  The problem of analyzing the effect of privacy concerns on the behavior of
selfish utility-maximizing agents has received much attention lately. Privacy
concerns are often modeled by altering the utility functions of agents to
consider also their privacy loss. Such privacy aware agents prefer to take a
randomized strategy even in very simple games in which non-privacy aware agents
play pure strategies. In some cases, the behavior of privacy aware agents
follows the framework of Randomized Response, a well-known mechanism that
preserves differential privacy.
  Our work is aimed at better understanding the behavior of agents in settings
where their privacy concerns are explicitly given. We consider a toy setting
where agent A, in an attempt to discover the secret type of agent B, offers B a
gift that one type of B agent likes and the other type dislikes. As opposed to
previous works, B's incentive to keep her type a secret isn't the result of
"hardwiring" B's utility function to consider privacy, but rather takes the
form of a payment between B and A. We investigate three different types of
payment functions and analyze B's behavior in each of the resulting games. As
we show, under some payments, B's behavior is very different than the behavior
of agents with hardwired privacy concerns and might even be deterministic.
Under a different payment we show that B's BNE strategy does fall into the
framework of Randomized Response.
