A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Güth, Werner; Kliemt, Hartmut Article (Un)bounded rationality in decision making and game theory: Back to square one? Games Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Güth, Werner; Kliemt, Hartmut (2010) : (Un)bounded rationality in decision making and game theory: Back to square one?, Games, ISSN 2073-4336, MDPI, Basel, Vol. 1, Iss. 1, pp. 53-65, http://dx.doi.org/10.3390/g1010053 This Version is available at: http://hdl.handle.net/10419/98552 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. 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Werner Güth 1,* and Hartmut Kliemt 2 1 Max Planck Institute of Economics, Kahlaische Straße 10, 07745 Jena, Germany 2 Frankfurt School of Finance and Management, Sonnemannstraße 9-11, 60314 Frankfurt am Main, Germany; E-Mail: [email protected] * Author to whom correspondence should be addressed: E-Mail: [email protected]. Received: 18 February 2010; in revised form: 15 March 2010 / Accepted: 19 March 2010 / Published: 23 March 2010 Abstract: Game and decision theory start from rather strong premises. Preferences, represented by utilities, beliefs represented by probabilities, common knowledge and symmetric rationality as background assumptions are treated as “given.” A richer language enabling us to capture the process leading to what is “given” seems superior to the stenography of decision making in terms of utility cum probability. However, similar to traditional rational choice modeling, boundedly rational choice modeling, as outlined here, is far from being a “global” theory with empirical content; rather it serves as a tool to formulate “local” theories with empirical content. Keywords: bounded rationality; methodology of decision; game theory JEL: C70; B40; A12 1. Introduction and Overview Let G (S1, S2 ,..., Sn ;1(), 2 (),,..., n (); Z) be an interactive structure corresponding to a finite stochastic normal form game model with players i 1,2,...,n( 2) whose strategy sets are Si and whose substantive payoff functions i s, z assign a monetary payoff to every strategy vector s (s1, s2 ,..., sn ) and chance move z Z . Games 2010, 1 54 The πi(.) values merely represent monetary rankings. Other than conventional utilities, they are not indicative of all evaluative considerations of the interacting individuals. Therefore the preference ranking of results can always deviate from the natural order suggested by monetary payoffs πi(.). As a participant involved in G – an objective interactive situation – each individual i 1,2,..., n can physically perform siiS . Human actors do not merely interact in the physical world, they also represent that world to themselves in mental models. Accordingly, assume that each individual i 1,2,..., n can and will form a mental model M i G , of the interaction. Each of these models represents G in terms of the subjective views of i 1,2,..., n . A priori, nothing guarantees that the mental models M i G as well as the first and higher order beliefs etc. of the several individuals i 1,2,..., n “coincide” with each other. In view of the complexity of human mental processes and the idiosyncratic nature of individual knowledge, M i (G ) M j (G ), i j, should generally be expected to apply. For the theoretician who intends to incorporate human mental processes and reasoning into his models, this creates an obvious difficulty: he would have to form a higher order model M(M1(G),M 2 (G),...,M n (G)) containing a representation of all individual models. At least in a way, he would need to know what all individuals know. But it seems impossible to represent all individuals’ idiosyncratic or “local” knowledge.1 To overcome this difficulty, conventional models of interactive decision making typically introduce strong (common) knowledge assumptions. Due to these assumptions on some abstract level of analysis, participants of the interaction are dealing with the same mental model as an object of common concern. Beliefs and desires, respectively, are assumed to be given; it is also assumed to be commonly known which of these aspects are private information and which are not. Though in some extremely simple situations of interactive decision making with clearly defined (competitive) aims, the substantive (typically monetary) payoffs may plausibly be assumed to be common knowledge and, at the same time, dominant concerns of individual decision making, this abstraction loses its plausibility in contexts in which more complex beliefs and desires exert their influence. Then individual rankings of states of affairs may be expected to diverge from easily observable substantive (monetary) payoffs. In such cases “common” (and even weaker “shared”) knowledge assumptions become exceedingly precarious.2 The mental models become idiosyncratic and can diverge to an extent rendering it impossible to assume that a “common object of reasoning” does in fact exist and is commonly known as a “matter of common concern.” Though, in general, M j (G ) M i (G ) G cannot be ruled out, we intend to consider cases in which beliefs and aspirations (standing for desires) are idiosyncratic. Whenever we want to emphasize the potentially idiosyncratic character of variables, we will indicate this by putting a prime to them. Beyond this merely “cosmetic” step, we will, by means of specific examples, introduce and illustrate several additional elements of a language that can be used to build models of situations of (interactive) 1 An argument forcefully made in [1]. 2 Simply put, in characterizing representative utility u, we cannot have it both ways: maintain the common accessibility of substantive payoffs as determining u as well as the flexibility of subjective rankings which may diverge from substantive payoffs in any arbitrary way and yet be represented by u. Games 2010, 1 55 decision making that do not rely on the rather extreme assumptions of traditional game theory.3 Basically, our aim is to develop a “theory” rather than only a language. It would, however, be premature to claim that our language allows to develop a general theory. In section 2, we succinctly introduce the basic tools we suggest to use in building models of (interactive) decision-making situations. In section 3, we illustrate the intended use of the tools by forming a model of a non-interactive situation that, in section 4, we extend to interactive situations. While the first two examples are still in line with structures corresponding to stochastic normal form games, the example in section 5 explicitly models sequential aspects of a process of interactive decision making. In section 6, we emphasize that what we are proposing is a language to formulate models and not yet a model or theory. The language as such is mostly devoid of empirical content. However, the traditional utility maximization approach does no better in that regard. As we shall indicate, it merely nurtures a delusion of analytical power and predictive content without in fact delivering on its promise. A bounded rationality approach, on the other hand, does not support such illusions. Conclusions follow in section 7. 2. Language Tools for Model Building There are i 1,2,..., n participants who are involved in an objective situation of the same structure as G. Assume that each participant i 1,2,..., n is aware of the number of others also involved. Let us assume, too, that there is a strategy set for each of the actors as well as a representation for the stochastic aspects of the interaction. Let us further make the rather daring assumption that each actor imagines only sets of strategies and sets of chance moves that are in fact subsets of the sets in G (i.e., all primed variables are elements of the sets to which the underlying variables belong). Finally, assume that each of the i 1,2,..., n participants “subjectively” anticipates (is of the opinion) that she cannot control any chance move z ' Z she might imagine the strategy constellation fixed by her co-players . s' i s'1,...,s'i1,s'i1,...,s'n S j j i j i Being involved in an objective situation of the type G, each participant i 1,2,..., n must decide which scenarios (',szij ')( XSZ ) she takes into account in forming her mental model of the ji situation. Each participant or – in more familiar parlance – player i 1,2,..., n forms her idiosyncratic set of “relevant possibilities” or “scenarios,” i.e., a set i with x SxZj and the interpretation ji that (sz 'ii , ') if and only if i does not rule out (sz 'i , ') . 3 Although we often simplify in a rather daring way as well, the underlying assumptions are not constitutive or defining characteristics of our language.