  A long line of research on secure computation has confirmed that anything
that can be computed, can be computed securely using a set of non-colluding
parties. Indeed, this non-collusion assumption makes a number of problems
solvable, as well as reduces overheads and bypasses computational hardness
results, and it is pervasive across different privacy-enhancing technologies.
However, it remains highly susceptible to covert, undetectable collusion among
computing parties. This work stems from an observation that if the number of
available computing parties is much higher than the number of parties required
to perform a secure computation task, collusion attempts in privacy-preserving
computations could be deterred.
  We focus on the prominent privacy-preserving computation task of multi-server
$1$-private information retrieval (PIR) that inherently assumes no pair-wise
collusion. For PIR application scenarios, such as those for blockchain light
clients, where the available servers can be plentiful, a single server's
deviating action is not tremendously beneficial to itself. We can make
deviations undesired via small amounts of rewards and penalties, thus
significantly raising the bar for collusion resistance. We design and implement
a collusion mitigation mechanism on a public bulletin board with payment
execution functions, considering only rational and malicious parties with no
honest non-colluding servers. Privacy protection is offered for an extended
period after the query executions.
