On the Evolution of Partial Respect for Ownership

An early prediction of game theory was that respect for ownership—“Bourgeois” or \(B\) behavior—can arise as an arbitrary convention to avoid costly disputes. However, its mirror image—the dispute-avoiding “anti-Bourgeois” or \(X\) behavior through which owners concede their property to intruders—also corresponds to an evolutionarily stable strategy (ESS) under the same conditions. It has since been found repeatedly that first finders of valuable resources are frequently left unchallenged in nature, while evidence for ceding property to intruders without a contest is rare at best. An early verbal rationale for the observed rarity of \(X\) was that two individuals employing such behavior over repeated rounds would be interchanging roles repeatedly, a potentially inefficient outcome known as “infinite regress.” This argument was formalized only recently, through a Hawk–Dove model with ownership asymmetry and a fixed probability \(w\) that two individuals meet again. The analysis showed that if \(w\) and the cost of fighting exceed thresholds determined by the costs of assuming and relinquishing ownership, then \(B\) becomes the only stable convention. However, contrary to expectation, and despite the inefficiency of the \(X\) equilibrium, the analysis also showed that “infinite regress” does not invariably render \(X\) unviable. Nevertheless, this model dealt only with ESSs at which respect for ownership is either absolute or entirely absent. Here, we extend the model to allow for polymorphic evolutionarily stable states, and we use it to explore the conditions that favor partial respect for ownership. In this way, we produce an analytic model that predicts a range of degrees of partial respect for ownership, dependent on model parameters. In particular, we identify a pathway through which any degree of respect for ownership can evolve from absolute disrespect under increasing \(w\) with increasing costs of fighting.