The Evolution of Conflict under Inertia∗

In Norman (2003a), the introduction of individual strategy switching costs, and thus inertia, into stochastic evolutionary coordination games was found inter alia to strengthen the mixed-strategy equilibrium as a shortto medium-run equilibrium. This paper considers the impact of such switching costs on the conflict scenario of HawkDove games. The “attractive” mixed-strategy equilibrium of HawkDove games represents a far better candidate for long-run equilibrium than its unstable counterpart in coordination games, and yet robust selection results have proved elusive, with conditions on the selection dynamics generally being required. Such a condition remains a necessity in the switching cost model with state-independent mutations. However, a more realistic model of state-dependent mutations driven by stochastic switching costs overcomes this problem, and identifies a threshold mean switching cost, above which the mixed-strategy equilibrium is selected in the long run for a wide class of switching cost distributions. ∗Discussions with my supervisors, David Myatt and Chris Wallace, as well as with Margaret Meyer, Kevin Roberts and seminar participants at the Department of Economics, Oxford University, are gratefully acknowledged. The usual disclaimer applies.