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The auditing game only has a PBNE in mixed strategies.
In a PBNE in mixed strategies, insurers choose their audit strategy in order to make policyholders without a loss indifferent between their actions.
Proposition 1: If [beta] > c, [pi] < 1/2 and [phi] > [[kappa].sup.c] hold, the unique PBNE in mixed strategies for a given fraud detection system with [phi] > [delta] > 0 has the following properties:
A PBNE in mixed strategies will only exist if a policyholder is able to make the insurer indifferent between its action.
Since all six elements of the PBNE have been found, the proof is done.
Constraints (4) and (3) represent the PBNE strategies of the players.
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