WP 2021-05 Modeling Norm-Governed Communities with Conditional Games

Posted On June 16, 2021
Categories Working Papers, WP 2021
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AUTHORS: Don Ross, Wynn C. Stirling and Luca Tummolini

ABSTRACT: The role of informal norms in constraining available equilibria in social dynamics has increasingly interested social scientists. There is as yet no general theory of norms to play the role of a ‘default model’ against which innovations and refinements can be assessed. The ambition to produce such a model is complicated by different, and apparently incompatible, ways in which economists and sociologists respectively conceptualise norms.

A feature of norms that is emphasised in recent models is their conditionality: agents’ choices to conform their actions to norms are sensitive to the extent to which they observe corresponding behaviour in those with whom they interact (Bicchieri 2006, 2017). There is a weak sense in which conditionality is sown into the very fabric of game theory: whether a given choice is an element of an equilibrium strategy for an agent is a function of what other agents choose. Therefore, whether an action in a strategic setting maximizes an agent’s utility function in ex ante expectation depends on whether it is a best reply to other players’ expected choices. But this only captures what Bicchieri (2006, 2017) calls ‘empirical’ expectations.

The sociological conception of norms models them as exogenous social structures that agents encounter as elements of their environments. This conception reflects the fact that norms often display intertemporal and cross-generational persistence on a scale that is longer than individual preferences. Furthermore, agents can under some circumstances go on following norms that are no longer preferred by majorities, or even by anyone at all, if they are trapped by ’pluralistic ignorance’ - unawareness by each that others share their distaste for the norm.

On this ’social facts’ conception of norms, they are subject to conditional preference in a special sense that goes beyond equilibrium dependence (though must be compatible with whatever definition of equilibrium features in the analysis). We show how to model norms for application to choice data estimation in a way that incorporates this deeper understanding of conditionality.

Specifically, we attend to the utility structure proposed by Kimbrough and Vostroknutov (KV) (2016, 2020) for application to public goods games, dictator, ultimatum, and trust games run in the laboratory. This work represents a significant advance within the constraints of economic theory. However, KV’s model only accommodates norms for which social welfare increases in the number of followers. Thus it does not allow for representation of norms that survive due to pluralistic ignorance and trap societies in inferior states relative to all plausible welfare criteria until something breaks informational symmetry. Although KV represent norms as social facts in the sense that agents have preferences about them as norms, norms so understood lack a kind of causal force that sociologists regard as distinctive to genuine norms. As Kuran (1995) recognises, persistent norms shape preferences. A norm that endures for a time due to preference falsification may cause agents’ preferences to shift to accommodate it, and may consequently cease to be a barrier to Pareto improvement because it alters the location of the Pareto frontier, even while leaving market-valued wealth or income unimproved. That is, there are social adaptive preferences. Such endogenous preference change is generally beyond the reach of economic theory, for good reasons.

We model sociological dynamics of norm formation by using the resources of conditional game theory (Stirling 2012, 2016). This extension of standard game theory is designed to bring the social phenomenon of mindshaping (Zawidzki 2013) within the ambit of strategic choice. Mindshaping occurs when agents coordinate with one another by aligning partially uncertain preferences. The model we develop is not intended to improve or replace the KV model of choice under norms. It is, rather, intended to represent a strategic process by which the norms that the KV models treat as exogenous arise. The games we model and those modelled by KV mutually constrain one another according to a relationship described by Ross (2005) under the label of ‘game determination’. This can be understood, as a step along a path to unifying sociological and economic theory in the formalism of game theory, conservatively using only established game solution concepts.

After presenting and simulating our formal model, we extend the account of Binmore (1994, 1998) by inserting our sociological ‘layer’ between his evolutionary and static game-theoretic analyses of norms. Specifically, the relationship between the sociological and economic analyses is analogous to the Nash program for using cooperative and noncooperative game theory in tandem to exploit the strengths and avoid the limitations of each.