This thesis aims to explore the effect of overconfidence on people's decision
making. To approach this topic, a standard binary detection problem is
considered, and its associated individual decision rule and decision fusion
rule are derived. Following an axiomatic and empirical approach, a variant
of the Prelec function from cumulative prospect theory is then developed to
model the effect of overconfidence as a function of level of training. Next, the
probability of detection after decision fusion is derived, and a combinatorial
optimization is considered which aims to select a subgroup of people/agents
to maximize the overall probability of detection.
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