Social Power and Non-cooperative Game Theory
| Author | William Bosworth, |
| DOI | 10.1177/09516298221081810 |
| Published date | 01 April 2022 |
| Date | 01 April 2022 |
| Subject Matter | Articles |
Social Power and Non-
cooperative Game Theory
William Bosworth
School of Politics and International Relations, Australian National
University
Abstract
This paper defends the use of non-cooperative game theory for analysing questions of governance.
To do so it posits a way of extending the resource account of social power from cooperative
games to noncooperative games in a way that side steps a range of criticism. This involves iden-
tifying tipping points in the reputations of certain agents for paying and punishing those in their
thrall. These tipping points are what give threats and offers their credibility in the absence of
enforcement mechanisms and stabilise the distribution of social resources in society.
Keywords
Power, governance, bargaining, bayesian games, reputation, tipping points
The question of who governs is arguably the question of political science. It was posed
by Robert Dahl (2005) [1961] to empirically assess whether inequalities in the market
translated into inequalities in governance at City Hall. If true, Dahl argued Marx was
essentially right. The formal equality bestowed to citizens through the vote was little
more than an ideological smokescreen. If not, there was hope yet for American
capitalism.
Dahl’s study ended with optimism. He used observable measures to identify policy
conflicts amongst his city’s (New Haven, Connecticut) representatives and counted
who was ultimately successful and who was not. It was observed that different groups
were decisive across the discrete policy areas of urban redevelopment, public education,
Corresponding author:
Dr William Bosworth, School of Politics and Internaional Relations, Australian National University, Canberra,
ACT 0200, Australia.
Email: william.bosworth@anu.edu.au
Article
Journal of Theoretical Politics
2022, Vol. 34(2) 262–279
© The Author(s) 2022
Article reuse guidelines:
sagepub.com/journals-permissions
DOI: 10.1177/09516298221081810
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and political nominations. Dahl concluded New Haven was a ‘polyarchy’, where the
many (poly) govern (arkein) and implied radical institutional change should be accord-
ingly tempered.
The rational choice interpretation, however, suggests genuine political conflict may
never reach city hall to begin with. It takes the mobilisation of resources to secure
representation and individual rationality regularly dictates sub-optimal outcomes for
groups. The very difference between the inequalities of the market and the inequalities
of governance, by this interpretation, boils down to questions of coordination.
Consumers may collectively have the aggregate resources to secure representatives
to advocate tighter regulations on business, for instance, but because of incentives
for freeriding that come with such large groups, cannot mobilise those resources to
do so. A similar kind of explanation can be proffered for why the poorest 99.9% do
not expropriate the wealthiest 0.1%, how 18th Century slaveholders in the
Caribbean managed to maintain control over their brutal sugar plantations despite
being outnumbered 10 to 1 (Petley, 2018), and why some women consciously perpe-
tuated oppressive patriarchal conventions they knew hindered their and their daugh-
ters’life prospects (Wollstonecraft, 1993: 276). Coordination problems like this are
described with non-cooperative game theory.
Yet there is a theoretical loose end that has left the rational choice approach vulnerable
to criticism on grounds ranging from ideological bias (Wolfinger, 1971: 1078; Polsby,
1980: 96-7; Connolly, 1974: 126-30; Barry, 2002; Lukes, 2005: e.g. 110-11) through
to incommensurability (Morriss, 2002: 138-44). Pluralists question why the inequalities
in the ability to coordinate wealth should matter in light of high levels of voter coordin-
ation. ‘Elitists’on the other hand argue the interpretation focuses too heavily on the
coordination problems of the oppressed, glossing over the culpability of elite oppressors
like capitalists, colonialists, and men. It begs the question which kinds of strategic non-
action are relevant to the question of governance and how they might exacerbate or miti-
gate other coordination problems.
This paper proposes an answer by joining the rational choice analysis of the coopera-
tive games initially used to describe governance with the non-cooperative games charac-
terising coordination problems more generally. This is complicated by the fact that
cooperative games assume over the possibility of sub-optimal equilibrium with the
axiom of Pareto optimality. Without further elaboration, however, different strategies
for measuring governance will be underdetermined, opening the door to charges of par-
tiality (e.g. see Wolfinger 1971: 1078). Radicals will focus on the coordination problems
associated with wealth and clientalism; conservatives will focus on voter coordination.
Without further refinement here, empirical studies risk generating answers to who
governs that are tinged with ideology.
The cooperative game
John Harsanyi (1962a,b) based the original rational choice interpretation of governance
on cooperative bargaining games. His formal analysis suggests the opportunity costs
associated with getting others to do what they would prefer not to are what make the
question of governance in and of itself important. The ability to get others to do what
Bosworth 263
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