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# Decision Analysis: Game theory

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The Baseball Players' Association has voted to go on strike if a settlement is not reached with the owners within the next month. The players' representative, Melvin Mulehead, has two strategies (containing different free agent rules, pension formulas, etc.); the owners' representative, Roy Stonewall, has three counterproposals. The financial gains, in millions of dollars, from each player strategy, given each owner strategy, are shown in the following payoff table:

a. Determine the initial strategy for the players and for the owners.
b. Is this a pure or a mixed strategy game? Explain.

#### Solution Summary

Solution contains the initial strategy for the players and for the owners and explain if this is a pure or a mixed strategy game.

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## In the following problem you need to determine whether a threat by an incumbent firm is credible and if it will deter a would be entrant, establish a way to make the threat be made credible, and demonstrate the process of backward induction to find an equilibrium.

Maytag wants to prevent Whirlpool from entering the market for high priced, front load washing machines. Front load washing machines clean clothes better and use less water than conventional top load machines. Even though front load machines are more costly to manufacture than top loaders, Maytag is nonetheless earning economic profit as the only firm making front loaders for upscale consumers. The following table show the annual profits (in millions of dollars) for Maytag and Whirlpool for the pricing and entry decisions facing the two firms.

(see attached document)

a) Can Maytag deter Whirlpool from entering the market for front load washing machines by threatening to lower price to \$500 if Whilrpool enters the market? Why or why not?

Suppose the manager of Maytag decides to make an investment in extra production capacity before Whirlpool makes its entry decision. The extra capacity raises Maytag's total costs of production but lowers its marginal costs of producing extra front load machines. The payoff table after this investment in extra production capacity is shown here:

(see attached document)

b) Can Maytag deter Whirlpool from entering the profitable market for front load washing machines? What must be true about the investment in extra production capacity in order for the strategic move to be successful? Explain.

c) Construct the sequential game tree when Maytag makes the first move by deciding whether to invest in extra production capacity. Use the roll back technique to find the Nash equilibrium path. How much profit does each firm earn? (Hint: the game tree will have three sequential decisions: Maytag decides first whether to invest in extra plant capacity, Whilrpool decides whether to enter, and Maytag makes its pricing decision.)

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