Shyam Ponappa: Tata’s Corus buy: A game theory analysis

I hope Professor Noonan agrees that this is a very insightful read on the game theory analysis of Tata’s acquisition of Corus. I’ve copied the text below with few comments/remarks (in []) from myself to explain the “game” aspect of the deal:

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.

[vduvvur: And hence when the deal was being made, there would've been a negotiation going on between the parties about the mix of price vs. employee benefits. It is similar to the Riverside DEC case we did in SDA where DEC could help Riverside with certain financial incentives to adapt a new technology, and Riverside could choose certain particular forms of help and mix them to ensure they receive max benefits]

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 [vduvvur: the bliss point could be seen as the BATNA, where each party maximize their payoffs], 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. [vduvvur: this indifference curve can be seen as the Pareto frontier, along which lies the maximum value created from the transaction]

# 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 (Figure 2).

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).