Theory of conditional games

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<ul><li><p>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</p><p>Journal of Economic MethodologyPublication details, including instructions for authors andsubscription information:</p><p>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.</p><p>To cite this article: Don Ross (2014) Theory of conditional games, Journal of EconomicMethodology, 21:2, 193-198, DOI: 10.1080/1350178X.2014.910936</p><p>To link to this article:</p><p>PLEASE SCROLL DOWN FOR ARTICLE</p><p>Taylor &amp; Francis makes every effort to ensure the accuracy of all the information (theContent) contained in the publications on our platform. However, Taylor &amp; Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor &amp; Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to orarising out of the use of the Content.</p><p>This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &amp;Conditions of access and use can be found at</p><p></p></li><li><p>BOOK REVIEWS</p><p>Team choice formalized</p><p>Theory of conditional games, by Wynn C. Stirling, New York, Cambridge University</p><p>Press, 2012, XIII 236 pp., $101.00 (hc), ISBN 978-1-107-01174-8</p><p>Critics of applications of game theory in social modeling (e.g. Gilbert, 2008; Hollis, 1998)</p><p>sometimes claim that it rests on problematically individualistic foundations. If this charge</p><p>is taken to mean that players in games must be interpreted as caring exclusively about their</p><p>own well-being, then it is simply false; there is no challenge to writing down a utility</p><p>function for a player i according to which is utility is increasing in another agent js</p><p>welfare. A more interesting version of the criticism is that the concept of agency in</p><p>applications of game theoretic models is scale-free: individual players are the only loci of</p><p>utility functions, and thus remain the only sites of agency as games are scaled up to model</p><p>increasingly complex and dynamic social interactions. Game theorists should indeed</p><p>respond to this criticism by asking how their mathematics can be extended to</p><p>accommodate the fact that collective agency, as an empirical matter, is often, or even</p><p>typically, not linearly composed from the agency of individual people; nor, more radically,</p><p>can collective choices always be identified with equilibria in games among their individual</p><p>members where no preferences except the individuals preferences are considered.</p><p>Corporations, for example, often have objectives that are neither aggregations of the</p><p>objectives of the individual people that work for them, nor mere strategic compromises</p><p>resulting from the bargaining of managers and employees; and these corporate-revealed</p><p>preferences often have more influence on the dynamics of individual managers and</p><p>employees-revealed preferences than vice-versa.</p><p>The best known response to this challenge has consisted in accounts of team reasoning</p><p>(Bacharach, 2006; Sugden, 1993, 2000, 2003). In these models, agents can move back and</p><p>forth between evaluating strategy choices in games from the perspective of their individual</p><p>utility functions, and also from the perspective of utility functions they associate with</p><p>teams to which they belong. Motivations for such modeling are based on interpretations of</p><p>observed human behavior, both casual and scientific.</p><p>On the casual front, members of sports teams typically claim to act so as to optimize</p><p>victory prospects rather than their own milestones, and their actions often appear to bear</p><p>out these claims. Though this is the most common example of a situation that exemplifies</p><p>team reasoning, it is far from decisive. Perhaps players of team sports simply generally</p><p>derive highest individual utility from winning. Furthermore, such players risk social</p><p>sanctioning if they are suspected of selfish play, so could be interpreted as responding to</p><p>individual costs. Soldiers in battle furnish a more convincing field of examples. It is widely</p><p>agreed that although most non-professional soldiers will behave in strongly risk-averse</p><p>ways until their platoon-sized units are directly threatened, heroic responses are common</p><p>in defense of buddies. Thus it is suggested that such soldiers show dispositions to frame</p><p>their agency in different ways under different circumstances.</p><p>On the scientific front, we can consider evidence that majorities of laboratory subjects,</p><p>put into sequences of games with non-repeating partners that have the structure of one-shot</p><p>Prisoners Dilemmas (PDs), usually begin by cooperating but then switch to defection as</p><p>Journal of Economic Methodology, 2014</p><p>Vol. 21, No. 2, 193207</p><p>Dow</p><p>nloa</p><p>ded </p><p>by [</p><p>Uni</p><p>vers</p><p>ity o</p><p>f C</p><p>hica</p><p>go L</p><p>ibra</p><p>ry] </p><p>at 2</p><p>3:06</p><p> 15 </p><p>Nov</p><p>embe</p><p>r 20</p><p>14 </p></li><li><p>sequences progress (Ledyard, 1995). In Bacharachs model of this behavior, such subjects</p><p>tend to initially deploy team reasoning frames, under which they face not PDs, where</p><p>defection is the unique equilibrium strategy, but rather assurance games, which include</p><p>Pareto-dominant cooperative equilibrium vectors. But, according to the hypothesis, such</p><p>team framing is undermined by minorities who adopt individual agent frames and</p><p>therefore enjoy defectors profits at the expense of cooperators. Learning about the</p><p>existence of such defectors gives rise to cascade processes in which accelerating</p><p>proportions of subjects switch to individual framing in the later games, until almost all</p><p>have converged on modeling their interactions as PDs and therefore choose defection. This</p><p>example is particularly useful for Bacharach because it can be taken as illustrating not only</p><p>team reasoning per se, but also the kind of frame-switching between individual and team</p><p>agency that constitutes his core empirical hypothesis about human behavior.</p><p>In Ross (2014) I argue in favor of modeling team choice or team agency rather than</p><p>team reasoning. This is to distance myself from Bacharachs (2006) view that team</p><p>framing is recommended by a normative theory of solution concept refinement. Without</p><p>such refinement, Bacharach argues, agents have no basis for converging on Pareto-</p><p>dominant solutions in Hi-lo games. My skepticism about this argument derives from</p><p>naturalistic scruples over using philosophical rationality criteria to drive axiomatization in</p><p>game theory. But whether or not someone thinks that game theory ought to incorporate a</p><p>conviction that agents should converge on dominant payoffs in Hi-lo games, people in</p><p>experimental situations designed to reflect Hi-lo models do find these payoffs, and so this</p><p>tendency should be endogenous in game-theoretic models of people. We need not be</p><p>dissatisfied with Nash equilibrium as a general solution concept in order to be interested in</p><p>a mathematical account of team-centered choice. Peoples choices indeed continuously</p><p>reveal preferences that appear to be conditional on the welfare of groups with which they</p><p>contingently identify their agency. We will only be able to model the structures of such</p><p>preferences for example, to estimate risk-sensitivity coefficients associated with them,</p><p>which might differ from risk-sensitivity coefficients expressed when people frame</p><p>themselves as acting alone if we can write down conditional utility functions that can</p><p>provide the basis for behavioral identification. Thus even if we are not convinced by</p><p>Bacharach that we should want a direct game-theoretic account of team reasoning </p><p>though surely anyone should be interested in a psychological theory of partial agency</p><p>fusion we still have solid grounds for wanting a game-theoretic account of choice</p><p>conditional on the existence of a team, and furthermore for wanting this theory to be</p><p>unified with the standard game-theoretic account of equilibration among maximizers of</p><p>expected individual utility.</p><p>Provision of such a theory is the task taken up in Wynn Stirlings (2012) elegantly</p><p>constructed book. It must be pointed out immediately that Stirling does not cite Bacharach</p><p>or any of the preceding and subsequent supporting work by Sugden. I am thus using the</p><p>occasion of the present review to set Stirlings work in the wider context which, in my</p><p>opinion, provides its greatest potential source of value, at least to theorists. Bacharachs</p><p>(posthumous) book, though widely cited, has so far had little impact in the game theory</p><p>literature, due (I speculate) to its largely informal approach. Stirlings book, which is</p><p>developed mathematically following an opening verbal chapter that sets out motivations</p><p>and intuitions, will likely find a more receptive audience among game theorists, but if read</p><p>in isolation from Bacharachs work might not attract the attention it merits from</p><p>researchers who apply game theory to human behavior.</p><p>Stirlings objective is to develop a formalization of group preference that is not based</p><p>on unidirectional aggregation of individual preferences, but yields representation of</p><p>Book Reviews194</p><p>Dow</p><p>nloa</p><p>ded </p><p>by [</p><p>Uni</p><p>vers</p><p>ity o</p><p>f C</p><p>hica</p><p>go L</p><p>ibra</p><p>ry] </p><p>at 2</p><p>3:06</p><p> 15 </p><p>Nov</p><p>embe</p><p>r 20</p><p>14 </p></li><li><p>individual preference as a limiting case. What makes this an ambitious undertaking is the</p><p>constraint Stirling imposes of not treating group preferences as exogenous social facts.</p><p>Intuitively, the problem space Stirling assigns himself might seem to be constricted to</p><p>nothing: how can group preferences arise endogenously given individual preferences and</p><p>social relations, but not be functional aggregates of individual preferences and, in</p><p>consequence, be undone by Arrows (1951) impossibility theorem? Stirlings trick arises</p><p>from his recognizing that agents can choose strategies that reveal conditional preferences</p><p>reflecting assessments of comparative consequences for group dynamics of different</p><p>hypothetical choice vectors; and these assessments can themselves result from game-</p><p>theoretic analysis. What gets the rabbit out of the hat, in short, is recursion. Theoretical</p><p>unification can then be achieved by constructing unconditional preference as a limiting</p><p>case of conditional preference. (In some appropriate applications, we could regard</p><p>unconditional preferences as those that people act so as to maximize without sensitivity to</p><p>information about others preferences.) In that context, in turn, implications for</p><p>equilibrium solutions can be formally investigated.</p><p>I will describe the basic intuition by reference to toy scenarios. Stirling cites Keeney</p><p>and Raiffas (1976) example of an imaginary farmer who postpones formation of an</p><p>individual preference ordering over different possible plots of land he might purchase until</p><p>he gets information about his wifes preferences. His preferences, that is to say, are</p><p>conditional on hers; but clearly this need not entail that he simply plans to adopt whatever</p><p>his wifes preferences turn out to be. A limitation of this kind of example is that it invites</p><p>us to ignore the possibility of conflict, especially if we are prone to romantic images of</p><p>frictionless harmony, of the kind that motivate and simultaneously impair the prospects for</p><p>some marriages. Ross (2014) proposes a richer illustration. Consider a Board of Directors</p><p>that must decide whether to embark on a risky takeover bid. Compare two hypothetical</p><p>processes by which views of Board members are elicited. In process (i) the Chair sends out</p><p>a prior agenda with attached analyses of the alternatives. In process (ii) she circulates the</p><p>same analyses, but citing concerns around security does so only after the members have</p><p>assembled in the boardroom. An experienced executive will recognize that her choice</p><p>between these processes might have a determining influence on the outcome. Process (i)</p><p>encourages Board members to form unconditional preferences they will bring into the</p><p>meeting and defend against one anothers arguments. Process (ii) may lead instead to their</p><p>monitoring one another while they decide which option is best. In both processes differing</p><p>individual preferences are likely to be expressed through non-unanimous votes. But the</p><p>distribution of these preferences might vary across the two cases because process (ii)</p><p>encourages revelation of preferences that are influenced by information about the</p><p>preferences of (particular) others, and can thus be better calibrated for their effects on</p><p>subsequent corporate governance dynamics.</p><p>The foregoing example implicates two distinct ideas, each of which must be</p><p>successfully formalized in the course of developing a full formalization of team choice. The</p><p>first idea is conditional preference itself: some preferences may stabilize only given</p><p>information about particular preferences of particular others. The second is what Stirling</p><p>calls concordance. This refers to the extent of controversy or discord within a group that its</p><p>members perceive to be implied by a given set of (conditional or unconditional) preferences.</p><p>As illustrated by the example of the Board of Directors, human decision-makers might be</p><p>expected to have preferences driven by these expectations, which themselves will typically</p><p>be based on appreciation of expected distributions of conditional preferences. Stirlings</p><p>opening chapters formalize these two ideas. At this stage of the book some readers may</p><p>worry that the mission is under-constrained: what would distinguish a successful</p><p>Book Reviews 195</p><p>Dow</p><p>nloa</p><p>ded </p><p>by [</p><p>Uni</p><p>vers</p><p>ity o</p><p>f C</p><p>hica</p><p>go L</p><p>ibra</p><p>ry] </p><p>at 2</p><p>3:06</p><p> 15 </p><p>Nov</p><p>embe</p><p>r 20</p><p>14 </p></li><li><p>formalization from an unsuccessful one except appeal to conceptual intuitions? The answer</p><p>to this worry becomes clear when one considers the work of subsequent chapters. The</p><p>enterprise is disciplined by Stirlings commitment to ensuring that hi...</p></li></ul>