Abstract
Extensive interdisciplinary literatures have built on the seminal spatial dilemmas model, which depicts the evolution of cooperation on regular lattices, with strategies propagating locally by relative fitness. In this model agents may cooperate with neighbors, paying an individual cost to enhance their collective welfare, or they may exploit cooperative neighbors and diminish collective welfare. Recent research has extended the model in numerous ways, incorporating behavioral noise, implementing other network topologies or adaptive networks, and employing alternative dynamics of replication. Although the underlying dilemma arises from two distinct dimensions—the gains for exploiting cooperative partners (Greed) and the cost of cooperating with exploitative partners (Fear)–most work following from the spatial dilemmas model has argued or assumed that the dilemma can be represented with a single parameter: This research has typically examined Greed or Fear in isolation, or a composite such as the K-index of Cooperation or the ratio of the benefit to cost of cooperation. We challenge this claim on theoretical grounds—showing that embedding interaction in networks generally leads Greed and Fear to have divergent, interactive, and highly nonlinear effects on cooperation at the macro level, even when individuals respond identically to Greed and Fear. Using computational experiments, we characterize both dynamic local behavior and long run outcomes across regions of this space. We also simulate interventions to investigate changes of Greed and Fear over time, showing how model behavior changes asymmetrically as boundaries in payoff space are crossed, leading some interventions to have irreversible effects on cooperation. We then replicate our experiments on inter-organizational network data derived from links through shared directors among 2,400 large US corporations, thus demonstrating our findings for Greed and Fear on a naturally-occurring network. In closing, we discuss implications of our main findings regarding Greed and Fear for the problem of cooperation on inter-organizational networks.
Highlights
In this paper, we investigate a classic model of the evolution of cooperation—the spatial dilemmas model of Nowak and May [1, 2]–and apply it to the problem of cooperation among organizations
Classical game theory assumes that variations in Greed and Fear have no effect within the Prisoner’s Dilemma, and work on the spatial dilemmas model typically assumes that Greed and Fear have similar effects, we demonstrate that Greed and Fear have strong, divergent, and interactive effects in the model
Given questions about sensitivity of the Nowak and May model to asynchronous updates of agents’ strategies [68, 69], we confirmed that our results are robust to this issue: First we replicate the original spatial dilemmas model on a Moore neighborhood with synchronous updates, and we apply it to an alternative network topology with random asynchronous updates
Summary
We investigate a classic model of the evolution of cooperation—the spatial dilemmas model of Nowak and May [1, 2]–and apply it to the problem of cooperation among organizations. The model considers social dilemmas, where agents may be driven to behave in noncooperative ways either to exploit others’ generosity (Greed) or to avoid exploitation by others (Fear). Classical game theory assumes that variations in Greed and Fear have no effect within the Prisoner’s Dilemma, and work on the spatial dilemmas model typically assumes that Greed and Fear have similar effects, we demonstrate that Greed and Fear have strong, divergent, and interactive effects in the model. Stepping beyond the spatial dilemmas interaction topology, we apply the model to a network of empirical inter-organizational relationships and demonstrate robustness of our conclusions for a realistic network topology. We discuss the distinct implications of Greed and Fear for organizational contexts
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