Perfect or Bounded Rationality

The paper focuses on empirical studies of a class of very simple games of the reward allocation, dictator and ultimatum type. It is demonstrated that true explanations of social phenomena cannot conceivably be derived in terms of the perfect rationality concept underlying neo-classical economics. Analyzing the simple paradigm games it is explored in some depth, if speculatively, how experimental game theory might bring us closer to a new synthesis or the nucleus of a general theory of “games and boundedly rational economic behavior” with more explanatory power. 1. Introduction and overview Evaluated in entrepreneurial terms neo-classical economics is a success among the social sciences. The numbers of professionals is ever increasing and economics is well respected in adjacent fields of social inquiry. Some of its core techniques are widely used by other social scientists while economics is so selfconfidently tackling all sorts of social science issues within its “optimization” or “rational choice” paradigm that one may indeed speak of “economic imperialism”. Political science departments at least in the US lean more and more towards “economic theories of politics” while journals like “Public Choice”, “Theory and Decision”, “Economics and Philosophy” or “Rationality and Society” are flourishing. Game and decision theory in particular provide a modern “lingua franca” for social science (reaching even into biology). The prisoner’s dilemma, the battle of the sexes and the chicken game which all originated from elementary rational choice modeling of social phenomena have taken hold on the minds of social scientists across the board. We see the world as full of “games and decisions” ((Luce, D. and H. Raiffa 1957)), study the “economic games that people play” ((Maital, S. and S. L. Maital 1984)) and Güth/Kliemt Cambridge-Khalil-2 2 generally use “games as models of social phenomena” ((Hamburger, Henry 1979)). The existence of the common decision and game theoretic language along with common paradigm examples of elementary social problems is extremely valuable in facilitating communication about social research. However, 1 For instance the project “game theory in the behavioral sciences” organized in the academic year 1987/1988 at the ZiF – center for interdisciplinary research – of the university of Bielefeld brought together an interdisciplinary group from fields as economics, philosophy, mathematics, political science, sociology and very markedly biology. Due to their training in modern decision and game theory people in the group could actually talk to each other quite easily across the borders of distinct disciplines as traditionally defined. It may be noted in passing that the two authors of the present paper (an economist and a political philosopher) met the first time at the ZiF and started to find out how much common ground there was between them. It may also be instructive to note that we later on – in the academic year 1999/2000 – co-organized jointly with Joachim Frohn and Reinhard Selten a project “making choices” which focused on bounded rationality as opposed to the game equilibrium models that were the focus of the earlier project. It indicates, we think, part of the dynamics of social science research. The role of the ZiF in our research and also preparing the ground for writing this paper is gratefully acknowledged; for further documentation of the work in the two projects see the volumes edited by Selten, Reinhard ed. 1991a. Game Equilibrium Models I Evolution and Game Dynamics. Berlin / Heidelberg / New York / London / Paris etc.: Springer Verlag. Selten, Reinhard ed. 1991b. Game Equilibrium Models II Methods, Morals, and Markets: Springer Verlag. Selten, Reinhard ed. 1991c. Game Equilibrium Models III Strategic Bargaining. Berlin / Heidelberg / London etc.: Springer-Verlag. Selten, Reinhard ed. 1991d. Game Equilibrium Models IV Social and Political Interaction. Berlin / Heidelberg / New York etc.: Springer-Verlag., Frohn, Joachim, Werner Güth, Hartmut Kliemt, and Reinhard Selten eds. 2001. Making Choices I & II. München: Accedo., Güth/Kliemt Cambridge-Khalil-2 3 interpreting decision and game theoretic language literally implies that human individuals do optimize and choose intentionally on the basis of given preferences. These implications are widely off the mark and should not be accepted. They are at root of a neo-classical orthodoxy that quite naturally leans towards the view that the true art of the economist consists in fitting everything to a description in decision theoretic terms. To describe human action as the result of “optimization under constraints” amounts to “economic story telling”. Evidence from psychology and in particular experimental economics and thus from “inside” economics itself (see (Kagel, John H. and Alvin E. Roth 1995)) seems to indicate that “explanations” of human behavior based on rational choice and optimization except for the simplest cases must be rejected. More often than not full rationality is a mistaken and misleading assumption. It may not even count as an idealization of the “true” behavioral laws if we assume that behavior is fully rational and optimizing. For, real behavior is in all likelihood guided by principles completely different from optimization and rational choice. It is “boundedly rational”. If that be true then we obviously need a theory of boundedly rational behavior. Yet explanations in terms of bounded rationality have their disadavantages as well. They are typically based on strongly domain dependent theories of quite Ahlert, Marlies and Hartmut Kliemt eds. 2001. Making Choices in Organ Allocation. Stuttgart: Lucius und Lucius. 2 In the German speaking countries a fundamental critique of looking at the world from the point of view of decision theory rather than through the perspective of behavioral science has been offered in particular by Hans Albert since the early sixties, see the collection of papers Albert, Hans. 1967. Marktsoziologie und Entscheidungslogik. Neuwied/Berlin.: Luchterhand.. 3 That the effort to describe things in decision theoretic terms imposes the discipline of making modeling assumptions explicit in our story telling is a great advantage over traditional verbal approaches that should not be underestimated. Güth/Kliemt Cambridge-Khalil-2 4 short range. Using them leads to a fragmented view of the world. As opposed to that decision and game theoretic language convey the impression of a unified view of the world that renders diverse phenomena more intelligible by putting them in (the same) perspective. Yet if we look more closely at the way the general language of decision and game theory has to be adapted to specific domains by often ad hoc assumptions it is obvious that the rational choice theorists’ claims to universality and unity of their theories are based on a kind of collective self-deception. They have a common language – not a small accomplishment – but not a common theory with empirical content and explanatory power. It may well be that in the end there are no convincing general theories of human behavior at all. But if that is so we should take pains to expose as openly as we can where and why our theories of human behavior in social contexts fail and what their limitations are. Nothing can be won by concealing the failure to formulate general theories with empirical content behind a veil of deceptively general optimization models. If the theories that carry empirical weight are in the end quite common sensical, so be it. If we can only give some advice how domain specific theories can be formulated without being in a position to contribute substantial general information why not accept that? It may be part of the human condition that human behavior cannot generally be foreseen or explained by human beings. Therefore the formation of social theories may remain an “art”. We may be able to train people in the art of forming short-range domain specific theories. In management science and the best of business administration studies this is done even though general theories of social behavior with explanatory content are lacking. And people well-trained in the techniques of formulating short-range (or “ad hoc”) theories carry high market value. If in view of the complexities of social life people have to form their theories in a case by case manner according to their good judgment, why 4 With out subscribing to it in full we would like to point out that this view is to some extent supported by insights reaching from Aristotle’s arguments about the role of judgment to Güth/Kliemt Cambridge-Khalil-2 5 not accept this and see how we can improve our ways of theory formation at least at the margin? Why not seek ways of coping with our ignorance as well as possible without engaging in self-deception? In a first step of our programmatic discussion we will discuss the merits of generality in social theory formation (2.). We then turn to claims of generality as contained in the neo-classical theories of fully rational behavior (3.). The next section deals with some neo-classical repairs and the difficulties that they encounter (4.). The deficiencies of in explaining the results of reward allocation, dictator and ultimatum games in a perfect rationality framework are discussed then (5.). A speculative sketch of some attempts to explain experimental results in a bounded rationality framework follows (6.). Final remarks conclude the paper (7.). 2. Generality of social theories? The integration of otherwise diverse experiences into one body of knowledge is among the chief purposes of theorizing. General theories shed light on relationships, bring to attention common aspects and build bridges between seemingly separate matters. Standard examples are found in natural science. For instance, with plain common sense hardly anybody would suspect that the movement of planets and the fall of an apple from a tree have something in common. But natural science tells us that there is a common aspect. Insights of natural science into the common traits of apparently unrelated phenomena are essential to the success of that great enterprise to which we refer as (natural) science. In the realm of social phenomena it would obviously be desirable to have access to theories of comparable scope that could impose some unity on our diverse experience. Classics like most prominently David Hume thought that those who succeeded to develop a theory of “human nature” would modern arguments about the limits of artificial intelligence as expressed in Dreyfuss. ???? The limits of artificial intelligence????. Güth/Kliemt Cambridge-Khalil-2 6 hold the key to a universal theory of the social world (see [Hume, 1739/1978 #253]). In the famous opening passage of Hume’s “treatise of human nature” he says: “Here then is the only expedient, from which we can hope for success in our philosophical researches, to leave the tedious lingering method, which we have hitherto followed, and instead of taking now and then a castle or village on the frontier, to march up directly to the capital or center of these sciences, to human nature itself; which being once masters of, we may every where else hope for an easy victory.” But social science, after Hume, developed into domain specific theories rather than focusing on human nature and on universal behavioral assumptions about human actors. Economics is no exception to this. From its beginnings at least to the middle of the 20-th century in particular neo-classical economics saw itself as a domain specific theory confined to market behavior, to exchange and commercial relationships as narrowly defined. Only in the second half of the 20th century neo-classical economics ventured into new territory beyond the realm of the “commercial”. The theory of games developed, public choice theory originated as a theory of non-market decision making (the aforementioned journal “Public Choice” started out as “papers on non-market decision making”), the law and economics movement and the new institutional (and constitutional) economics took off (with contributions reaching from (Buchanan, James M. and Gordon Tullock 1962), over (Milgrom, Paul and John Roberts 1993) to (Young, H. Peyton 1998)). Since then the so-called “new world of economics” (see (McKenzie, Richard B. and Gordon Tullock 1979)) laid out a theoretical image of the social and institutional world that promises a unified view of all social phenomena. It is a world of rational decision makers, of utility maximizers who act on the basis of given preferences (see for instance (Becker, Gary 1976)). 5 Incidentally, Hume’s treatise was translated into German language by a psychologist who indeed saw Hume as one of the “giants” (in the sense of Merton) on whose shoulders he tried to stand as a psychologist. Güth/Kliemt Cambridge-Khalil-2 7 In all contexts from family to politics the same rational, expecting, maximizing, men (REMM, see (Meckling, W. 1976)) are acting. The corresponding theory of rational decision-making forms the core of the economic approach to human behavior. It promises to connect diverse phenomena in one unified body of mathematical social theory. Thereby social science seems to reach a stage of universality and mathematical precision comparable to that of, say, Newtonian mechanics. If it were in fact true that the behavioral assumptions underlying “rational economic man” would form a universally applicable model of human behavior leading to valid explanations in social realms as diverse as competition of parties at the polls and competition of firms for nearby customers (phenomena as diverse as the fall of apples and the movement of planets) the world of social science would be fundamentally altered. However, regardless of the charms of the economic approach to human behavior its unity of language and of description is not matched by unifying behavioral laws applicable to several realms. True enough, humans command the faculty to act opportunistically on the basis of a model of the action situation. Therefore the over-socialized model of man according to which human behavior is to be explained exclusively in terms of internalized values, norms and rules is certainly mistaken. In that regard the economists and more generally rational choice theorists are right. But this is not to say that they have a more valid theory to substitute the theories that they criticize. The economic approach that models behavior as universally opportunistic case-by-case maximization of utility is at least as far off the mark as the classical sociological one. It either has no empirical content or in its concrete specifications is as fragmented as other social theories. If the behavioral model of the economic approach to human behavior is reduced to the maximization of pecuniary income (classical profit rather than utility maximization) the model has empirical content. But in this narrow traditional interpretation it is obviously neither universally applicable to all realms of human behavior (in particular not to those in which pecuniary motives play no Güth/Kliemt Cambridge-Khalil-2 8 role) nor is it the sole valid explanation of behavior in the presence of pecuniary incentives. Motives other than pecuniary ones do play a role throughout – even when pecuniary motives are present. To rescue its model of behavior from the most obvious counter arguments the neo-classical economic analysis must either be confined to very narrow domains like special competitive markets in which it applies “in the limit” or it must be rendered void of most of its empirical content by auxiliary assumptions that are often ad hoc. A richer motivational structure as such would still be compatible with the aim of formulating general theories if domain specific circumstances were merely initial conditions for quite general motivational and behavioral laws; e. g. “in contexts of type x in which the ‘profit motive’ is perceived as a legitimate concern it will be dominant while in other contexts of type y the ‘fairness’ motive dominates”. In that case the richer structure would link different realms containing types of situations x, y as characterized in general terms. But instead of this desirable linking of realms we rather find bits and pieces of theories of motivation that might explain behavior in specific realms without really transcending the limits of those realms or linking them at least to each other. In particular to include new components in the utility functions of individuals as seems fit according to the exigencies of diverse situations taken separately is not a convincing strategy. Only if a serious endeavor to formulate a more general or even ‘universal’ such function is made eventually the pragmatic efforts of developing a richer theory need not be a bad thing. But the issue of empirical content and the search for true behavioral laws must be kept firmly in view. 6 If we incorporate motives other than the pecuniary ones into the utility functions of individuals then neo-classical economics becomes fragmented beneath the surface of its unified decision theoretic language. The diverse specific motives that, pending on situational complexities, sometimes do and sometimes do not trigger behavioral responses must be taken into account; e.g. sometimes the profit motive is operative and dominant and sometimes not. Güth/Kliemt Cambridge-Khalil-2 9 Economists for all their claims that they are searching for an empirical science of behavior do not seem to keep focused on the pursuit of behavioral laws. In particular the thesis that maximization under constraints can be an answer to the fundamental theoretical challenge of developing general theories is as strange as it is common among economists. Things that quite naturally could and should be expressed otherwise are put into the Procrustes bed of “economic maximization under constraints”. Even though very clearly there is no such maximization process in the human psyche things are made to look “as if” actors maximize under constraints across the board. However, to say that individuals act “as if” they maximize is not good enough. First, it is, to put it mildly, very unlikely that even the weaker thesis of “as if” maximization would with some plausibility apply universally. Second, even if all individual behavior could be described “as if” it were maximizing, we would have an explanandum (a – very astonishing – phenomenon to be explained) rather than an explanans (an explaining set of hypotheses and conditions for their application). For it is obviously true that conscious and intentional maximization of a given objective function is not at root of human choice 7 Of course, one might remark here that Gary Becker’s approach is different in this regard. Is he not a critic of “ad hocery”? Indeed he insists that in the last resort human motives have to be treated as invariant between situations. In the last resort there is one human nature that is inter-individually invariant. To explain differences in overt behavior economists have to rely on observable external constraints. The internal technology of producing the ultimate satisfactions of basic needs differs but not the needs and ultimate motives as such. Without going into the details of the Beckerian methodology let us acknowledge that it tries to cope with some of the more obvious criticisms of the neo-classical approach to human behavior in a quite ingenious way. However, it still insists on the “maximization subject to constraints” paradigm. It rescues mathematical elegance and unity of mathematical method at the price of substantial unifying theories. In particular, Beckerian differences in human capital, in the technology of creating ultimate satisfactions seem quite arbitrary ways to “explain” differences in choice making behavior. Güth/Kliemt Cambridge-Khalil-2 10 making and thus cannot be the true causal law. Third, human behavior is sometimes so-well adapted to circumstances that an omniscient maximizer could not do better. Yet, again, the well-adapted behavior is definitely not the result of conscious maximization. It is in all likelihood the outgrowth of other processes that somehow led to the observable optimal result. Merely to identify overt behavior as optimally adapted – or at least as stable in the sense of, say evolutionary stability – does not provide an explanation. Optimality as well as stability rather require an explanation in terms other than optimization (the origin of predictable behavior is discussed from a more or less neo-classical perspective in several studies as for example (Heiner, R. 1983)). Wherever results corresponding to the predictions of full rationality should be observed – and we are very reluctant to concede that they are ever observed – an explanation in behavioral laws of boundedly rational behavior is required. Rather than feeling reassured in our economic views of the world we should ask: Why is it so that the anomaly of seeming full rationality is observed? What are the circumstances that led to such a phenomenon under general behavioral laws? If optimality in the sense of “as if” rationality is widespread how can we explain this extraordinary and astonishing fact? What are the general behavioral laws that can explain behavioral observations? We will not be in a position to offer fully convincing answers to these questions. Turning to the task of outlining what can and to our opinion should perhaps be done let us start with a more specific brief look at the traditional theories of perfect rationality that were involved in making stronger claims to generality and then gradually bring in a more realistic perspective on choice making. 3. (Commonly known) Perfect Rationality and its difficulties Let I:={1, 2, ..., n}, n≥1, be the set of players and let Γ denote the class of all games G in a domain with G=(S1, S2, ..., Sn; u1, u2, ..., un); Güth/Kliemt Cambridge-Khalil-2 11 where for all i∈I the Si≠ø are finite strategy sets, S:= i S i=1 n ∏ is the set of all strategy profiles s=(s1, s2, ..., sn) ui are mappings ui: S → R, ui(s)∈R, which represent the individuals’ preferences by a conventional cardinal utility measure. If n=1 optimality of choice behavior requires that the single actor, 1, must choose s*∈ S such that u=u1is maximized over S; i.e. s*∈ argmax{ u(s): s∈S}. In cases with n≥2 it is not clear what optimal behavior in the sense of maximizing ui requires of each actor from i∈I={1, 2, …, n}. If the behavior of all others is known to i and fixed then, i needs to maximize against s-i:=(s1, s2, si-1, si+1,..., sn) such that an optimal result is reached. The information condition (see on how “truly perfect information” in hierarchies can guarantee Pareto efficiency (Thompson, Earl and Roger Faith 1981)) that the actions of all others are fixed and known can conceivably be fulfilled only for one individual. In all other cases the question of how to deal with situations in which the actions of other actors are not known (either not fixed yet or unknown for other reasons) emerges at least for some actors. This raises the question which criteria of optimal behavior could be applied by those individuals. Though there is no commonly accepted answer to this question most economists would tend to require as a minimum that choices be in equilibrium (but even this is contested, see for instance (Sugden, Robert 1991)). A strategy vector s*∈S is in equilibrium (see (Cournot, Auguste 1838), (Nash, John F. 1951)) iff ∀ i∈I: s*i∈argmax{ ui (si, s*-i): si=∈Si }. As stated not all individuals can be informed about all choices as fixed or made by all other individuals. In that sense ignorance as to some of the choices of others necessarily (in a logical sense of necessity) applies when the other n-1 of the choosers make their choices. For instance, in a two person sequential game Güth/Kliemt Cambridge-Khalil-2 12 one actor must move first and thus without knowing the choice of the other actor. He can have views on which actions the other actor will take but he cannot know in advance the other choice as made. In simultaneous move games, to which we confine attention for the time being, all n choice-makers must fix their choices without knowing the choices of others. So in making these choices none can maximize against the known choices as made by others. Even in very idealized circumstances in which the game is not only known to all players but common knowledge among them – i. e. they know that all know that all know … that all know the game – players cannot maximize in any simple sense that would correspond to the case n=1. As a consequence of this, though in equilibrium each player maximizes against the choices of each other individual, it is not clear how even fully rational individuals would get to the equilibrium by their actual choices. To put it slightly otherwise: What kind of play could we recommend to players who intend to act as rational utility maximizers in such situations? This question has no easy answer if any. For example, consider a standard battle of the sexes game: