Chapter 5
Moves, Tactics, and Strategies Defined and Played in Epinets
We extend the use of epinets to the characterization of dynamic network processes. We use them in two distinct ways: first, as instruments for specifying changes in the epistemic states of linked or interacting agents and, second, as a tool kit for representing strategic interactions. Using epinets to represent interactions among epistemically linked agents allows us to resolve ambiguities inherent in game-theoretic approaches and to explicitly model subtle phenomena such as mind games, dialogical games, and information brokerage games.
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We have thus far dealt with the structure of epinets: who knows what, who knows whom, what is known to be known by whom, and so on. We have examined network-level phenomena such as brokerage and closure through an epistemic lens, affording insight into the individual, collective, and interactive belief and knowledge structures that enable cohesion, co-mobilization, and coordination. We also have extended the epinet concept to show how an agent’s status can be textured and refined using the epistemic states of networked agents as important qualifiers. As noted, trust is tricky: it requires the deployment of a special kind of epistemic logic that relies on subjunctive propositional forms to characterize a trust-based relationship in a noncircular way.
Our project required that we make some nontrivial departures from the lexicon of epistemic game theory: we replaced “semantic” state spaces comprising events (collections of states of the world) in favor of “syntactic” state spaces comprising truth-functional propositions and their interpretations. We relinquished often-deployed assumptions of completeness and commonality of the resulting propositional state spaces in order to accommodate intuitive epistemic states such as ignorance and oblivion. In doing so, we gained an epistemic modeling language for network phenomena that tracks the subjective experience and intuition of networked agents. This made it possible to “measure” epinets via tools such as questionnaires and surveys; at the same time, it made it possible for us to build and test models of the correlates of different degrees of epistemic cohesion and sharedness and of trust within a network.
It is true that the resulting models do not have the well-behaved “equilibrium” features of game-theoretic models or the simplicity of structure-disturbance-action-performance explanations of standard social network analyses; however, they do lay bare the hidden epistemic content of a network, which in many cases is what makes its inner world turn. What, however, about the dynamics of epinets?
From Structure to Dynamics: Epinets as Trackers of Epistemic State Changes
We have inherited at least two different conceptions (along with associated imagery) of the informational dynamics of networks. One is the strategicagentic view: human agents make decisions based on information they use to update their existing beliefs and on objectives they seek to maximize, conditional on the information they have and their own constraints of body, mind, time, and resources. Networks are quintessentially about interaction, and interaction is about interdependence. Thus, a theory of decisions with interdependent outcomes made by agents who are aware of these interdependencies is needed. And that is what game theory supplies, albeit, as we have argued, at a cost that we cannot afford: equilibrium, one of the key elements of game theory’s explanatory engine, is predicated on a number of epistemic preconditions that are not good descriptors of “what humans do” with their minds; they are also not reasonable assumptions about rational agents whose positive and negative introspection is less than perfect.
A second conception is the system-dynamic view of information as flowing through a network that resembles a cellular telecommunications system (minus the humans), the World Wide Web, or the biochemical signaling pathways of a complex neurological, enzymatic, or immunological subsystem—coupled to the automatic, rule-based behavior of the networked agents, whose states change as a function of information regarding changes in the states of other agents with whom they are linked. This is a “passive” view of the informational dynamics of networks because information conveyance is not purposefully corrupted, it has no higher-order effects (such as the establishment of mutual and common knowledge) and it determines the behavior of the agents receiving it.
In spite of the (largely emergent) complexity of these models of network dynamics (Watts and Strogatz 1998; Albert and Barabási 2002), the interaction rules and agent-level (node-level) decision, action, and tie formation rules that govern their evolution are mechanical, simple, and often deterministic, which raises questions about the degree to which the resulting dynamics represent networks of human agents endowed with considerably more insight and intelligence—even if they are less reliable in the implementation of action plans. Network epistemics—the part of our modeling approach that relates to the nature, structure, and spread of information within a network—can significantly advance the degree to which modelers of social network dynamics can incorporate into their models “who-knows-what-and-whom-when” insights and data that can be used to tailor their models’ governing assumptions.
In view of these options, we are in the predicament of navigating our modeling enterprise between the Scylla of the “unbounded rationality” of game-theoretic models to derive equilibrium results on the basis of what rational agents need to know to converge to an equilibrium set of strategies (albeit at the pain of assuming they know too much), and the Charybdis of the “mechanistic social action” used by network theorists to make predictions about the evolution of collective processes in social networks (albeit at the cost of assuming that human agents either know too little or can do too little with what they know).
The epinet approach facilitates this tricky passage. It broadens the set of epistemic conditions placed on networked agents ex ante by rational choice and game-theoretic approaches, and it allows us to incorporate subtle and important epistemic states as descriptors of what agents know—including confidence, trust, and oblivion—while at the same time permitting incomplete and incommensurate state spaces among individual agents. It allows the incorporation of inferential moves and logics that represent what agents can do with what they know more loyally than either the ‘logically omniscient’ approaches of game theory or the mechanized models of network dynamics.
More important, this approach allows the dynamic evolution of epistemic conditions within a network—from oblivion into knowledge and awareness, or from trust into its opposite (as we saw in Chapter 4)—as a function of individual agents’ actions. Epinets allow us to track both the ways in which agents learn to change their behavior by virtue of new information and the ways in which they proactively shape the informational and epistemic landscape of the network as a whole.
In this chapter, we illuminate what happens to the traditional concerns of modelers of many different persuasions about describing, explaining, and predicting the dynamics of social interactions among networked agents. If the modeling language of epinets is to be truly useful as an explanation-generating engine and modeling tool, then it should serve as a source of both explanatory concepts akin to those of game theory (equilibrium, subgame perfection, learning) and predictions regarding network dynamics (topological structure, asymptotic evolution of centrality measures, probability of finding at least n agents that have at most k ties to other agents under certain assumptions). To show that this is possible, we break down the core discipline of using epinets to measure social networks, map out different information and epistemic regimes within them, and specify a range of epistemic moves and strategies that agents can use to bring change to the structure of their epinets.
Specifying and Measuring Epinets
Specifying an epinet entails articulating the agents that make up the network or subnetwork of interest along with the epinet’s individual, collective, and interactive epistemic states. True to the primitives of the EDL introduced in Chapter 2 (e.g., Figure 2.1), this involves specifying not only agents but also the truth-bearing statements—the “propositions”—that constitute the basis for the epinet. Propositions admit different interpretations that may be specific to the epinet’s agents. For instance, if P = Agent A 1 was at a lunch with 30 other people, seated at five tables at which [famous person X] was present, one interpretation may be that A 1 had lunch with X; an alternative interpretation may be that A1 was in the same room with X. These are both viable interpretations of P because they may be considered true if P is true, but it is not the case that P is considered true if they are true. They are partial or distorted representations of P.
To ascertain differences among interpretations, we can examine differences in their material and logical implications, as well as differences between these implications and the implications of P. For instance, having had lunch with X suggests a level of familiarity and access to X that may entail being able to introduce A 2 to X or being able to ask a specific and personal favor of X, which P may not necessarily entail and which is certainly not entailed by an interpretation of P as having been in the same room with X for 90 minutes.
The first step in specifying an epinet is determining an identifiable set of agents, an epistemic core (a set of relevant propositions that to various degrees are known, believed, known to be known and believed, and so on, by the agents), and a set of individual epistemic states. In the foregoing example, depicted in Figure 5.1, agents A1 and A3 know some interpretation of P and are aware of knowing that interpretation (they know they know it); A2 is oblivious of both P and its different interpretations (she does not know it and does not know she does not know it); A3 and An are both knowledgeable and aware of a different interpretation of P (they know and know they know); whereas A4 knows the same interpretation of P that A3 and An know, but is not aware of knowing it (perhaps because she has temporarily forgotten it).
A network or subnetwork defined by a set of high-density interactions or “close ties” may be characterized by an epistemic core (comprising propositions and their interpretations), and specification of agents and epistemic cores proceeds in a “bootstrapping fashion”: adding a proposition adds more agents, who in turn add more propositions, up to the point where additional agents do not add additional elements to the epistemic core and where additional propositions added to the epistemic core do not add additional agents. Alternatively, one can specify boundaries on the epistemic core of a network (a technical field of knowledge) and add agents according to the rule Who knows P? where P is some element in that core; or one can ex ante specify the set of agents (membership in some professional organization, department, or field of activity) and construct the set of propositions that are constitutive of those agents’ membership (related, for instance, to a set of common goals and principles).
FIGURE 5.1 Epinet of Networked Agents: Individual Epistemic States
Measuring Knowledge and Belief(s). “Measuring epinets” is well within the standard tool kit of networks researchers, but “measuring the epistemic cores” of the associated network is not. We can measure beliefs via questionnaires and surveys, provided that we take into account the possible effects of the phenomenon of “cheap talk,” the demand characteristic of distorting private information, and the information impact of using a survey instrument. An agent cannot be oblivious of a proposition that appears as a question on a survey because the instrument has made him aware of it, regardless of whether or not he knows its truth value or the answer to the question.
We can also measure the set of propositions that the agents in an epinet know or believe by deploying standard belief elicitation protocols that have been used in decision analysis for many years, via bets on the truth value of particular propositions: “How much will you bet on a lottery that pays $ X if P is true and $0 otherwise?” elicits a number, $Y, which can be used in conjunction with $X to measure an agent’s subjective degree of belief in the true value of P as p(P) = X/(X + Y). Of course, here, too, agents’ answers may not indicate true beliefs because “How much would you bet?” creates very different incentives from those created by “How much will you bet in this situation here and now?” Even when a “real” experiment can be conducted, the answer may vary as a function of the absolute values of X and Y and the subject’s risk and uncertainty preferences. Specifying an epinet’s epistemic core is, again, a bootstrapping process of ascription (Moldoveanu 2011) followed by experimentation: once a plausible epistemic structure is ascribed to the network, the hypotheses that emerge regarding what agents know can be tested.
Specifying Interactive Epistemic States. An epinet can be specified further by the addition of the interactive epistemic states of its agents vis-à-vis its epistemic core. Returning to our example as presented in Figure 5.2, A1 knows that A3 knows an interpretation of P that is different from his own (but the opposite is not the case), and A3’s interpretation of P is mutual knowledge (level 2 common knowledge [NC2]) between A3 and A4. This allows the modeler to make conjectures regarding certain interactions that could take place among subsets of agents on the basis of existing interactive epistemic conditions in the network: since mutual knowledge of a salient proposition or interpretation enables co-mobilization in scenarios in which joint outcomes depend on the truth value of that proposition, we can look for co-mobilization possibilities among the agents who share mutual knowledge of a salient proposition.
FIGURE 5.2 Epinet of Networked Agents: Interactive Epistemic States
Moreover, the epinet can be used as a “self-correction tool” for the modeler. If it becomes clear or plausible that A4 knows that A3 knows some interpretation of P, then we may not be able to consistently claim that A3 is not aware of that interpretation. The ascription of epistemic states can thus be revised recursively to maintain the coherence of the overall model. (Of course, coherence of the model of an epinet is not the same as coherence of the epistemic states of the agents being modeled: we can coherently model noncoherent epistemic states of networked agents, but that requires a set of assumptions about the informational and computational endowments of the agents that make up the epinet—in this case, a situation in which A4 acts as if she knows that A3 knows their shared interpretation of P, but does not act as if she knows that interpretation, which is a very special condition indeed.)
Epistemic Trails and Conductivity
Unlike energy, mass, momentum (at nonrelativistic speeds) and money (in the absence of inflation), information is not conserved: one agent’s passing of a bit of information to another agent does not cause the transmitter to lose that information. For this reason, information flows through networks are difficult to track in the same way that the flow of money and matter can be tracked (via tracking local changes created by a conservative exchange process). The modeling tool kit of epinets allows us to build real-time descriptions and predictive models of the information dynamics in teams, groups, organizations, or other collaboration and interaction networks.
Gossip, rumor mills, and information cascades are all processes by which social capital is exercised, amplified, extinguished, or wasted (Burt 2005). They can be used to study the echo of individual actions in groups or the bandwidth of the individual signals that are amplified by the informational rumor mills that interactions generate. What is needed to make the study of information propagation in networks as precise as that of strategic form games is a representation of information flows textured enough to make predictions about the nature, structure, and consequences of information-bearing signals passing through the network (in the form of gossip and rumor, for example).
Epinets track the flow of information among agents simply and intuitively via epistemic state changes among the agents in them. As proposition P propagates, the epistemic states of various agents vis-à-vis P change as P “makes the rounds”: an agent oblivious of P before being informed of it may come to know or believe P after some relevant interactions. P’s dissemination thus produces an epistemic trail (or “wake”) made up of changes in the epistemic states of networked agents vis-à-vis P.
An epistemic network may differentially conduct information-bearing signals passed among and between agents, and it is the function of trust ties (including conduits and corridors) to represent the information-carrying properties of social networks. Trust ties can be characterized (as in Chapter 4) using modal modifications of epistemic logic that yield subjunctive forms of the type Alice trusts Bob if she knows that if Bob knew P he would communicate it to her (trust in integrity) and/or Alice trusts Bob if she knows that if proposition P were true he would know it (trust in competence) or, combining the two forms, Alice trusts Bob if she knows that were P true he would communicate it to her.
Returning to our example, in Figure 5.3, a bidirectional trust link is introduced between agents A1 and A2 and between agents A3 and A4. Incorporating the trust links of these agent pairs completes the epinet. The inclusion of trust links and bridges allows us to predict the instantiation of preferential information flows within the network (who says what to whom and when) and the limits and boundaries of valid information flows.
FIGURE 5.3 Epinet of Networked Agents: Trust and Epistemic Links
Epistemic Dynamics of Trust
Because we use propositions to model epistemic states of agents and networks, we can examine the structures induced by already existing epistemic structures by looking at the consequences and implications of the states’ corresponding propositions. We saw an example of this in Chapter 4, where we showed that there are forms of trust that are transitive: A trusts C if A trusts B and B trusts C. The informational and social lubricant functions of trust can in turn be studied via epinets by mapping the epistemic structures that are induced by trust in relationships.
In Figure 5.4, the trust between agents A1 and A2 induces an epistemic structure in which each agent discloses fully to the other about proposition P, regarding which each has a different interpretation (stage 1), and about their private interpretations of it (stage 2). If P encodes a firm’s pattern of sales performance over the past three quarters that generates one interpretation, Sales have been relatively flat over the past eight quarters, and another, Sales have spiked rapidly over the past three quarters (which are both valid), then the trust link between A1 and A2 induces a (new) information structure in which the partial truths of the two interpretations are pooled and become distributed (and common) knowledge, along with the information set (proposition P) on which the interpretations are based.
FIGURE 5.4 Epinet of Epistemic Links across a Trustful-Trusting Tie
The epistemic wake that information leaves in a network is dependent on the trustworthiness of the information’s source. A pathological liar’s alerting me to the two-faced nature of my boss may not convince me that she is two-faced, but I will not henceforth be oblivious to the possibility that the liar is right. Alice’s telling Bob that he is about to be fired in a situation in which he was previously oblivious of the possibility changes Bob’s epistemic state from oblivion to knowledge or belief regardless of whether or not he considers the information coming from Alice to be trustworthy (he can assign an arbitrarily small probability to the possibility referred to by the proposition I will be fired within the next N days.
Since epinets deal in propositions and interpretations rather than in events and states of the world, we can also track the specific distortions of information that intervene when information is communicated across networks. And we can make predictions about the relative speed, accuracy, secrecy, covertness, and reliability with which information in networks flows across certain links (such as trust and security). As a result, we can be both more precise in the rendition of informational effects in networks and more detailed in our conjectures regarding the network structures that are more apt to carry reliable, timely, and accurate information.
Modeling and Tracking Information Flows in Epinets: The Case of a CEO Ouster
The use of epinets to track the flow of information in a network via epistemic state changes among networked agents is illustrated in Figure 5.5. The agents are the top management team and the board of directors of a medium-sized public company. The epistemic core of the network is a proposition expressing a decision by the board to replace the CEO because of consistently poor revenue performance over the past ten quarters. The specific decision, initiated by one board member and ratified at an emergency board meeting (which did not include the CEO) at 8:00 A.M. on Day 1 (T0 in the figure), was to replace the current CEO with an acting CEO (one of the board members) at a subsequent meeting (which was to include the CEO) scheduled after the end of public market trading at 5:00 P.M. on Day 2.
FIGURE 5.5 Information Propagation on an Epinet
The CEO was aware that the board of directors was concerned with the company’s performance, but was oblivious to his own imminent departure. For reasons having to do with the maintenance of public market confidence and with potentially damaging actions that the outgoing CEO could take vis-à-vis sensitive client relationships, the board decided that news of the CEO’s departure would be kept secret until the board meeting at which the change would be announced. However, it was also thought prudent, in view of recent unrest and ambiguity in the company’s product development team, to communicate the news on a “confidential-do-not-repeat” basis to the vice president of engineering, who was instructed to maintain strict confidentiality as to the time and date of the executive changes and at the same time to convey to the development team that the board had full confidence in the company’s ongoing viability and future health. The specific proposition regarding which the epistemic states of the agents were tracked was thus P = the CEO will be replaced by the board of directors at 5:00 P.M. on Day 2.
Figure 5.5 shows the interaction network among the protagonists comprising the board of directors and the top management team (which can be thought of as either a collaboration network or an interaction network). Edges (single lines) indicate mean interaction frequencies greater than ten per week. These frequencies were estimated on the basis of interviews with six executives and board members regarding their patterns of mutual interactions and their estimates regarding patterns of alter interactions within the network. The figure also shows trust links within the network (double lines) representing bidirectional “high-trust” links between pairs of executives.
Trust relationships were evaluated on the basis of responses to a 360-degree feedback survey of the top management team (the results of which were made public) that addressed professional competence (trust in competence), information distortion and withholding (trust in integrity), and disposition toward the good of the company as a whole, as evidenced by behavior (trust in integrity). Discussions were also held with three board members regarding the specifics of information propagation among directors and between the board of directors and the top management team.
The specific decision regarding the removal of the CEO was initiated by board member B3 and coordinated by board member B2, who shared a “high-trust” link with B3. It was agreed that the sensitive information would be passed to the vice president of engineering at 12:00 P.M. on Day 1 (T1 in the figure), with the clear instruction that the specific time and date of the executive changes were not to be disclosed to anyone in the company under any circumstances. The vice president of engineering was also told that the conveyance of this information was on the basis of a closely held “circle of trust” comprising B2, B3, and himself, which implied that the resulting clique was a “security neighborhood” whose members shared common knowledge about clique membership and the trust connections that held the clique together.
The ensuing propagation of the sensitive information (specifically proposition P) is tracked in the figure, and was reconstructed through interviews with various members of the network (including the vice president of engineering and the vice president of business development) on Days 1 and 2 and after the critical announcement at the end of Day 2. The propagation of proposition P closely tracked the network’s “superconductive” trust corridor. At 8:00 A.M. on Day 2 (T2), the vice president of engineering conveyed the critical information to the company’s chief operating officer, who, by 12:00 P.M. on Day 2 (T3), had informed the soon-to-be-outgoing CEO. In turn, the CEO informed the vice president of business development of the board’s impending action before 5:00 P.M. on Day 2 (T4). Thus, by the time of the announced board meeting, most of the company’s top management team and director-level managers knew about the impending change and its specifics.
The accounts given by the conveyors of the information are just as interesting as the specific topology of the information flows within the network. The vice president of engineering, for instance, insisted that the chief operating officer “looked as if he already knew” at the time their conversation took place and therefore saw the conveyance of the information not as imparting anything new but rather as establishing common knowledge of a proposition of which there was already distributed knowledge. There is an obvious tension between this account and the specific circumstances under which the vice president of engineering was informed of P; those circumstances were that no one else on the management team knew what was taken into confidence regarding P. This tension highlights a real contradiction, as the vice president of engineering either truly believed that the chief operating officer had come into possession of the critical information through other channels, which contradicts the trust that he had placed in the instructions received and the certification that he was the only recipient of this information, or he did not truly believe it, in which case he breached the trust that had been explicitly placed in his cooperation.
Note that the notion of a contradiction is specific to the propositional state space structure of epinets, which allows the rules of logic to be used to examine consistency conditions among the various propositions that form the core of an epinet. In contrast, semantic state spaces do not permit examination of such contradictions among various beliefs, which are, in that case, numerical degrees of belief assigned by agents (or ascribed by modelers to agents) to various collections of states of the world (“events”).
Moves and Strategies in Epinets
We are now in a position to define moves and strategies on epinets. We use the same basic principle to create an analogue to the game-theoretic idea of a strategy or move, and we define a move on/in an epinet as an action undertaken by an agent that changes the epistemic states of one or more of the other agents in the same epistemic network. This definition is meant to track a strategy in a game, which is a choice made by an agent that changes the game’s state space (the space of possible outcomes and associated payoffs). If Alice sacrifices her queen in a game of chess, for instance, the epinet corresponding to the game represents her move as a change in the epistemic states of Alice and Bob (her opponent) regarding both the fact of the sacrifice of the queen and its imputed implications.
Unlike the game-theoretic notion of a strategy, the epistemic network conception of a move is that it is specifically meant to track epistemic state changes. Alice’s choice to defect on Bob in a repeated two-player version of the prisoner’s dilemma game (a “strategy” in the game-theoretic rendition of the game) is a move in the epistemic network linking herself, Bob, and the set of propositions that encapsulate their representations of the possible outcomes of the game if and only if it changes the epistemic states of Alice and Bob relative to proposition P: Alice defected.
The differences between the two conceptions are several. First, the “epistemic state of the game” is a complex object made up of Alice, Bob, what Alice knows, what Bob knows, what Alice knows Bob knows, and so forth. Thus, Alice may know P (it is her intent to defect, and defection is the effect of her action), but Bob may not know this (he may think that Alice made an error because she does not understand the game or because there is a defect in the scorekeeping mechanism).
Moreover, a move that changes Alice’s and Bob’s first-order beliefs regarding P is different from one that changes their higher-level epistemic states regarding P. This stipulation makes it possible for the epinet modeler to track “all of the differences that make a difference” in the resulting interaction. If Bob knows P and knows that Alice knows P, he will likely have a very different view of Alice (and of the game) than he would if he did not know P and did not know that Alice knew P. Moreover, if Alice knows that Bob knows she knows P, she may take a very different approach to her subsequent interactions with him (perhaps trying to get him to believe that she has made an “honest mistake” or justifying her choice by other means) than she would if she either did not know Bob knew she knew P or if she knew that Bob did not know she knew P.
Moreover, the trust that Bob has in Alice (and vice versa) is causally relevant to how Bob interprets any account that Alice offers for her choice, just as the trust that Alice places in Bob is causally relevant to Alice’s interpretation of Bob’s acceptance of that account. Epinets expand the descriptive arsenal of game-theoretic approaches in ways that track agents capable of (at least finite) reasoning that uses first-order and epistemic logic, and moves on epinets are meant to allow modelers to track the choices that agents make at the level of epistemic state space expansions, contractions, and modifications.
We reserve the term “strategies” on epinets to refer to sequences of moves made by an epistemic agent that are designed to produce a particular effect. Thus, Alice’s objective in the repeated prisoner’s dilemma game she plays with Bob may be to “come out ahead” at the end of N moves, given that she knows that at the outset she enjoys Bob’s trust. Her strategy in the game, in that case, is a coherent set of epistemic moves aimed at prolonging Bob’s state of uncertainty regarding her intentions in the production of a series of outcomes that jointly corroborate proposition P: Alice defected on move k. These epistemic moves can range from those that cast doubt in Bob’s mind about his ability to correctly interpret the structure of the game and to determine the truth value of P, to those meant to repair Bob’s trust in Alice’s integrity and competence notwithstanding the fact that he has made the correct inference regarding the truth value of P. Alice’s strategy is the sequence of moves in the epinet that she chooses to make to maximize her overall objective.
Kinds of Moves. Moves on epinets have different epistemic effects, and it is useful to distinguish among them on the basis of these effects. Two classes seem particularly important. One class comprises divisive and collusive moves made at the level of the interactive epistemic structure of the network (what agents think other agents think), which impact the relational structure of the network at the level of agents. The second class comprises distortive and clarifying moves made at the level of the propositions that represent the network’s epistemic core.
Divisive and Collusive Moves. Divisive moves foster asymmetries or imbalances in the agents’ epistemic states and therefore weaken the epistemic network’s potential for co-mobilization and coordination. They are moves that shift the epinet away from common knowledge of propositions relevant to networked agents at the level of interactive belief structures; moves that undermine the epistemic reach and clout of networked agents; and moves that undermine the epinet’s trust and security structures.
Divisive moves can be easily illustrated in the context of a clique (Alice, Bob, and Charlie) that is also a trust neighborhood (Alice strong-form trusts Charlie, who strong-form trusts Bob, who strong-form trusts Alice, or ATC & CTB & BTA) and that initially shares common knowledge of a collective purpose and of a set of propositions that are relevant to its pursuit. Divisive moves (which Alice can make) are those that take the clique from a state of common knowledge of relevant propositions and a strong-form trust to a state of distributed or private knowledge and a breakdown of trust. Alice can, for instance, undermine the trust between Bob and Charlie by selectively timing her interactions and signals to each of them so as to weaken the belief each has about the propensity of the other to share relevant and valid information. Or she can undermine the commonality of the epistemic core of the group by selectively informing Charlie (Bob) of information that she withholds from Bob (Charlie) and that differentially facilitates her and Charlie’s (Bob’s) capacity to coordinate or co-mobilize over that of Bob and Charlie.
Divisive moves can furthermore be classified as auditable/inauditable and ex post deniable/undeniable according to their discoverability after they are made. Alice can deniably and inauditably provide selective information to Charlie (Bob) via communication channels that are memoryless (such as word of mouth), and she can make these channels plausibly deniable by avoiding any discoverable tracks they may leave such as invitations to one-on-one meetings; she can “bump into” Bob (Charlie) and impart the selective information without leaving a trace of the interaction.
Moreover, Alice can develop covert communication channels with Bob and Charlie by using previous experiences separately shared with each of them to encode information that she communicates to them, even when all members of the clique are present (the quintessential “common knowledge–establishing” event in game-theoretic analyses). She can, for instance, cultivate a common shared interest with Bob in Durrenmatt’s plays and refer to Charlie’s actions in the presence of both Charlie and Bob using passages and leitmotifs from those plays in a way that makes the coded message she is delivering (“This is a Fraulein Doctor expression”) common knowledge among the three but leaves the uncoded part (Charlie is trying to manipulate us) covert to Charlie (who has not read Durrenmatt’s The Physicists).
In this case of encrypted communication, Alice introduces a relevant proposition (Charlie is trying to manipulate us) of which Charlie is oblivious, in spite of the fact that he is aware of the precise substance of the (encrypted) signal that she has communicated to Bob. The communication is moreover covert vis-à-vis Charlie if he does not know that Alice has actually used an encrypted communication protocol that employs a private key (say, the proclivities of characters in a play that only the transmitter and receiver have read and that each knows the other to have read) to which only she and Bob have access.
Finally, the covertness of the communication is deniable ex post if, on “discovery” by Charlie that Alice has used an encrypted message to communicate to Bob about him in his presence, Alice can explain her choice of language by pointing to a feature of the code that leads Charlie to misinterpret her intent and the effect of her communication on Bob (for instance, that Charlie is like the character in question not in his manipulativeness but rather, for instance, in his sensitivity to situational details).
Collusive moves, in contrast, are moves that drive an epinet toward common knowledge of a common epistemic core; moves that extend the epistemic reach and clout of an agent within an epinet; and moves that establish, extend, and repair information propagation structures like trust and security neighborhoods, conduits, and corridors.
Consider a triad in a network of dense interactions—where the densest interactions link Frieda to Gail and Hal—which, in spite of the frequency of mutual interactions, is divided in the epistemic states of its members as to propositions regarding issues of common interest and is moreover not a trust neighborhood. A collusively minded epistemic agent, Frieda, can move to increase the coherence of the clique’s distributed epistemic states (who knows all and only the propositions of common interest) and interactive epistemic states (who knows others know and others know she knows all and only the propositions of common interest) by (1) distributing the information she knows and knows Gail and Hal do not know (because of both ignorance and oblivion), (2) credibly signaling to Gail and Hal that she knows they know the information that she is sending them, and (3) signaling to Gail and Hal that she is sending them all and only the information that she knows (and is therefore oblivious of whatever information she is not sending).
Although there is no signaling move that is sufficient for the development of trust among clique members, Gail’s collusive signaling move clearly facilitates trust in competence and trust in integrity through the diligence of her communicative protocol. To the extent that trust is extended to one whose signaling is directed to the evolution of a coherent set of epistemic states of the clique as a whole in spite of private incentives (e.g., looking informed when in fact one is not, which drives Frieda to signal that she knows more than she does and thereby decreases Hal’s and Gail’s ability to be maximally informative in their own signaling moves), Frieda’s moves help to turn the triad into a trust neighborhood.
Distortive and Clarifying Moves. Distortive and clarifying moves are those that operate on the epistemic core of the network (i.e., propositions that are jointly and severally relevant to the agents in an epinet) rather than on its interactive structure. However, these moves often have indirect effects on the network’s relational structures through their influence on the interactive belief structures that their deployment induces.
Distortive moves ambiguate, confuse, and otherwise distort the network’s epistemic core. They come in different forms, depending on both the intent of the agent making them and the effect of that agent’s making them at a particular time.
Lies are straightforward modifications of the truth value of a proposition known by the liar to be true (false). P = Amy will arrive on the 7:00 P.M. British Airways flight from Heathrow Airport—said of someone who will not arrive on that flight—is a lie in both intent and effect if it is uttered by someone who knows Amy will not arrive on that flight and if it induces a belief in the interlocutor that tracks the truth value of P—that is, if it causes the receiver to come to know P by hearing the liar utter it, or if it strengthens the receiver’s belief in the truth of P by hearing the liar utter it. Lies can therefore differ with respect to their intent and effect in ways that depend on the trust structure of the link across which they are communicated: if Alice lies to Bob by uttering P and Bob knows that Alice is a liar, then the intent and effect of the lie do not track one another.
Lies can induce straightforward modifications of the trust structure of an epinet, depending on their verifiability. In the case of P—a sentence with an easily ascertainable truth value—the utterance of the lie can trigger a modification of the trust structure of the link, even though the inferential link from the ascertainment of the lie to a specific form of trust that was broken is not determined. On ascertaining that Alice has lied, Bob may modify his knowledge that she is competent (she would know P if P were true: trust in competence), or he may modify his knowledge that Alice is sincere (she would assert P if she knew it: trust in integrity), depending on other considerations.
Of course, lies need not induce breaches of trust in competence or integrity and can even strengthen trust in a relationship. White lies are those uttered by an agent who knows that the utterance will not induce a change in the epistemic state of the receiver vis-à-vis the content of the message. If, for instance, Alice and Bob have an understanding that they will try to forestall an attempt by Charlie to find Alice, Alice’s stating P to Bob at a table at which Charlie is present is a white lie vis-à-vis Bob, provided that Bob knows Alice knows that P is false and that Alice knows Bob knows this (and that she is only saying it so that Charlie hears it and is misguided).
Whether or not an utterance conveys a lie depends on the interactive epistemic states of the transmitter and the receiver in ways that color and texture the perceived intent and effect of the communication. Pink lies are those that, though well intentioned, do not accomplish the “encryption” effect that white lies achieve: If Alice does not know that Bob knows she is purposefully lying in order to mislead Charlie, then Alice’s intent in uttering P is a lot fuzzier than in the case in which she does know it. Moreover, if Bob in fact does not know that Alice is lying in order to mislead Charlie, then the effect may be that of a straightforward (“black”) lie.
Palters are distortions of the propositional content of a message that are aimed at inducing a set of level 1 and higher epistemic states in the receiver that (1) are relevant to the truth value of a proposition P and (2) do not track P’s truth value. They may, for instance, be held to be true when P is true, but the opposite is not the case. Unlike lies, palters do not involve outright distortions of the truth value of P via relevant messages. The goal is to “color” the truth, not to change it outright.
Palters convey either more or less than P does and therefore represent departures from the implicit trust-related norm of saying (and knowing) “the truth, the whole truth, and nothing but the truth.” M = I had lunch with Barack Obama yesterday, uttered by Kim to Jill, is a palter relative to Kim’s knowledge that she had lunch at a table with five other people—none of whom was Obama but had been invited by him, along with twenty-five others, to lunch at five tables, one of which was occupied by Obama—because it induces an epistemic state in Jill that does not track P. Jill’s interpretation of M may be that Kim is on terms with Obama that are cordial enough to warrant a lunch conversation, which is not similarly warranted by P.
Once again, palters differ with respect to both intent and consequence: M may be a palter in intent but may not be one in consequence provided that Kim has a “calibration mechanism” that filters Jill’s utterances to compensate for “reading too much” into what she says. Also, the degree to which M is a palter in intent is, again, subject to what Jill knows about the way in which Kim processes signals coming from her: if Kim knows that Jill filters her signals to compensate for palters (especially in a public setting) and furthermore knows that Kim knows it, then the intent of the palter is not as nefarious as it would be if Kim and Jill did not possess this knowledge. The interactive epistemics of the situation therefore provide a natural “baseline” for adjudicating the palter’s intent and effect.
Palters can function as “self-defining truths”—that is, they can work as performatives and not just as declarative or constitutive terms. P = I have heard many people say she is having a hard time with the new curriculum design, uttered by someone who (without knowledge of any facts) has been saying for some time, to anyone who will listen, that there are troubles with the new curriculum design is a palter in the sense that (1) it does not convey the full epistemic structure of the link of communications that has led to P being true, even though, (2) P is now true (in view of the speaker’s tireless paltering efforts). This example highlights the degree to which it is not only the epistemic content of an epinet or only the epistemic structure of the epinet in which a message is transmitted, but also the epistemic dynamics of a message that can make a material difference in the epinet’s ensuing structure and dynamics.
We use the term bullshit—a colloquialism that, following Frankfurt (2005), we attempt to rescue from lay and imprecise usage—to denote moves on an epinet that (1) attempt to change or modify the receiver’s epistemic state relative to a proposition of common interest, in a situation where (2) the transmitter does not know anything about the proposition’s truth value. Unlike liars and palters, bullshitters are either ignorant or oblivious of the truth value of relevant propositions. They are simply interested in changing the epistemic state of the receiver vis-à-vis one or more propositions of common interest. P = We are doing very well with the new product design uttered by a director in a division whose quarterly budget is predicated on the performance of the current product suite, in the absence of any data or facts that confirm or inform the assertion, is a typical example of bullshit.
The difference between bullshit and palters is easy enough to grasp definitionally but difficult to tease apart in practice without further information about the epistemic states of agents in the epinet. P = We are doing well but not great, uttered by a program director giving guidance to university faculty regarding enrollment, may represent a palter if the speaker knows the current year-over-year demand characteristic for program applicants, or it may be bullshit if the director in fact does not know it and is simply trying to come off well. This suggests that one can differentiate between bullshit and palters by designing questions (“How do you know?” “What is the basis for saying . . . ?”) that help distinguish between the two classes of distortive moves in a particular setting. The resolving power of such questions, of course, depends on the degree to which the bullshitter/palter’s answers are themselves intelligible to the questioner and on the extent to which they are auditable/verifiable.
Relative to our inventory of distortive moves, clarifying moves are easy enough to define as moves that drive the signals exchanged by epinet agents toward a content that tracks all and only the truth value of the epinet’s epistemic core. We can distinguish here between two types of moves. Sanctioning moves seek to alter the trust neighborhoods and interactive epistemic states of a network as a function of the messages that various agents emit (e.g., publicly unmasking liars and thereby undermining their epistemic role within the network by undermining the trust that others in the epinet might have in their competence and integrity). Substantive moves have to do with auditing, filtering, and classifying the messages that are passed by one or more agents within the network without publicly undermining the agents’ epistemic roles.
Sanctioning moves act on the epistemic structure of the network as a whole, while substantive moves operate on the propositional content of messages passed between agents. The former may thus be aptly considered escalations of the latter to the level of structural interventions on epinets. Among clarifying moves, we can also distinguish between interrogatory moves, which attempt to unpack the propositional structure and epistemic content of a message through a series of questions that may be guided by insight into potential breaches of trust, and declarative moves, which openly challenge and criticize particular utterances as fallacious, obfuscating, mendacious, or otherwise distortive. As before, both moves induce a set of interactive epistemic states vis-à-vis both the message passer (liar? bullshitter? palter?) and the mover (tendentious? fair?) that affect whether the utterance succeeds in achieving its purpose, notwithstanding the mover’s intent.
Epistemic Stability, Robustness and Immunity: In Lieu of Equilibrium
Using epinets to model social interactions in general and social networks in particular requires us to update the standard explanatory tool kit of rational choice theory and its interdependent rational choice offspring (game theory) to account both for the propositional state spaces that epinets use and for the textured description of individual epistemic states (oblivion) and interactive epistemic states (almost-common knowledge, knowledge of someone else’s oblivion) that we have introduced. Epinets allow us to track epistemic state changes of interacting and networked agents at a level of precision and empirical operationalizability that is not possible using standard state space models that assume agents at least know and understand their own state spaces and share state spaces of events and states of the world about which they have updatable beliefs.
Without common priors assumptions, game-theoretic analyses cannot “get off the ground,” so to speak, without the modeler ascribing a common state space to the set of interacting agents. This may work well enough for games that are “prestructured”—as they are in certain auctions and laboratories—but not so well for those played out “in the wild.” In such cases, the particular epistemic states—and belief hierarchies—of the networked agents must be tested, discovered, and elicited rather than imputed or ascribed.
The net result of this explanatory maneuver is that the tried and true explanatory trope of equilibrium—a set of strategies that are mutual best responses such that no agent has the incentive to unilaterally deviate from her/his own course of action—needs to be replaced by a set of explanatory concepts that track the more complex state space description afforded by the epinet approach. In particular, to the extent that equilibrium relies on a common set of priors and, at the very least, on a common state space for the “game” being played, it does not survive the discovery that different agents inhabit different epistemic state spaces and perhaps use radically different ways of interpreting a state space that is, in the semantic approach, “the same” at the level of events.
There is no way for an agent to update beliefs or knowledge of a state space that has components of which s/he is oblivious. Moreover, if the state space comprises propositions rather than the raw, unstructured qualia that constitute “events,” and if different agents have different elementary languages in which they formulate their propositions, then obliviousness of the proposition-generating languages of other agents also precludes the use of standard equilibrium concepts to explain, predict, rationalize, or justify the outcome of an interaction or a set of interactions.
Within the epinet formalism, then, we must replace the standard notion of equilibrium with a more textured set of explanatory concepts that relate to an epinet’s informational and epistemic regimes. In particular, we can describe general forms of “homeostasis” within an epinet using the following concepts.
Stability. The (epistemic) stability of an epinet relates to the degree to which sets of epistemic states (individual, collective, interactive) are time-invariant in situations in which the truth values of the propositions in the epinet’s epistemic core do not change and the epinet’s interactive epistemic structures (mutuality, commonality, distribution, trust, security) remain unchanged in the face of changes to the truth values of these propositions. Stable epinets, in other words, maintain their information transmission structure in the face of new information (e.g., trust conduits and corridors remain unchanged in response to changes in “the world,” as do epistemic cliques that enable co-mobilization and coordination), and their epistemic cores do not change in the absence of new information.
Robustness. Robustness relates to the degree to which the epinet preserves its epistemic core in the face of unintentional errors of communication (“white noise”) among networked agents and the degree to which the epinet’s epistemic structures (mutuality, commonality, trust, security) remain unchanged as a result of unintentional, random errors of new information registration and communicative mishaps. Thus, it is a measure of the degree to which the stability of the epinet is “fault-tolerant,” where “fault” is strictly taken to mean the random errors and unintended actions that convey information to networked agents.
Immunity. Immunity is a measure of the degree to which the epinet preserves its epistemic core in the face of intentional distortions, deletions, and misrepresentations of information (which can take the form of lies, paltering, and bullshit, as well as breaches of trust in the form of errors of omission) in situations in which the truth values of propositions in its epistemic core do not change. It is also a measure of the degree to which the epinet preserves its interactive epistemic structures (mutuality, commonality, trust, security) in the face of attacks by insiders or outsiders designed to undermine its integrity and stability.
Immunity, then, is a form of robustness to intentional attacks (Albert, Hawoong, and Barabási 2000). Central to the notion of epinet immunity is the degree to which trust and security neighborhoods, conduits, and corridors can survive “malware” in the form of attacks on the very structures that safeguard the passage of reliable, accurate, and timely information among its agents.
Taken together, stability, robustness, and immunity form a set of explanatory concepts that replace the standard notion of equilibrium in situations in which an epistemic network is a complex, evolving entity, an always-already-happening process of information transmission, reception, distortion, and correction. They are all “dynamic equilibrium” states that allow modelers to bridge the “passive signaling” imagery of standard social networks and the active choice-functional representation of standard game theory models, in the absence of a complete and shared “bird’s-eye” view of all epistemic states of the agents in the network.
The reader will notice that we have stayed at the level of referring to stability, robustness, and immunity as “measures” without positing a specific formulation for each. In each case, a measure can be a probability of survival after a period of time or following a critical event, it can be a percentage of an epinet’s links that remain intact after a threatening event, or it can be the degree to which specific epistemic states (almost-common knowledge about P) required for coordination or co-mobilization survive an attack or an error. Different interpretations may be useful for different epinets, which is why we have not pressed any one particular measure.
Summary
An epinet is an always-already-happening process of information transmission, reception, distortion, and correction or filtering—quite aside from being an identifiable structure whose topology can be analyzed at any given point in time. We have shown that flows of information can be tracked by epinets via epistemic state changes that they induce. We have accounted for the ways in which agents’ choices and decisions shape information flows in an epinet by introducing the concepts of epistemic moves and strategies that are meant to capture purposeful interventions by networked agents on the epistemic landscape.
We have seen that the moves and strategies that epinets enable us to speak about require concepts of homeostasis that are different from game-theoretic equilibria, and we have sought to distinguish among different levels of an epinet’s invariance to changes and challenges to its structure. Finally, we have defined stability, robustness, and immunity in ways that are both intuitive and amenable to translation in the language of epinets.