Appendix 4. Management via information market.

Our information market model is based on Brock and Hommes (1997), who demonstrated a wide range of dynamic behaviors in a simple model of agent choice. At each time step, agents decide among two or more alternatives. For example, in the Market Management model, agents decide whether to use freely available information or to purchase more sophisticated information. In the Land Manager model, farmers decide whether to invest in phosphorus-intensive or phosphorus-conservative activities. The alternative actions lead to different ecosystem dynamics, different learning, and future perceptions of the system, and thereby influence future decisions. The agents choose between actions on the basis of their expectation of total value that can be obtained from each alternative. Specifically, the proportion of agents Ni choosing action i(i = 1 . . . n) is

Ni = exp(χi Vi) / Σ exp(χi Vi)

(A.4.1)

 (Brock and Hommes 1997), where Vi is the value expected under action i; χi is a parameter that determines the intensity choice between the two actions.