Two firms, Folger\'s (player A) and Maxwell House (player B) are the only seller

Question

Two firms, Folger's (player A) and Maxwell House (player B) are the only sellers of a newly developed coffee product. Both players are seeking market share, and the one who gains the most market share will be the one who spends the most on advertising and promotion. Each firm must decide how much to spend on advertising. Each firm may adopt either a higher (H) budget or a low (L) budget. The normal form representation of the game is below: What is the non-cooperative simultaneous move (i.e. not sequential) nash equilibrium of the game? Remember to specify the player and the strategy, NOT the payoffs. A strategy is dominant if, regardless of what any other players do, the strategy earns a player a larger payoff than any other (technically, greater than or equal to). What this translates into is you play the dominant strategy regardless of what the other guy does because of this payoff structure. Does the game above have a dominant strategy for player A or player B? How might you change the payoffs for player A, so that L is a dominant strategy

Explanation / Answer

a)

Non Cooperative simultaneous move

Firm B adopt low budget-Payoff of A when budget is L is 7 and when budget is H is 6. Thus player A has more payoff when adopt low budget

Firm B adopt High Budget- Payoff of A when budget is L is 5 and when budget is H is 6. Thus playerA has more payoff when adopt High budget

Firm A adopt low budget- Payoff of B when budget is L is 5 and when budget is H is 4. Thus player B has more payoff when adopt low budget

Firm A adopt High budget- Payoff of B when budget is L is 4 and when budget is H is 3. Thus player B has more payoff when adopt low budget

b)

The payoff of A depends on what strategy B chose. If B choses L, then A payoff is maximized at L and If B chooses H A payoff is maximised at H. Thus A don’t have any dominant strategy

Payoff of B is maximized at L when A chooses L and also L when A chooses H. Thus payoff of B is maximised when it chooses L or adopt low budget irrespective of what A chooses. Thus B has dominant strategy by adopting low budget

c)

If payoff of A at L when B is H is changed from 5 to 6(5+1), then A will also have dominant strategy as below.

L

H

L

7,5

6,4

H

6,4

6,3

Thus A payoff of Maximized by choosing L irrespective of what B chooses. Thus Form A dominant strategy will be to adopt low budget

L

H

L

7,5

6,4

H

6,4

6,3

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