Two oligopolistic aluminum manufacturers are engaged in bitter competition with

Question

Two oligopolistic aluminum manufacturers are engaged in bitter competition with one another. The biggest firm. Big Aluminum Giant (BAG), is deciding whether to expand capacity or hold the line. The smallest firm. Little Aluminum Giant (LAG), is also considering expansion. The table below shows payoffs for the firms under various scenarios: What is the Nash equilibrium outcome in this game of capacity expansion? Why? How docs dominance play a role in arriving at your answer? Suppose the game is played sequentially, with BAG moving first. What is BAG'S best strategy? Docs it lead to the same equilibrium you found in the simultaneous game? Suppose instead that the payoffs to the game are as follows:

Explanation / Answer

A)

Here the nash equilibrium is where LAG expands and BAG dosen't. The dominant strategy of BAG is not to expand, But LAG is to best response to expand. So the nash equilibrium is (Expand, Dont expand)

B)

Here the BAG's strategy is choose to not expand, LAG is to expand. So the manufactures payoff is maximised. Here the sequantial game gives same conclusion for the simultenous game.

C)

We know that mixed strategy nash equilibrium means that a player plays his available pure stragies with certain probabilities.

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