Theory of conditional games

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  • This article was downloaded by: [University of Chicago Library]On: 15 November 2014, At: 23:06Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

    Journal of Economic MethodologyPublication details, including instructions for authors andsubscription information:

    Theory of conditional gamesDon Rossaba School of Economics, University of Cape Town, Private Bag,Rondebosch 7701, Cape Town, South Africab Center for Economic Analysis of Risk J. Mack Robinson School ofBusiness, Georgia State University, 35 Broad Street NW, Atlanta30303, GeorgiaPublished online: 23 Apr 2014.

    To cite this article: Don Ross (2014) Theory of conditional games, Journal of EconomicMethodology, 21:2, 193-198, DOI: 10.1080/1350178X.2014.910936

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    Team choice formalized

    Theory of conditional games, by Wynn C. Stirling, New York, Cambridge University

    Press, 2012, XIII 236 pp., $101.00 (hc), ISBN 978-1-107-01174-8

    Critics of applications of game theory in social modeling (e.g. Gilbert, 2008; Hollis, 1998)

    sometimes claim that it rests on problematically individualistic foundations. If this charge

    is taken to mean that players in games must be interpreted as caring exclusively about their

    own well-being, then it is simply false; there is no challenge to writing down a utility

    function for a player i according to which is utility is increasing in another agent js

    welfare. A more interesting version of the criticism is that the concept of agency in

    applications of game theoretic models is scale-free: individual players are the only loci of

    utility functions, and thus remain the only sites of agency as games are scaled up to model

    increasingly complex and dynamic social interactions. Game theorists should indeed

    respond to this criticism by asking how their mathematics can be extended to

    accommodate the fact that collective agency, as an empirical matter, is often, or even

    typically, not linearly composed from the agency of individual people; nor, more radically,

    can collective choices always be identified with equilibria in games among their individual

    members where no preferences except the individuals preferences are considered.

    Corporations, for example, often have objectives that are neither aggregations of the

    objectives of the individual people that work for them, nor mere strategic compromises

    resulting from the bargaining of managers and employees; and these corporate-revealed

    preferences often have more influence on the dynamics of individual managers and

    employees-revealed preferences than vice-versa.

    The best known response to this challenge has consisted in accounts of team reasoning

    (Bacharach, 2006; Sugden, 1993, 2000, 2003). In these models, agents can move back and

    forth between evaluating strategy choices in games from the perspective of their individual

    utility functions, and also from the perspective of utility functions they associate with

    teams to which they belong. Motivations for such modeling are based on interpretations of

    observed human behavior, both casual and scientific.

    On the casual front, members of sports teams typically claim to act so as to optimize

    victory prospects rather than their own milestones, and their actions often appear to bear

    out these claims. Though this is the most common example of a situation that exemplifies

    team reasoning, it is far from decisive. Perhaps players of team sports simply generally

    derive highest individual utility from winning. Furthermore, such players risk social

    sanctioning if they are suspected of selfish play, so could be interpreted as responding to

    individual costs. Soldiers in battle furnish a more convincing field of examples. It is widely

    agreed that although most non-professional soldiers will behave in strongly risk-averse

    ways until their platoon-sized units are directly threatened, heroic responses are common

    in defense of buddies. Thus it is suggested that such soldiers show dispositions to frame

    their agency in different ways under different circumstances.

    On the scientific front, we can consider evidence that majorities of laboratory subjects,

    put into sequences of games with non-repeating partners that have the structure of one-shot

    Prisoners Dilemmas (PDs), usually begin by cooperating but then switch to defection as

    Journal of Economic Methodology, 2014

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  • sequences progress (Ledyard, 1995). In Bacharachs model of this behavior, such subjects

    tend to initially deploy team reasoning frames, under which they face not PDs, where

    defection is the unique equilibrium strategy, but rather assurance games, which include

    Pareto-dominant cooperative equilibrium vectors. But, according to the hypothesis, such

    team framing is undermined by minorities who adopt individual agent frames and

    therefore enjoy defectors profits at the expense of cooperators. Learning about the

    existence of such defectors gives rise to cascade processes in which accelerating

    proportions of subjects switch to individual framing in the later games, until almost all

    have converged on modeling their interactions as PDs and therefore choose defection. This

    example is particularly useful for Bacharach because it can be taken as illustrating not only

    team reasoning per se, but also the kind of frame-switching between individual and team

    agency that constitutes his core empirical hypothesis about human behavior.

    In Ross (2014) I argue in favor of modeling team choice or team agency rather than

    team reasoning. This is to distance myself from Bacharachs (2006) view that team

    framing is recommended by a normative theory of solution concept refinement. Without

    such refinement, Bacharach argues, agents have no basis for converging on Pareto-

    dominant solutions in Hi-lo games. My skepticism about this argument derives from

    naturalistic scruples over using philosophical rationality criteria to drive axiomatization in

    game theory. But whether or not someone thinks that game theory ought to incorporate a

    conviction that agents should converge on dominant payoffs in Hi-lo games, people in

    experimental situations designed to reflect Hi-lo models do find these payoffs, and so this

    tendency should be endogenous in game-theoretic models of people. We need not be

    dissatisfied with Nash equilibrium as a general solution concept in order to be interested in

    a mathematical account of team-centered choice. Peoples choices indeed continuously

    reveal preferences that appear to be conditional on the welfare of groups with which they

    contingently identify their agency. We will only be able to model the structures of such

    preferences for example, to estimate risk-sensitivity coefficients associated with them,

    which might differ from risk-sensitivity coefficients expressed when people frame

    themselves as acting alone if we can write down conditional utility functions that can

    provide the basis for behavioral identification. Thus even if we are not convinced by

    Bacharach that we should want a direct game-theoretic account of team reasoning

    though surely anyone should be interested in a psychological theory of partial agency

    fusion we still have solid grounds for wanting a game-theoretic account of choice

    conditional on the existence of a team, and furthermore for wanting this theory to be

    unified with the standard game-theoretic account of equilibration among maximizers of

    expected individual utility.

    Provision of such a theory is the task taken up in Wynn Stirlings (2012) elegantly

    constructed book. It must be pointed out immediately that Stirling does not cite Bacharach

    or any of the preceding and subsequent supporting work by Sugden. I am thus using the

    occasion of the present review to set Stirlings work in the wider context which, in my

    opinion, provides its greatest potential source of value, at least to theorists. Bacharachs

    (posthumous) book, though widely cited, has so far had little impact in the game theory

    literature, due (I speculate) to its largely informal approach. Stirlings book, which is

    developed mathematically following an opening verbal chapter that sets out motivations

    and intuitions, will likely find a more receptive audience among game theorists, but if read

    in isolation from Bacharachs work might not attract the attention it merits from

    researchers who apply game theory to human behavior.

    Stirlings objective is to develop a formalization of group preference that is not based

    on unidirectional aggregation of individual preferences, but yields representation of

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  • individual preference as a limiting case. What makes this an ambitious undertaking is the

    constraint Stirling imposes of not treating group preferences as exogenous social facts.

    Intuitively, the problem space Stirling assigns himself might seem to be constricted to

    nothing: how can group preferences arise endogenously given individual preferences and

    social relations, but not be functional aggregates of individual preferences and, in

    consequence, be undone by Arrows (1951) impossibility theorem? Stirlings trick arises

    from his recognizing that agents can choose strategies that reveal conditional preferences

    reflecting assessments of comparative consequences for group dynamics of different

    hypothetical choice vectors; and these assessments can themselves result from game-

    theoretic analysis. What gets the rabbit out of the hat, in short, is recursion. Theoretical

    unification can then be achieved by constructing unconditional preference as a limiting

    case of conditional preference. (In some appropriate applications, we could regard

    unconditional preferences as those that people act so as to maximize without sensitivity to

    information about others preferences.) In that context, in turn, implications for

    equilibrium solutions can be formally investigated.

    I will describe the basic intuition by reference to toy scenarios. Stirling cites Keeney

    and Raiffas (1976) example of an imaginary farmer who postpones formation of an

    individual preference ordering over different possible plots of land he might purchase until

    he gets information about his wifes preferences. His preferences, that is to say, are

    conditional on hers; but clearly this need not entail that he simply plans to adopt whatever

    his wifes preferences turn out to be. A limitation of this kind of example is that it invites

    us to ignore the possibility of conflict, especially if we are prone to romantic images of

    frictionless harmony, of the kind that motivate and simultaneously impair the prospects for

    some marriages. Ross (2014) proposes a richer illustration. Consider a Board of Directors

    that must decide whether to embark on a risky takeover bid. Compare two hypothetical

    processes by which views of Board members are elicited. In process (i) the Chair sends out

    a prior agenda with attached analyses of the alternatives. In process (ii) she circulates the

    same analyses, but citing concerns around security does so only after the members have

    assembled in the boardroom. An experienced executive will recognize that her choice

    between these processes might have a determining influence on the outcome. Process (i)

    encourages Board members to form unconditional preferences they will bring into the

    meeting and defend against one anothers arguments. Process (ii) may lead instead to their

    monitoring one another while they decide which option is best. In both processes differing

    individual preferences are likely to be expressed through non-unanimous votes. But the

    distribution of these preferences might vary across the two cases because process (ii)

    encourages revelation of preferences that are influenced by information about the

    preferences of (particular) others, and can thus be better calibrated for their effects on

    subsequent corporate governance dynamics.

    The foregoing example implicates two distinct ideas, each of which must be

    successfully formalized in the course of developing a full formalization of team choice. The

    first idea is conditional preference itself: some preferences may stabilize only given

    information about particular preferences of particular others. The second is what Stirling

    calls concordance. This refers to the extent of controversy or discord within a group that its

    members perceive to be implied by a given set of (conditional or unconditional) preferences.

    As illustrated by the example of the Board of Directors, human decision-makers might be

    expected to have preferences driven by these expectations, which themselves will typically

    be based on appreciation of expected distributions of conditional preferences. Stirlings

    opening chapters formalize these two ideas. At this stage of the book some readers may

    worry that the mission is under-constrained: what would distinguish a successful

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  • formalization from an unsuccessful one except appeal to conceptual intuitions? The answer

    to this worry becomes clear when one considers the work of subsequent chapters. The

    enterprise is disciplined by Stirlings commitment to ensuring that hi...