Conditional Game Theory As a Model for Coordinated Decision Making

Conditional Game Theory as a Model for Coordinated Decision Making Wynn C. Stirling1 and Luca Tummolini2 1Department of Electrical and Computing Engineering, Brigham Young University, Provo, Utah, U.S.A. 2Institute of Cognitive Sciences and Technologies, Italian National Research Council, Rome, Italy Keywords: Game Theory, Coordination, Social Influence, Social Utility, Network Theory. Abstract: Standard game theory is founded on the premise that choices in interactive decision situations are strategically rational—best reactions to the expected actions of others. However, when studying groups whose members are responsive to one another’s interests, a relevant notion of behavior is for them to coordinate in the pursuit of coherent group behavior. Conditional game theory provides a framework that facilitates the study of coordinated rational behavior of human social networks and the synthesis of artificial social influence networks. This framework comprises three elements: a socialization model to characterize the way individual preferences are defined in a social context; a diffusion model to define the way individual preferences propagate through the network to create an emergent social structure; and a deduction model that establishes the structure of coordinated individual choices. 1 INTRODUCTION An important class of collectives comprises entities that possess the ability to respond to the social Coordinated decision making is one of the fundamen- influence that they exert on one another. Examples in- tal attributes of intelligent behavior. Indeed, the word clude cooperative groups, such as teams and business intelligent comes from the Latin roots inter (between) entities, mixed organizations such as families, which + legere˘ (to choose). Accordingly, much effort has can encompass both cooperative and conflictive influ- been devoted to defining what it means for a choice to ence, and adversarial groups such as tennis players be “rational.” And appending the modifier “coordina- who exert conflictive influence on each other. Team ted” adds a level of complexity that moves beyond the members coordinate by cooperating in the pursuit of hypothesis that each of the individual decision makers a common goal, business partners coordinate by di- should behave as if it were solving a constrained max- viding the labor, family members coordinate by re- imization problem without overt regard for the wel- specting (or not) each other’s opinions and priorities, fare of others. and tennis players (an anti-team?) coordinate by op- Coordination, as used in this paper, has a precise posing each other in some systematic way. meaning, as expressed by the Oxford English Dictio- In terms of overall functionality, it is often the case nary: that the propensity of a group to coordinate is more [To coordinate is] to place or arrange (things) relevant than the propensity of the individuals to op- in proper position relative to each other and to timize. It is more relevant for a team to win the game the system of which they form parts; to bring than for each player to maximize the number of points into proper combined order as parts of a whole he or she scores. It is more relevant for a business (Murray et al., 1991). entity to settle on a productive division of labor than Coordination is a principle of behavior on a paral- for each partner to maximize individual control. It is lel with, but different from, performance. Individuals more relevant for a family to function in a civil and perform; the group coordinates. Performance deals equitable way than for the members to focus exclu- with operational measures of efficiency and effecti- sively on what is individually best for themselves. It veness of individual behavior in terms of individual is more relevant to the conducting of a war for each payoffs. Coordination, however, is an attribute of or- opponent to seek victory rather than simply to destroy ganizational structure regarding how the members of as many enemy resources as possible. a group function together. Focusing on performance without considering 295 Stirling, W. and Tummolini, L. Conditional Game Theory as a Model for Coordinated Decision Making. DOI: 10.5220/0006956702950302 In Proceedings of the 10th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2018) - Volume 2: KEOD, pages 295-302 ISBN: 978-989-758-330-8 Copyright © 2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved KEOD 2018 - 10th International Conference on Knowledge Engineering and Ontology Development coordination is an incomplete characterization of influenced by the preferences of others. The first con- group behavior. Similarly, focusing on coordination dition is the usual scenario for standard game theory, without considering performance is an incomplete but the second condition introduces a social compo- characterization of individual behavior. A football nent that is not explicitly modeled by the standard the- team may possess the organizational structure requi- ory. With a social influence network, there can be a red to win the game, but that structure is useless if difference between what constitutes rational behavior the players do not attempt to maximize the number of when viewing the anticipated behavior of others as a goals scored. A business firm may be well organized constraint on the pursuit of narrow self-interest (e.g., in terms of individual responsibilities, but unless the material benefit) and what constitutes rational beha- partners exert control, the entity will not prosper. A vior from a socially oriented perspective of viewing family may possess fair and equitable rules of con- oneself as a part of a coordinated whole—a society. duct but will still be dysfunctional if the members do Thus, the ability of the individuals to make their choi- not pursue their individual goals within that context. ces in a way that responds to social influence, while Tennis players may collectively understand the rules at the same time retaining their individuality and con- and best practices of the game, but unless each is able cern for their own welfare, is of prime importance. to execute those practices, playing the game will be This position paper argues that conditional game unrewarding. Coordination without performance is theory, introduced by (Stirling, 2012) and (Stirling unproductive, and performance without coordination and Felin, 2013), provides a framework within which is equivocal. A full understanding of the functiona- to model social influence networks. Conditional game lity of a group requires the assessment of both attri- theory comprises three components: a socialization butes. Coordination occurs when individual contri- mechanism by which indviduals may incorporate the butions appropriately fit together to form a coherent interests of others into their own self-interest without organizational structure. compromising their individuality; a diffusion mecha- Coordination requires individuals to possess some nism by which the preferences resulting from an ex- notion of social connectivity in addition to concerns panded view of self-interest can be conglomerated to for their own material welfare. There are two extreme produce a comprehensive social model that accounts methodologies for incorporating coordination into a for all social interrelationships; and a deduction me- multilateral decision scenario. One way is for the par- chanism by which coordinated individual decisions ticipants to come to a social engagement with a global may be deduced from the social model. A criti- view of the way the group is intended to behave. Un- cal feature of this theory is that it is consistent with der this view, coordination is built-in: Each partici- the fundamental assumptions of game theory; in fact, pant performs its ex ante assigned part. Another way conventional noncooperative game theory is a special is for participants to come to the engagement with lo- case of this extended theory. cal views of how they will behave as they interact with others. Under this view, coordination is emergent: It occurs (or not) as each participant responds to the so- 2 SOCIALIZATION cial influence exerted by others. We argue that the latter approach is the appropriate way to design a col- With conventional game theory, preferences are lective of autonomous decision makers (agents), and categorical—fixed, immutable, and unconditional. present a general framework for the analysis of human The mathematical mechanism used to express cate- social networks and the design and synthesis of artifi- gorical preferences is a payoff function. Given a col- cially intelligent networks. For coordination to be de- lective of agents X ,...,X for n 2, let A denote signed into such a network, however, the social relati- { 1 n} ≥ i a finte set of actions for Xi, and let the Cartesian pro- onships must be defined operationally—they must be duct set A = A A denote the outcome set. characterized via mathematical expressions that ex- 1 × ··· × n The function ui: A R quantifies the payoff to Xi as a plicitly model social influence. function of the combined→ actions of the collective. Of A social influence network comprises a group of course, Xi is free to define its preferences in whatever agents whose choices can depend on the attitudes and way it chooses, be it egocentric, altruistic, or other. opinions of others as well as their own welfare. More Once defined, ui is the formal expression of Xi’s no- precisely, it is a collective of agents

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