Asymmetric Outcomes in Two-Actor Conflict Dynamics: Stability, Bifurcations, and Emergent Behaviors

TL;DR

This paper analyzes a generalized two-actor conflict model, revealing bifurcations and stable states, providing insights into social phenomena like false support and non-strict consensus, with implications for understanding competitive and cooperative dynamics.

Contribution

It introduces a new parameter to a conflict model, generalizing feedback, and demonstrates bifurcation phenomena and the absence of limit cycles, enhancing the model's descriptive power.

Findings

Existence of supercritical pitchfork bifurcations under certain feedback conditions.

The model does not admit limit cycles in any case.

Provides insights into social phenomena such as false support and non-strict consensus.

Abstract

In this paper we present an analytical and numerical study of a generalized model of two-actor cooperative-competitive conflict of the Continuous Opinions and Discrete Actions (CODA) type. Theoretically, we note that the in troduction of a new parameter allows generalizing feedback as strong and weak. Furthermore, we show that for positive-positive and negative-negative feedback there exists a supercritical pitchfork bifurcation, and that the model does not admit limit cycles in any case, and we study the effect of different parameter values and initial conditions by using a difference equation approximation of the model. Additionally, our model offers important insight on social phenomena such as false levels of support among cooperators, often observed in agreement negotiations; instances of ``non-strict consensus'' when two people support the same political position, albeit with different intensities; and competitive situations, such as in competitions with disproportionate profit and losses. Thus, this generalized model offers an enhanced descriptive power compared to previously proposed models.