Influence of Social Motivation over Belief Dynamics: a Game-theoretical Analysis

This paper provides a game-theoretical description of social and motivational influence over belief dynamics of two arguing agents that hold contrasting views. The formal analysis shows how social influence depends on both (1) the agent’s own motives and (2) her beliefs concerning the motives of the other agent. Moreover, game-theoretical modelling of dialogical interaction with mutual ignorance of the agents’ motivational profiles reveals that (3) some information on the counterpart’s motivations have greater diagnostic value than others, and (4) such discontinuity in informational value again depends on the agent’s own motivations. Hence this gametheoretical analysis captures several features of the rich interplay between motivations and beliefs, and it allows for prediction of the specific motivational pressure being exerted on the agent’s belief dynamics, given her current frame of mind. Here the model is applied both to agents with exhaustive knowledge of each other preferences, and to agents with only partial assumptions on the motivational profile of their counterpart. In the final sections, we discuss the extension of this analysis to the single-agent case, and future empirical verification of the predictions generated by the model, via social experiments (e.g. experimental economics) and computational models (e.g. agent-based social simulation). INTRODUCTION Social influence over belief formation and change had been theoretically modelled and empirically verified both in social psychology (Asch, 1952; Kruglanski, 1980; Kunda, 1990; Castelfranchi & Miceli, 1998; Forgas, 2000) and in philosophical epistemology (Goldman, 1999). These studies suggest that beliefs do not simply capture a relation between an agent and the world, as the classical notion of episteme as ‘true belief’ implies. Beliefs are also social entities, depending on social relations for their origins and support (they often derive from social sources and are justified by the fact that others believe so; Asch, 1952), for their use (e.g. communication, coordination), and for their functions (e.g. to be shared, to provide a common ground). In contrast with these results, standard formalisms of belief dynamics such as AGMstyle belief revision (Alchourrón et al., 1985; Gärdenfors, 1988), Truth-Maintenance Systems (Huns & Bridgeland, 1991; Doyle, 1992) and probabilistic models (Berger, 1985; Boutilier, 1998) usually fail to consider motivation, both social and individual, as a relevant factor in defining and shaping the agent’s belief set. While the coordination of motivation and beliefs is a typical problem in agent architectures (Castelfranchi, 1998), the influence of motivation over belief formation and change is not usually investigated. The same applies to Bayesian analyses: although the connection between decision-making and beliefs is an obvious focus of interest (Berger, Influence of Social Motivation over Belief Dynamics: A Game-Theoretical Analysis 2 1985), these approaches typically keep utility (motivation) quite separate from probability (belief), without addressing the influence of the former on the latter. As for AGM belief revision, it might be said to be implicitly driven by the ‘motivation’ of maintaining a coherent set of beliefs, avoiding contradictions when faced with new information in contrast with previous convictions (Harman, 1986; Gärdenfors, 1988; Levi, 1991). However, this is rather a basic assumption of the model, which does not play a specific role in orienting the agent toward believing or disbelieving any particular claim. This lack of interest for social and motivational influence in formal models of belief dynamics is quite puzzling, if contrasted with the overwhelming evidence of such influence provided by both empirical and theoretical research in cognitive psychology (Festinger, 1957; Kruglanski, 1980; Swann, 1990; Castelfranchi, 1996; Paglieri, 2004), social psychology (Asch, 1952; Kunda, 1990; Miceli & Castelfranchi, 1998; Forgas, 2000), economics (Kahneman & Tversky, 1979) and computer science (Picard, 1997). In natural cognitive agents (e.g. humans), motivation does play a role in shaping the agent’s beliefs, both by focusing her attention on those issues and data she considers more relevant and urgent (Kruglanski, 1980; Kunda, 1990), and by orienting her assessment of available information according to specific patterns, such as social conformity (Asch, 1952), confirmatory tendency (Festinger, 1957), selfverification (Swann, 1990), denial (Miceli and Castelfranchi, 1998). Moreover, similar motivational biases are not necessarily irrational or anti-adaptive: while relevancebased belief assessment can lead to tunnel vision and even obsession, some kind of goaldirected focusing is indeed needed for any resource-bounded agent, in order to efficiently perform belief revision (Cherniak, 1986); confirmation and self-verification can degenerate in wishful thinking and selfdelusion, but they are also basic defence mechanisms to preserve from loss of motivation, and they often serve as simple effective heuristics for specific tasks (Todd & Gigerenzer, 2000). However, the aim of this paper is not to make the case for motivational influence over belief dynamics in general, but rather to focus on social motivation within a specific formal framework, i.e. game theory. The basic research questions addressed here are the following: Provided social motivation does play a role in belief dynamics, what exactly is this role? Is it always one and the same, or does it depend on the motivational profile of the agent, i.e. different motivations might affect in different ways the agent’s belief dynamics? Is there any way of predicting the specific social impact over belief change, given the agent’s motivations? Our work tackles these questions by applying a game-theoretical approach to belief change in a dialogical setting, in which two agents (called P and ∼P) debate a controversial point on which they have mutually excluding views, and each of them has to decide whether to maintain her own view or change it and assume the view of the opponent. Different motivational profiles (i.e. preference orderings over possible outcomes) are defined and contrasted, highlighting the emergent belief revision strategies of the agents – with either complete or partial assumptions on each other preferences. The formal analysis emphasizes social influence in shaping individual beliefs, and the pivotal role played by motivation in this process. MOTIVATED DIALOGUES: TWO AGENTS ARGUING WITH EACH OTHER Imagine two agents confronting each other on a given issue, on which they hold contrasting and mutually excluding views. Let us call these agents P and ∼P, simply to signify their initial disagreement on the issue under consideration. Each agent is faced with an alternative: either she maintains (M) her own view, or she revises (R) it in favor of the opponent’s claim. This produces four possible outcomes. Fabio Paglieri, Cristiano Castelfranchi