Any person suffering damage pursuant to the provisions of this article shall report the damage to a locally designated official whose duty it shall be to have the damage investigated. The claim for damage shall be filed under oath and in a manner and form as may be prescribed by the local governing body. If the claimant and the designated local official agree as to the amount of damage, the local governing body may approve the amount and order payment thereof from the special damage stamp fund established by this article. No claim for damages shall be paid to any person who does not permit the hunting of big game or elk by licensed hunters on his property. However, the fact that a landowner places reasonable restrictions on the number of licensed hunters who are permitted to hunt big game or elk on his property shall not disqualify him from filing a claim for damages pursuant to this section. In the event that no agreement as to the amount of damages can be reached, the claimant may initiate an action in the general district court of the county in which the damage occurred.