Binary Role Theory and the Evolution of Cooperation in World Politics

Stephen G. Walker, Kai He, and Huiyun Feng


In this chapter, we address two important general questions about world politics. First, how do the actions of states as a whole combine to generate the emergent properties of world order? Second, how can leaders as agents guide the evolution of cooperation as an emergent property of world order? Our approach to these puzzles is a bit paradoxical, as it proceeds in two seemingly contradictory steps. In step one, we propose an agent-based model that would seem to violate the system-level focus of the questions. However, we solve the paradox in step two by showing how agent-based actions generate the emergent properties of interest in interaction with other environmental features at the level of the international system. This upward shift in the level of analysis in our model entails the central systemic process of interest to us, namely, “order transition,” which we specify theoretically with binary role theory and then illuminate empirically with the analysis of three agent-based cases of order transition between key pairs of states in world politics.

Our strategy of inquiry is an application of complex adaptive systems analysis in the social sciences, an interdisciplinary research program that uses agent-based modeling methods to generate systems of agents whose features resemble complex systems found in the natural and life sciences (Axelrod 1984; Gell-Mann 1994; Axelrod and Cohen 1999; Jervis 1997; Miller and Page 2007; Mitchell 2009). Our assumption is that this particular approach to understanding the origins, the duration, and the transformation or destruction of complex natural systems may shed some light on how to understand more deeply the complex dynamics of order transition in social systems between states in world politics. This approach is congenial with the conceptualization of international order as a set of emergent properties from the interactions among agents (state and non-state actors) about issues across multiple dimensions, e.g., military, economic, and diplomatic, which may vary in number and variety over time and make international order a dynamic construct entailing order transition as a process that varies spatially across regions and temporally over time (Johnston 2019, 22-25).'

Axelrod and Cohen (1999, 7, italics and bold removed) summarize the characteristics of complex adaptive systems analysis as follows: “When a system contains agents or populations that seek to adapt, we will use the term complex adaptive system.” An agent is an element in a system that can act “more or less purposefully” as a strategy that can vary and copy other strategies in interactions with other agents in a process of selection (changing strategies) that results in adaptation, that is, “improvement according to some measure of success” (Axelrod and Cohen 1999, 4-7). Complex adaptive systems analysis addresses the normative question: “In a world where many players are all adapting to each other and where the emerging future is extremely hard to predict, what actions should you take” (Axelrod and Cohen 1999, xi)?

The distinctive feature of this approach is to focus on the two-way interactions between agents (A) and environment (E), i.e., {A E} rather than focusing primarily on the one-way actions of each on the other, i.e., {A —> E} or {A <— E}. The two-way interaction emphasis is the defining feature of complex adaptive systems analysis, because a system is defined abstractly as the interdependent interactions of elements (agents) that define a system in an environment, which generates effects as emergent properties (Jervis 1997). The effects of the system of interest in our case are the norms-based, power-based, and rule-based features that define order or disorder at regional and global levels in the international system of world politics.

Perhaps the most well-known example of complex adaptive systems analysis in political science is Robert Axelrod’s analysis of the prisoner’s dilemma game, in which he asks an agent-based question to get a system-level answer: which strategy by players as agents in the prisoner’s dilemma game is the optimum strategy for winning the game as a systemic outcome (Axelrod 1984; Mitchell 2009, 213-224)? In this case, the process of two-way interactions defined by the strategies (actions) of the players is the immediate mechanism that generates the emergent property (outcome) of interest in a social system (the game).

The prisoner’s dilemma game also illustrates one of the methods associated with complex adaptive systems analysis, computational modeling, which is to use rules to represent the internal logic of the system of interest that is the game in this instance. “The rules of play of a game describe the possible choices of the players at each stage of play” (Brams 1994, 226). These rules are computations (definite procedures) that describe the game (Mitchell 2009, 56-64). In turn, the game may model (represent) the operation of a system of interest in the real world, such as describing how states compute strategies (make rule-based choices), which generate different outcomes as emergent properties of order in a regional or global system.

We shall employ computational models of strategic interaction from game theory to describe and explain the emergence of different levels and dimensions of international order in an abstract international system, in order to isolate and identify the logic associated with the mechanisms of order transition in a relatively simple international system. Our expectation is that this modeling effort can illuminate the menu of choices available to agents such as Russia, China, NATO, and the United States who are members of a more complex system of interest in the real world. In turn, these insights may help us to understand the dynamics of the current international order and the menu of possible transitions to a future international order available to policy makers at regional and global levels of the international system.

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