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Tata's Corus buy: A game theory analysis
November 02, 2006
Tata Steel's acquisition of Corus shows how coordinated strategies can yield greater benefits even in a competitive marketplace. The strategic fit of Corus's range of high-end products and know-how, and its access to developed markets, combined with Tata's low-cost access to ore, efficient basic steel production, and its own market access certainly provide a solid starting point.
What they have done is breaking out of the self-limiting constraints of non-cooperative reasoning that actually ends up being suboptimal. Instead, a coordinated solution through collaboration has led to the potential for greater gains for both.
The game plan
Starting with an expectation of a good potential fit, let us see how Tata and Corus have together won out. Visualise a two-dimensional (X-Y) space with Tata's objective function along the horizontal axis (X) and Corus's along a vertical axis (Y).
The essential requirement for this analysis is that there is an objective function, i.e. a line that measures increasing overall benefit, which can be defined separately for each party along one of these axes.
We may surmise that Tata's primary concern was to pay no more than reasonable compensation for Corus in order to result in a profitable combination, shown as a percentage cut from a notional asking price on the horizontal axis.
Corus's objective function could be the retention of maximum sustainable benefits with employment participation (assuming that the management and union are in sync). This is shown as a percentage on the vertical axis.
Mapping Tata's and Corus's responses in terms of the percentage cut in price and percentage benefits retained, we get one set of points for Tata and another set for Corus.
A line through the first set represents Tata's response function or strategy, and a line through the other set represents Corus's response function. For a given cut in price, Tata favours fewer benefits than Corus expects, and for a given benefit level, Corus wants less of a price cut than Tata.
The Hamada diagram
The Hamada diagram enables a graphic depiction of game theory, and this analysis is an adaptation.* Tata's ideal solution, referred to as its "bliss point", is on its strategy line corresponding to a high price cut.
This is where it has its highest economic welfare. Corus's bliss point, likewise, is on its strategy line where retained benefits are high. Each party's economic welfare decreases as it moves away from its bliss point; each party's indifference curves are therefore concentric around its bliss point.
For Tata Steel, as the cost of acquisition reduces moving right along the horizontal axis, Tata can concede more benefits to Corus's employees.
For Corus, the management and employees seek a sustainable long-term solution that yields benefits with participation.
Despite their premium product line, image, and access to markets for these products, their high-cost structure militates against easy solutions. This realisation impelled Chairman James Leng of Corus to initiate discussions with potential alliance candidates.
Tata's and Corus's responses intersect (coincide) at N, the non-cooperative or Nash equilibrium.
This is the norm for non-zero-sum games when players adopt conflicting, mistrustful strategies, so competitive responses force the solution to a point where neither can benefit by acting unilaterally.
Coordinated solutions, however, can make both better-off, i.e. deliver a bigger price cut together with more benefits. This is because efficiency occurs where the respective indifference curves are tangential to each other, whereas they intersect at the point of Nash equilibrium.
These tangential points are on the "contract curve" joining the two bliss points. A coordinated solution on this line is efficient, and at the midpoint C, is Pareto optimal (most efficient).
As things are never as simple as they seem, consider some real-world complexities. One set arises from limits imposed by either side for economic, political or emotional reasons, e.g. a reserve price by Corus that is short of the Pareto optimal level at C, which would introduce an asymptote (vertical line) at AC, and/or a cap on benefits by Tata (a horizontal line) at AT.
The response functions themselves are likely to be curved rather than straight, and will tail off parallel to the asymptotes. Therefore, the solution at C may be infeasible, and the best-feasible-solution may be suboptimal at S.
Still, the take-away is that the model helps us understand aspects of reality by abstracting some of its elements, so we can better focus on them. Its usefulness is in the insights into the rationale for going beyond our self-imposed barriers in seeking better solutions, and these are necessarily collaborative solutions that can take us beyond non-cooperative equilibrium.
"It begins to seem that the only zero-sum games are literal games that human beings have invented � for our own amusement. 'Games' that are in some sense natural are non-constant sum games." **
This has wide applications in a variety of real-life situations far removed from macroeconomics, where the Hamada diagram originated, and can work for public-private partnerships as well as for private sector alliances or acquisitions.
Take the recent airlines association formation, or the standoff between Delhi Metro versus the rest: the champions of the Bus Rapid Transit Systems, the High Capacity Bus System, etc.
There is every reason to jettison silo mentalities and dogmatic arguments, and instead seek coordinated solutions drawing on abilities beyond adversarial contention, polemic and disputation.
The first requirement is diverse skills and domain knowledge in the group evaluating situations and developing workable solutions. Good intentions are desirable, but expertise is absolutely essential.
The next is to focus, first of all, on the fundamental objective. Presumably, this should be defined in the public interest.
Finally, even if Pareto optimality is infeasible, the need is to design and develop a pragmatic, best-feasible-solution work plan, and execute it well.
** Roger McCain, "Game Theory: A Non-Technical Introduction to the Analysis of Strategy": http://william-king.www.drexel.edu/top/eco/game/game-toc.htmlThe author was formerly M&A Head at Citibank.
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