<PAGE>

                                                                   EXHIBIT 10.13

                            HARKEN ENERGY CORPORATION

                        AGREEMENT REGARDING COMPENSATION
                         IN EVENT OF A CHANGE IN CONTROL


This Agreement regarding Compensation In the Event of a Change In Control (the
"Agreement") is made and entered into this the 1/st/ day of February, 2000, but
to be effective as of the 30/th/ day of December, 1999, ("Effective Date") by
and between HARKEN ENERGY CORPORATION, a Delaware corporation, (the "Company")
and MIKEL D. FAULKNER an individual ("Executive").

WHEREAS, the Compensation Committee (the "Committee") of the Board of Directors
(the "Board") of the Company did adopt certain resolutions dated August 26, 1998
providing for an Executive Severance Policy for officers of the Company and
other members of management ("Executive Severance Policy") of the Company, as
therein defined, in the event of certain circumstances, including a Change of
Control, as hereinafter defined, occurring; and,

WHEREAS, the Committee has determined that is in the Company's best interest and
that of its shareholders to enter into this Agreement with Executive to further
expand on the benefits provided for under the referenced resolutions
("Resolutions") creating the Executive Severance Policy for certain named
Executive officers of the Company and its operating subsidiaries as provided for
in resolutions of the Committee dated December 30, 1999; and,

WHEREAS, Executive is as of the Effective Date an executive officer of the
Company or of one of its operating subsidiaries and has been identified by the
Committee as a person on whom the Company relies and whom it is in the Company's
best interest to retain in its employ; and,

WHEREAS, this Agreement, when duly signed and accepted by Executive shall
define, set forth and provide the benefits, payments and obligations of the
Company to the Executive in the event of the occurrence of a Change of Control,
in lieu and replacement of those similar benefits offered and provided to
Executive under the Executive Severance Policy as set out under the Resolutions;
and,

WHEREAS, the Committee has determined that the Company will receive significant
benefit and value from this Agreement in preserving for the Company the
employment and services of Executive in the event a Change of Control event
should occur, which value and benefit to the Company will at least be equal to
the obligations hereunder assumed by the Company.

NOW THEREFORE, for and in the mutual considerations recited and referred to
herein, the Company and Executive do hereby agree as follows:

Change of Control Payment

     1.   In the event any Change of Control event shall occur and Executive is
          at that date in the current employ of the Company, then the Company
          shall owe and pay to

<PAGE>

          Executive within thirty (30) calendar days following such triggering
          event, as additional earned income, a cash payment (the "Change of
          Control Payment") equal to twenty-four (24) times Executive's regular
          monthly salary which was last paid prior to the month in which such
          Change of Control event occurred.

Definition of In Company's Employ

     2.   In the event that Executive's employment with the Company shall have
          terminated or been terminated voluntarily or involuntarily, with cause
          or without cause within forty-five (45) calendar days prior to such
          Change of Control event occurring, then for purposes of this
          Agreement, the Executive shall be deemed to be in the Company's employ
          when the Change of Control event occurred and Executive shall be
          entitled to the benefits under this Agreement.

          In the event that Executive shall on the date such Change of Control
          event occurs be on leave of absence, vacation, short-term disability,
          sick leave or other similar situation in which Executive is not
          physically on the job, with the consent of the Company or as allowed
          under Company Policies, then in any such event Executive shall be
          deemed to be in the current employ of the Company on that date for
          purposes of this Agreement.

Termination of Employment in Change of Control

     3.   In the event of a Change of Control occurring as herein defined and
          Executive is in or is deemed to be in the employ of the Company as
          herein defined, then Executive shall be entitled to receive and be
          paid the Change of Control Payment irregardless of whether or not
          Executive's employment is thereafter continued or terminated by the
          Company or any successor or assignee of the Company. Such Change of
          Control Payment shall not be in lieu of nor in replacement of any
          severance, other benefits, rights or compensation Executive may
          otherwise be or become entitled to receive from the Company pursuant
          to any policies of the Company then in effect. The Company may not in
          any way request nor require the Executive to waive, delay, forfeit,
          exchange nor in any other way relinquish this Change of Control
          Payment nor the right to receive the same.

          In any event where Executive's employment with the Company is
          terminated voluntarily or involuntarily, with cause or without,
          whether in connection with a Change of Control or not, Executive's
          rights to severance, and other benefits to be paid by or due from the
          Company to Executive shall be without regard to this Agreement and the
          Change of Control Payment arising to Executive hereunder, save and
          accept, if Executive's employment is terminated in connection with and
          at the time of a Change of Control event then if Executive receives
          benefits under this Agreement he shall not also be entitled to receive
          similar benefits arising under the Executive Severance Policy if this
          Policy is triggered by the same Change of Control event.

                                        2

<PAGE>

Change of Control

     4.   A "Change of Control" event as contemplated and defined under this
          Agreement shall be deemed to occur upon any one or more of the
          following events occurring:

               i)   the Board shall approve, or the Company shall otherwise
                    sell, transfer or convey to a person or party not
                    wholly-owned and controlled by the Company, all or
                    substantially all of the assets of the Company in any one
                    transaction or a series of transactions;

               ii)  the consolidation or merger of the Company with or into
                    another person or company pursuant to a transaction in which
                    the outstanding voting stock of the Company is changed into
                    or exchanged for cash, securities or other property, other
                    than any such transaction where (a) the outstanding voting
                    stock of the Company is changed into or exchanged for voting
                    stock of the surviving corporation or its parent and (b) the
                    holders of the voting stock of the Company immediately prior
                    to such transaction own, directly or indirectly, not less
                    than a majority of the voting stock of the surviving
                    corporation or its parent immediately after such
                    transaction;

               iii) a "person" or "group" (within the meaning of Sections 13(d)
                    or 14(d)(2) of the Exchange Act) being or becoming the
                    "beneficial owner" (as defined in Rules 13d-3 and 13d-5
                    under the Exchange Act) of more than fifty percent (50%) of
                    the voting stock of the Company then outstanding;

               iv)  during any period of two (2) consecutive years, or less,
                    individuals who at the beginning of such period constitute
                    the Board (together with any new directors whose election by
                    such Board or whose nomination for election by the
                    stockholders of the Company was approved by a vote of a
                    majority of the directors then still in office who were
                    directors at the beginning of such period or whose election
                    or nomination for election was previously so approved) cease
                    for any reason (other than death) to constitute a majority
                    of the Board then in office;

               v)   the approval by the Board or by the stockholders of any plan
                    or proposal for the liquidation or dissolution of the
                    Company;

               vi)  any other event or series of events that results in a change
                    or right to change a majority of the members of the Board;
                    or

                                        3

<PAGE>

               vii) any event which causes a triggering of or a Change of
                    Control to occur as set forth under the Stockholder Rights
                    Plan adopted by the Board on April 7, 1998.

Indemnification of Executive

     5.   The Company agrees to indemnify and hold harmless the Executive from
          any claim, liability or action which may arise from any party, entity
          or source in regard to this Agreement or regarding any payment made by
          the Company to Executive pursuant to this Agreement.

Successors and Assigns

     6.

               a)   The Company covenants with Executive that it will require
                    any successor (whether direct or indirect, by purchase,
                    merger, consolidation or otherwise) to all or substantially
                    all of the business or assets of the Company to expressly
                    assume and agree to perform this Agreement in the same
                    manner and to the same extent that the Company is obligated
                    to perform it. Failure of the Company to obtain such
                    assumption and agreement prior to the effectiveness of any
                    such succession shall be a material breach of this
                    Agreement. As used in this Agreement, ("Company") shall mean
                    the Company as defined in this Agreement and any successor
                    to its business or assets as aforesaid which assumes and
                    agrees to perform this Agreement by operation of law, or
                    otherwise.

               b)   This Agreement shall inure to the benefit of and be
                    enforceable by the Executive's personal or legal
                    representatives, executors, administrators, successors,
                    heirs, distributees, devisees and legatees. If the Executive
                    should die within forty-five (45) days prior to the
                    occurrence of a Change of Control event and the Change of
                    Control Payment would otherwise have been payable to him
                    hereunder if he had continued to live, all such amounts,
                    unless otherwise provided herein, shall be paid in
                    accordance with the terms of this Agreement to the
                    Executive's spouse or, if there is no such spouse, to the
                    Executive's estate. This Agreement is personal to the
                    Executive and may not be assigned by him.

               c)   Except to the extent allowed hereunder, no party may assign
                    either this Agreement or any of his, her, or its rights,
                    interests, or obligations hereunder without the prior
                    written approval of the other party.

                                        4

<PAGE>

No Guaranteed Employment

     7.   This Agreement shall not constitute nor be construed nor interpreted
          as any guarantee nor contract for continued employment of Executive
          with the Company, any subsidiary or any successor company. The parties
          stipulate that as to any rights of ongoing or future employment, that
          the Executive is an employee at will.

Notices

     8.   For the purposes of this Agreement, notices and all other
          communications provided for in this Agreement shall be in writing and
          shall be deemed to have been duly given when delivered by hand or
          mailed by United States overnight express mail, or nationally
          recognized private delivery service on an overnight basis, return
          receipt requested, postage prepaid, addressed as follows:

                    If to the Executive:       Mikel D. Faulkner

                         Office Address:       c/o Harken Energy Corporation
                                               16285 Park Ten Place, Suite 600
                                               Houston, Texas 77084

                         Home Address:         1000 S. Peytonville
                                               Southlake, Texas 76092

                    If to the Company:         Harken Energy Corporation
                                               16285 Park Ten Place, Suite 600
                                               Houston, Texas 77084
                                               Attn: Corporate Secretary
                                               Tel: (281) 717-1300
                                               Fax: (281) 717-1400

          Notices may also be sent to such other addresses as either party may
          have furnished to the other in writing in accordance herewith, except
          that notice of change of address shall be effective only upon receipt.

Miscellaneous

     9.

                    (a)  Entire Agreement. This Agreement constitutes the entire
                         agreement between the parties with respect to the
                         subject matter hereof and supersedes all other prior
                         agreements and understandings, both written and oral,
                         between the parties with respect to the subject matter
                         hereof.

                                        5

<PAGE>

          (b)  Amendments, Waivers, Etc. This Agreement may not be amended,
               changed, supplemented, waived or otherwise modified or
               terminated, except upon the execution and delivery of a written
               agreement executed by the parties hereto.

          (c)  Specific Performance. Each of the parties acknowledges and agrees
               that the other party would be damaged irreparably in the event
               any of the provisions of this Agreement are not performed in
               accordance with their specific terms or otherwise are breached.
               Accordingly, each party agrees that the other party shall be
               entitled to an injunction or injunctions to prevent breaches of
               the provisions of this Agreement or any of them and to enforce
               specifically this Agreement and the terms and provisions hereof
               in any action instituted in any court of the United States or any
               state thereof having jurisdiction over the parties and the
               matter, in addition to any other remedy to which may be entitled,
               at law or in equity.

          (d)  Severability. Whenever possible, each provision or portion of any
               provision of this Agreement will be interpreted in such manner as
               to be effective and valid under applicable law, but if any
               provision or portion of any provision of this Agreement is held
               to be invalid, illegal or unenforceable in any respect under any
               applicable law or rule in any jurisdiction, then such invalidity,
               illegality or unenforceability will not affect any other
               provision of portion of any provision in such jurisdiction as if
               such invalid, illegal or unenforceable provision or portion of
               any provision had never been contained herein.

          (e)  No Waiver. The failure of any party hereto to exercise any right,
               power or remedy provided under this Agreement or otherwise
               available in respect hereof at law or in equity, or to insist
               upon compliance by any other party hereto with its obligations
               hereunder, and any custom or practice of the parties at variance
               with the terms hereof, shall not constitute a waiver by such
               party of its right to exercise any such or other right, power or
               remedy or to demand such compliance.

          (f)  No Third Party Beneficiaries. This Agreement is not intended to
               be for the benefit of, and shall not be enforceable by, any
               person or entity who or which is not a party hereto, other than
               the parties hereto and their permitted successors, devisees and
               assigns.

                                       6

<PAGE>

          (g)  Governing Law. This Agreement shall be governed by and construed
               in accordance with the laws of the State of Texas, without giving
               effect to the principles of conflicts of law thereof.

          (h)  Construction. The parties have participated jointly in the
               negotiation and drafting of this Agreement. In the event an
               ambiguity or question of intent or interpretation arises, this
               Agreement shall be construed as if drafted jointly by the parties
               and no presumption or burden of proof shall arise favoring or
               disfavoring any party by virtue of the authorship of any of the
               provisions of this Agreement. Any reference to any federal,
               state, local, or foreign statute or law shall be deemed also to
               refer to all rules and regulations promulgated thereunder, unless
               the context requires otherwise. The word "including" shall mean
               including without limitation. The singular shall include the
               plural and the masculine shall include the feminine and neuter
               and vice versa, as the context requires.

          (i)  Descriptive Headings. The descriptive headings used herein are
               inserted for convenience of reference only and are not intended
               to be part of or to affect the meaning or interpretation of this
               Agreement.

          (j)  Counterparts. This Agreement may be executed in counterparts,
               each of which shall be deemed to be an original, but all of
               which, taken together, shall constitute one and the same
               Agreement. This Agreement shall not be effective as to any party
               hereto until such time as this Agreement or a counterpart thereof
               has been executed and delivered by each party hereto.

          (k)  Further Assurances. The parties agree (i) to furnish upon request
               to each other such further information, (ii) to execute and
               deliver to each other such party documents, and (iii) to do such
               other acts and things, all as the other party may reasonably
               request for the purpose of carrying out the intent of this
               Agreement and the documents referred to in this Agreement.

IN WITNESS WHEREOF, the parties have caused this Agreement to be duly executed
on the day first set forth above.

                                                        EXECUTIVE


                                                         /s/ Mikel D. Faulkner
                                                        ------------------------
                                                        Name:  Mikel D. Faulkner

                                       7

<PAGE>

                                                       HARKEN ENERGY CORPORATION



                                                       By: /s/ Larry E. Cummings
                                                          ----------------------
                                                       Name:  Larry E. Cummings
                                                       Its:   Vice President




LEGAL/LMH/chgcontrolagrmdf

                                       8