Alternating Offer Game Approach:

1
Alternating Offer Games and Private Rulings of
the Australian Tax Office Liam Wagner
(LDW_at_maths.uq.edu.au) The Department of
Mathematics and St Johns College
Abstract The concept of submitting oneself to a
voluntary negotiation is by no means new to big
business. Formal bargaining has been quite
successful over the years in providing the venue
for agents to explore a more logical and
mathematical approach to bargaining. However in
more recent times external influences have been
applied to agents who provide better deals for
favoured executives. This external influence has
displayed itself in taxation negotiations to the
extent that tax office agents have been dismissed
for irresponsible conduct. We explore this
specific type of negotiation using an alternating
offer bargaining game to model the particular
influences, which create unfair rulings in
negotiations. By the constraints of this
systematic mathematical approach to negotiation,
we will explore the advantages of a more formal
game theoretic approach. In this presentation we
will also elaborate on finding Nash Equilibria in
alternating offer games.
The most important aspect of this type of game is
the preference relation each player uses during
such negotiations. We shall apply the conditions
outlined in Osb97, to our unique game.

• No agreement is worse than disagreement. Time
  Costs Money!!
• Time is finite Time Costs Money!!
• Preferences are stationary Both parties have the
  same goals throughout the game.
• Preferences are continuous The game should
  converge to an agreement formed by both parties
  based on their original preference relations.

Tax payer
Nash Equilibrium In games such as this, the Nash
Equilibrium is described in terms of a Sub-Game
Perfect Equilibrium. This form of solution is
essentially unique and can be found so that it
will obey the split the pie axiom of Osb97. The
importance of the existence and uniqueness of an
equilibrium shows us that the alternating offer
game can be applied to this form of negotiation .
Private Rulings The purpose of a Private Ruling
is to set out specific in terms how the rules
apply to a particular taxpayers business. Most of
the rulings sought by individuals are held and
made binding by the Australian Tax Office (ATO).
These rulings have long been thought of a as an
effective way of minimizing the administration of
the tax profile of large companies. Private
rulings also enable to the ATO to fine tune its
tax mix across a wide range of sectors by
negotiating special deals. In recent years a
great deal of controversy has developed around
the nature of this secretive method of tax
restructuring. Senior tax officials have been
charged with fraud over these secret rulings made
with big business. The system can be exposed to a
great deal of external influence as in the
Petroulias case Pet02, where a senior ATO
official was a former employee of a large company
seeking a private ruling. This form of
unnecessary risk which the ATO could conceivably
foresee, should be dealt with using specific
constructs placed on the negotiation process.
These tighter rules placed on the individual tax
agents and the applicants should yield binding
private rulings untainted by external influence.
Tax Office
Tax Payers Proposal for minimum payment Accepted
Agreement reached Private Ruling accepted
Mediation and Arbitration The next step in
confining the influence of external factors such
as prior knowledge of applicants and their
business is to apply implementation theory to our
original two player alternating offer game. We
use the concept of a mediator whose role is to
implement the confined solution concept. If we
use the dictatorial player idea expressed by
Gibbard-Satterthwaite Gib73 and Sat75, then
the game form will still express a sub-game
perfect equilibrium. This game will also have the
desired feature of a choice rule which is applied
to the undesired outcomes of the applicant and
ATO agent. This undesired outcome is most
definitely litigation and continued unsuccessful
rounds of negotiation. The mediator will assert
its preference profile of fair private rulings
which are in the best interest of both parties.
While also maintaining the right to bind the ATO
and applicant to a final ruling which shall
supersede the negotiation process.
Tax Office Withdraws Tax Payer Pays the Most Tax
Possible
Litigation Both Parties Reject Proposal

• Alternating Offer Game Approach
• We wish to construct an alternating offer game to
  describe tax negotiation with two
• players who have the desire to reach agreement.
  Our two players are both in agreement
• that a series of negotiated offers will lead to a
  satisfactory result. However
• there is still the possibility of withdrawal and
  the absolute failure which leads to
• litigation. The possibility of litigation is the
  strongest deterrent against either party
• from proposing unacceptable terms.
• This extensive form game with perfect information
  ltN,H,P, (³i)gt which is described
• as the bargaining game of alternating offers ltX,
  (³i)gt.
• The set X, of all possible outcomes is considered
  to be compact and connected subset

Results The application of an independent
mediator to the original construct of the
alternating offer game allows for free
negotiation but with the added safety of a
binding ruling. This binding ruling will be
enforced should the negotiation fail which could
lead to litigation. The independence of tax
agents can be strengthened by the presence of an
external mediator/arbiter whose role is to ensure
transparent negotiation within the bounds of
commercial in confidence.
Figure 1 Matrix of possible outcomes.
The initial step in this game is at t0, when the
tax payer (TP) submits an application for a
private ruling (PR). The proposal is a member of
X, but in this setting one would expect a minimum
amount of tax to be proposed on behalf of the TP.
It is unlikely that given the Australian Tax
Offices (ATO) preference relation on the set X a
companies proposal for minimum tax would be
accepted. Figure 1 is the matrix of possible
outcomes. In Figure 2, we show how the players
moves play out over two time intervals.

• References
• Gib73 Gibbard, A Manipulating of Voting
  Schemes A General Result 1973, Econometrica 41,
  pp.587-601
• Gin00 Gintis Game Theory Evolving 2000
  Princeton University Press
• Osb97 Osbourne and Rubinstein A Course in Game
  Theory 1997 The MIT Press
• Pet02 Petroulias v Willis 2002 NSWSC 1190
  (16th December 2002)
• Pet03 Petroulias v Willis 2003 NSWSC 106 (3rd
  March 2003)
• Sat75 Satterthwaite, M.A., Stragey-Proofness
  and Arrrows Conditions Existence and
  Correspondence Theorems for Voting Procedures and
  Social Welfare Functions, Journal of Economic
  Theory, 10, pp.187-217
• Woe02 Woellner et. al. Australian taxation law
  2003 CCH Australia, 2002.

Corresponding Addresses Department of
Mathematics,The University of Queensland St
Lucia, Brisbane 4067 Australia LDW_at_maths.uq.edu.au
http//www.maths.uq.edu.au/ldw