& its emphasis on ‘mathematicizing’ social interaction ignores the dynamic flavor of the negotiation interaction (Rapoport, 1959).” I consider this statement as false. We should observe that the article referred to by Rapoport (1959) is more than three decades old. Neale and Northcraft (1991, p. 150) are aware of the even older work by Zeuthen (1930) about bidding and concession rate strategies, but ignore the crucial dynamic model offered by Rubinstein (1982), which represented a breakthrough in the early 1980s and which received a high degree of attention, at least within the gametheoretic and economic community. Neale and Northcraft (1991) also ignore work by, among others, Binmore (1985), depicting how players work their ways towards equilibrium through “eductive” or “evolutive” routes, both highly dynamic. Of course, strategic game theory is inherently dynamic, and the weakest side of Neale and Northcraft’s (1991) framework is not to take this into account. Fourth, Neale and Northcraft (1991, p. 151) write that “game theory ignores the role of behaviors and cognitions in producing negotiated outcomes… The behaviors and cognitions of negotiators simply represent the unfolding or ‘playing out’ of the context’s influence on outcomes.” The issue can be illustrated by the “figure-ground theory” from cognitive psychology, where in our case figure corresponds to behaviors and cognitions while ground corresponds to context. The idea in “figure-ground theory” is that there may be several ways to look at a picture, with possible gestalt switches involved when switching conceptualization. One may either consider some parts (colors, contours, etc.) of the picture as the ground or background, and the other parts as the figure standing out in contrast providing the basic “content” or “idea” or “message” of the picture. Reversing the conceptualization, one may consider the latter parts as the background of the picture, and the former parts as the figure providing the “idea” of the picture. Clearly, any “figureground theory” involves choosing how to allocate the substance matter between ground and figure. This choice is partly one of taste. However, Neale and Northcraft’s (1991) strong insistence on a static conception of game theory, allocated to the ground or context, and a dynamic model of cognition and interaction, allocated to the figure, said to represent “the action,” strongly misrepresents game theory, which emerges as one of the more superior theories formalizing dynamic interaction we have available today.
4. Integrative frameworks for strategic and behavioral negotiation theory Let me incorporate dynamic game theory, incomplete information, and possibilities for socialmoral utility functions, into the framework in Figure 2. Elaborating, I develop Figure 3. In addition to static structural influences, Figure 3 incorporates dynamic structural influences, both caused by game-theoretic forces, static and dynamic, respectively. The idea is that the dynamic part of game theory may also be considered as a ground, as a structure into and upon which negotiation actions are embedded and superimposed. The
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Figure 3. Integrated behavioral and strategic framework for negotiation theory from a behavioral point of view.
eight game-theoretic parameters and concepts in Figure 3 account for the major part of the substance of what has happened within game theory over the last three decades, and within strategic negotiation theory since about 1982. The reader is referred to this literature, including the twenty-three articles listed in Figure 1, for a fuller explanation of these eight parameters and concepts. They can briefly be explained as follows: 1. The extensive form of a dynamic game specifies what set of strategies each player has available at each point in time, i.e., who is allowed to do what when. We can distinguish between simple and complex extensive forms, which may have different degrees of empirical support and explanatory relevance. There are tradeoffs involved regarding choosing between specific and general kinds of extensive forms, depending upon what aspects of the negotiations one seeks to model, and with what specificity one seeks to account for the various negotiation phenomena. 2. Equilibrium concepts abound in today’s literature. One equilibrium concept frequently used in strategic negotiation theory is sequential equilibrium, developed by Kreps and Wilson (1982). A sequential equilibrium requires that the players’ strategies continue to be mutually best responses in every node in the extensive form of the game, including nodes outside the equilibrium path. Preferences can be said to include four of the concepts in Figure 3; time discount factor, attitude towards risk, payoff structure, and own reservation price. The reason the
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first three of these are placed within static and dynamic structure is that these in most of today’s models are common knowledge, and thus constitute the commonly known structure or framework of the negotiations, whereas in games with incomplete information, reservation prices are typically chosen as one-sidedly or two-sidedly unknown. (One exception is Rubinstein’s (1985a) model, considering the time discount factor d as unknown.) 3. The time discount factors, possibly different for the two negotiators, specify how time is discounted (Rubinstein 1982). 4. Attitude towards risk specifies whether the actors are risk neutral, risk averse, or risk seeking. 5. Payoff structure specifies the objective or good the actors negotiate about. The objective may be divisible or not, the game may be purely distributive (a pie with size 1), or there may be integrative potential (negotiators differentially value elements of a dispute, nonconstant sum games). Further, the payoff structure may specify whether the actors maximize subjective expected von Neumann–Morgenstern (1944) cardinal utility, or, e.g., a social-moral utility function. 6. Reservation price refers to the indifference point regarding obtaining/not obtaining the objective, e.g., selling/not selling a house for a specified price. 7. Information structure specifies who knows what about whom. Information may be oneor two-sidedly incomplete, and refer to one or several parameters. 8. Finally, beliefs refer to the subjective probability distribution a negotiator formulates over the opponent’s reservation price, and are updated as negotiations proceed according to Bayesian statistics, e.g., according to what Fudenberg, Levine, and Tirole (1985) label “the successive skimming lemma.” In Figure 3, these eight game-theoretic parameters are divided into three clusters, pertaining to static structure (2), dynamic structure (4), and game-theoretic “cognition” parameters (2). Static structure affects structural influences, and dynamic structure affects interaction structures. Structural influences and interaction processes influence each other through negotiator cognitions, and also influence the negotiated outcome directly. This means that among other things the static structures of the payoff and information affect the negotiated outcome via negotiator cognitions and the interaction process, and also affect it directly. The justification for the latter is that negotiations frequently are such that payoff and information structures are given, forcing one particular negotiation outcome, regardless of such things as influence tactics and communication tactics. Attitude towards risk, whether neutral, risk-averse, risk-seeking, etc., is placed within dynamic structure, accounting for Kahneman and Tversky’s (1979) work on prospect theory and framing. Both Figures 2 and 3 assume game-theoretic parameters as context, the main difference being that Neale and Northcraft’s (1991) context in Figure 2 is purely static. We can alternatively consider behavioral aspects as contextual, i.e., we may consider philosophical aspects as extra-contextual, behavioral aspects as contextual, and strategic or gametheoretic aspects as where the real action is, specifying how the negotiation game actually is to be played. With no change of content, through simple manipulation of the boxes and arrows in Figure 3, I thus produce Figure 4.
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Figure 4. Integrated behavioral and strategic framework for negotiation theory from a game-theoretic point of view.
In Figure 4 behavioral characteristics are filtered through game-theoretic parameters. More specifically, Neale and Northcraft’s (1991) four cognitions are specified (compressed or forced) into game-theoretic beliefs and preferences. Static structural features, what Neale and Northcraft (1991) label game theory and agency theory, are specified into payoff structure, information structure, and attitude towards risk; and interaction processes (influence and communication tactics) are specified into extensive form, equilibrium concepts, and time-discount factors. This “reduction” of behavioral characteristics to game-theoretic parameters has both advantages and disadvantages. The approaches in Figures 3 and 4 can be said to represent two different schools or disciplines: the behavioral school and the game-theoretic school. Regarding the latter, a psychologist from the behavioral school will emphasize the disadvantages, e.g., that “mathematicizing social interaction” ignores qualitative behavioral “soft” aspects. A mathematical economist from the game-theoretic school will emphasize the advantages, e.g. that quantifying beliefs and preferences increases qualitative insight, makes for interaction which can be clearly and distinctly visualized with graphs and curves, enables one to hire an agent equipped with “hard” numbers for how to negotiate, etc. Choice between the behavioral and the game-theoretic framework can be made depending upon the nature of the negotiations. If negotiations involve highly charged feelings and emotions, few technical and quantitative issues, and/or initially in the explorative phase before the problem is adequately formalized, perhaps a behavioral approach is to prefer. If the reverse is the case, a game-theoretic approach may be preferable.
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5. Implications and applications of the integrated frameworks Let me first state, as Neale and Northcraft (1991, p. 176) do, that the “framework is not meant to represent a strictly causal model; rather the arrows in the framework reflect sources of influence that must be taken into account to appreciate the unfolding of a dyadic negotiation.” Figures 3 and 4 add eight game-theoretic “sources of influence,” divided into three clusters, contributing to a more equal balance of game-theoretic and behavioral “sources of influence.” One argument for the superiority of the interdisciplinary frameworks is thus that since a broader range of “sources of influence” is accounted for, the frameworks can be considered as more fully representing, and capturing, the richness of a negotiation problem. Neale and Northcraft (1991) associate “ground” and “figure” with static and dynamic factors, and, as an example, with two fundamental tasks of negotiation, claiming and creating of value, respectively. In this article we associate ground and figure with gametheoretic and behavioral negotiation theory, respectively, in Figure 3, and vice versa in Figure 4, considering both as static and dynamic. To the extent Neale and Northcraft’s (1991, pp. 178–179) “static-claiming/dynamic-creating dualism” is appropriate, this is accounted for in Figure 3 by considering “static structure” as a major “source of influence,” and deemphasizing “dynamic structure.” However, if empirical research shows that “claiming value” is a dynamic process, since a negotiator may retrieve, revise, and rescind his “claims” in a string of subsequent bids with possibly varying time intervals through time, this is accounted for in Figure 3 by also considering “dynamic structure.” If a “claiming/creating value” process is shown to embody aspects not captured by Figure 3, Figure 4 can be employed. This suggests the superiority of Figs. 3 and 4 as research tools because they allow for combining explanatory factors, or sources of influence, in a higher multiplicity of different ways. Neale and Northcraft’s (1991) notion of causality and “ultimate” sources of influence need to be further elaborated. Although Figure 2 is not strictly causal, Neale and Northcraft’s (1991) two-level framework implies some degree of causation from static contextual factors (ground) to dynamic negotiator factors (figure), and some degree of causation vice versa. This is illustrated with the two-way arrows in Fig. 2, and is exemplified with their (1991, p. 179) acknowledgement that “dynamic negotiator effects” may “fundamentally alter the nature of a dispute by taking it beyond the parameters initially defined by the context.” The corresponding two-way arrows in Figures 3 and 4 are between gametheoretic and behavioral factors. The flexibility of the two latter frameworks is enhanced because game-theoretic and behavioral factors can be ground and figure, respectively, or vice versa, according to what one’s research suggests as most appropriate. A creative researcher may even observe that the eight boxes, four as ground and four as figure, in Figures 3 and 4 (aside from the box labelled “Negotiated outcomes”) can be switched vertically with their closest neighbor in 24 different combinations, giving 16 different frameworks rather than the two in Figures 3 and 4. The eight game-theoretic and 11 behavioral concepts in Figures 3 and 4, and their relationships, are discussed extensively in the two respective literatures. The organization of and interdisciplinary relationships between the 19 concepts in Figures 3 and 4, and their logical and empirical underpinnings, are now further discussed and clarified, as sources
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for empirical and experimental research in a variety of different spirits. Let me employ Figures 3 and 4 respectively. Research in the behavioral tradition can employ Figure 3, and use some of the suggestions by Neale and Northcraft (1991). Incorporating gametheoretic aspects into behavioral models furnishes a mechanism for providing negotiators with “benchmarks,” in Raiffa’s (1982) sense, “for performance.” One example is work on social utility theory (Camerer 1987), which is a merger of game theory and social psychology. The method for creating this merger from Figure 3 is to identify those of the eight game-theoretic parameters that pertain to utility (that is, preferences, time discount factor, attitude towards risk, payoff structure, and own reservation price), and analyze how these interact with the corresponding behavioral social-psychological concepts. There is potential for a variety of such mergers, using the three clusters of eight game-theoretic parameters in Figure 3, presupposing sufficient supply of creative interdisciplinary researchers. Consider for example interaction processes, which include influence tactics and communication tactics in Figure 3. These are discussed over four pages by Neale and Northcraft (1991, pp. 161–164), and elsewhere. But they are not mathematicized, nor quantified, nor formalized, nor related to anything akin to “benchmarks for performance,” as in the game-theoretic literature. In Figure 3, dynamic structure (which includes extensive form, equilibrium concepts, time discount factors, and attitude towards risk) affects interaction processes. Having the substance of the definitions of these four game-theoretic concepts, as given in Section 4 and elsewhere, in one’s mind when going through Neale and Northcraft’s (1991, pp. 161–164) four pages, typically enriches one’s research design. More specifically, Neale and Northcraft (1991, p. 163–164) write under “communication form and settlements” that “more successful negotiators made more offers and stuck to them, rejected losers’ offers more often, and made fewer concessions.” A specific interdisciplinary research design can thus be created by using the earlier single-disciplinary design, and testing whether a “successful negotiator” continues to be successful if his time discount factor increases or decreases (relative to that of his opponent), if his attitude towards risk changes (neutral, averse, seeking), or if the extensive form of the game changes in the sense that he can retrieve, revise, or rescind bids in a different fashion. Similar research designs can be made by considering how static structure (payoff structure and information structure), beliefs, and reservation price affect the behavioral concepts. Generally, in Figure 3, the behavioral concepts can be related in a variety of different combinations to the game-theoretic factors presented as “ground.” Regarding research designs, hypotheses about how behavioral factors are linked to game-theoretic factors can be written, tested, and used in further theoretical development. When merging game-theoretic and behavioral concepts into interdisciplinary research designs, it is important to acknowledge that the former often have a stronger focus upon endogeneity issues. One example is Hart and Kurz’s (1983) model for endogenous formation of coalitions. Research designs within behavioral theory, on the other hand, often implicitly account for external factors, which can be illustrated by the above description of tests based upon “successful negotiators.” Indications that “better negotiators make fewer concessions” do not imply that making fewer concessions makes one a better negotiator. E.g., regressing golf scores on golf courses may show that the best scores correspond to the most challenging courses. However, concluding that in order to become a good golf player one should play challenging courses would be incorrect because it does
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not account for the self-selection property that golf players with advanced proficiency in playing golf (attained through a variety of different training procedures aside from playing challenging courses) tend to play more challenging courses. Another example is the well-known work by Peters and Waterman (1982) attempting to show why the more successful companies are more successful, based on studies of close to 50 successful companies. Here the self-selection property is evident. Unsuccessful companies and possible alternative procedures by which the successful companies have become successful are not accounted for. Hence the advice when constructing interdisciplinary research designs is that simply attributing successful behavior in some respect, e.g., the behaviors of successful negotiators, to good practice overlooks important endogeneity properties which are at the heart of game-theoretic analysis, and upon which game theory has traditionally focused. Research in the game-theoretic tradition can employ Figure 4. Consider for example the spirit exemplified by Ochs and Roth’s (1989) experimental study of sequential bargaining. Ochs and Roth (1989) can be said to use the five classes of suggestions in Section 2, and Figure 4, as they in our sense associate game-theoretic factors with “figure,” i.e., where the “real action” is (contrary to Neale and Northcraft 1991). They review four earlier designs, and produce a more general design employing, directly or indirectly, all the eight game-theoretic concepts in Figure 4. Ochs and Roth (1989) get support for a first-mover advantage, independent of the equilibrium prediction, and show that 81% of the rejected offers were followed by counterproposals that would earn less money. Ochs and Roth’s (1989) research design, and the designs they review, can be generalized and employed in a variety of different manners. The most obvious is to use the five classes of suggestions in Section 2 in different combinations. Another is to use the results such as those about first-mover advantage and how counterproposals follow rejected offers to design research, drawing connections to behavioral factors presented as “ground” in Figure 4. This involves writing hypotheses about how game-theoretic factors are linked to behavioral factors, and testing the hypotheses. Consider for example estimation of the opponent’s reservation price. Strategic or game-theoretic negotiation theory, using Figure 4, lets the negotiators formulate commonly known probability distributions, i.e., beliefs, over each others’ reservation prices. These beliefs are updated according to Bayesian statistics as negotiations proceed and increased information becomes available. The behavioral concepts in Figure 4 can be considered as affecting the game-theoretic beliefs and preferences in many different ways. Note, for example, with Simon (1955), that humans are “boundedly rational” in the sense of having limited capacity for processing information and preferences. Some work in this spirit is finding its way into contemporary game theory (Kreps 1990). Elaborating upon Simon (1955), Kahneman and Tversky (1979) suggest that negotiators are satisficing, framing situations according to subjective predispositions, attaching weight to aspects according to availability and representativeness, anchoring judgment in some salient features with subsequent adjustment, thereby acquiring insight into the opponent’s cognitive processes. They (1979) determine a nonlinear curve for utility functions, so that actors make assessments according to relative gains versus losses, where possibly social comparison theory and/or social deprivation theory have influence. These actors are risk averse in the domain of gains and risk seeking in the domain of losses, this curve being steeper for losses than for gains. If the opponent is known to be
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influenced by cognitive biases, one’s own negotiation behavior can be designed to benefit from this. For example, Neale and Bazerman (1985) find that negotiators with positive frames are more concessionary and successful than counterparts with negative frames, because, consonant with Kahneman and Tversky’s (1979) results, negatively framed negotiators are more risk seeking and thus unwilling to accept certain settlements. One conclusion from research on cognitive biases is that one may benefit by gaining increased insight into the cognitive faculties of one’s opponent, thereby updating a more adequate estimate over the opponent’s reservation price. However, another conclusion is that one should be aware that one’s opponent is similarly attempting to benefit from estimation of one’s own possible cognitive biases. In the long run, cognitive biases may be weeded out, but not necessarily. For contemporary game theory, these aspects lie hidden in the equilibrium concepts, and in the Bayesian updating mechanism based on Harsanyi’s (1967/68) theory about incomplete information. More specifically, this latter discussion about cognitive biases plays directly into the basic rationale of game-theoretic reasoning. The reason is the importance within game theory to place oneself in one’s opponent’s situation in order to gauge adequately a strategy’s strengths and weaknesses. Thus game theory requires one to ask such questions as whether a perceived cognitive bias on the part of an opponent is real, strategic, has some other rationale, or perhaps “no rationale.” Similarly, every opponent is asking himself whether the perceived cognitive bias(es) on the part of his opponent(s) is (are) real, strategic, has some other rationale, or perhaps “no rationale.” Moreover, every player is attempting to evaluate whether he himself is involved in any additional cognitive biases when assessing the others’ cognitive biases. Hence we get second order, third order,…, nth order evaluations of others’ cognitive biases, giving an infinite regress reasoning chain. During this mutual evaluation of cognitive biases, which may be modelled with Touring machines or other methods (Binmore 1985), every player attempts to “lock in” on what he perceives as a plausible equilibrium path for all the players, or a plausible focal equilibrium point (Schelling 1960) for all the players. If there are several plausible focal equilibrium paths, every player may attempt to evaluate whether there exist efficient focal equilibria, whether any of these are more beneficial to himself than other equilibria, whether they are perceived by others to be more beneficial to himself than others, etc., giving again an infinite regress reasoning chain. This discussion of cognitive biases illustrates how employment of behavioral concepts may enrich the game-theoretic conception. This may happen through a variety of different methods, such as refinement of the equilibrium concepts, further specification of how beliefs are generated and updated, etc. Research designs as described in the last two paragraphs involve combining the concepts in Figure 3 and 4, and other concepts, in sentences written as hypotheses that can be tested. As the hypotheses receive varying degree of empirical support and falsification, they, and the research designs to which they belong, can prove to be building blocks towards theory construction, enriching our understanding of negotiation theory.
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Acknowledgements I would like to thank the editor and an anonymous reviewer for helpful comments.
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