  Deception plays a key role in adversarial or strategic interactions for the
purpose of self-defence and survival. This paper introduces a general framework
and solution to address deception. Most existing approaches for deception
consider obfuscating crucial information to rational adversaries with abundant
memory and computation resources. In this paper, we consider deceiving
adversaries with bounded rationality and in terms of expected rewards. This
problem is commonly encountered in many applications especially involving human
adversaries. Leveraging the cognitive bias of humans in reward evaluation under
stochastic outcomes, we introduce a framework to optimally assign resources of
a limited quantity to optimally defend against human adversaries. Modeling such
cognitive biases follows the so-called prospect theory from behavioral
psychology literature. Then we formulate the resource allocation problem as a
signomial program to minimize the defender's cost in an environment modeled as
a Markov decision process. We use police patrol hour assignment as an
illustrative example and provide detailed simulation results based on
real-world data.
