Appendix S1 - Game-Theoretic Methods for Functional Response and Optimal Foraging Behavior

The first section of the Appendix, Decision trees and the functional responses, describes a general approach to construct functional responses from decision trees. The second section, Zero-one rule and the Nash equilibrium, generalizes the classical zero-one rule of the optimal foraging theory derived for the multi-prey Holling type II functional response to a more general functional responses. This section also shows how the zero-one rule relates to the Nash equilibrium of the underlying optimal foraging game. Appendix Foraging with simultaneous resource encounters derives the Nash equilibrium strategy (8), (10) and Appendix The Nash equilibria of the prey recognition game derives the Nash equilibrium (13), (14).
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