How to implement a transaction process between users using the Privatemsg module?
You may want to use the integration between the User Points module and the Rules module to "roll your own cookies", by writing some custom rules to transfer user points from one account to another.

As a sample, have a look at this rule, which is used in combination with voting of a node, whereas the author looses "-2" points, and the voter looses "-1" points:

{ "rules_votedown_question" : {
    "LABEL" : "votedown_question",
    "PLUGIN" : "reaction rule",
    "OWNER" : "rules",
    "TAGS" : [ "answers" ],
    "REQUIRES" : [ "rules", "voting_rules", "userpoints_rules" ],
    "ON" : { "voting_rules_insert_node" : [] },
    "IF" : [
      { "node_is_of_type" : {
          "node" : [ "node" ],
          "type" : { "value" : { "answers_question" : "answers_question" } }
        }
      },
      { "voting_rules_condition_check_vote_value" : { "vote" : [ "vote" ], "value" : "-1" } }
    ],
    "DO" : [
      { "userpoints_action_grant_points" : {
          "user" : [ "node:author" ],
          "points" : "-2",
          "tid" : "0",
          "entity" : [ "" ],
          "description" : "Receive downvote to [node:type-name] \u0022[node:title]\u0022",
          "operation" : "QuestionDownvoteReceived",
          "reference" : "By uid=[vote:uid], for [node:type-name] to q=\u003Ca href=\u0022\/node\/[node:nid]\u0022\u003E[node:title]\u003C\/a\u003E",
          "display" : "1",
          "moderate" : "default"
        }
      },
      { "userpoints_action_grant_points" : {
          "user" : [ "vote:user" ],
          "points" : "-1",
          "tid" : "0",
          "entity" : [ "" ],
          "description" : "Issue downvote to [node:type-name] \u0022[node:title]\u0022",
          "operation" : "QuestionDownvoteIssued",
          "reference" : "From uid=[node:author:uid], for [node:type-name] to q=\u003Ca href=\u0022\/node\/[node:nid]\u0022\u003E[node:title]\u003C\/a\u003E",
          "display" : "1",
          "moderate" : "default"
        }
      }
    ]
  }
}


If you simply adapt the amount of points (-2 and -1) to something like (eg) +25 and -25, you've a prototype to transfer (25) user points from one user to another.

If you replace the Rules event by an event like "Something is flagged" (created with the Flag module, and the "something" being a product), then a simple click could be used to indicate "I want to transfer 25 user points of mine to this user" (probably to trade that product in your case).

You could take this even a step further: since flags are fieldable, you could add these fields to such flag (to implement a bidding-system):


A field to indicate the amount of points to be "moved" (= like the price to be payed for the product?).
A field to indicate the price requested by the seller.
A field to indicate the price offered by a potential buyer.
A field for some text to be used for storing some message text. Possibly you may want to "deliver" that message text using the Message module, which has a great integration with Rules also (though it's not obvious to get started with the Message module).


Note: The above Rules example may need further refinements, e.g. if you want to ensure that after moving points van User A to User B, the remaining points for User A is not negative. Refer to "How to check whether one&#39;s current User Points are negative with the Rules module?" for details about how you can implement such refinement also.