Question

Synergy and Dynaco are the only two firms in a specific high-tech industry. They face the following payoff matrix as they decide upon the size of their research budget: Synergy’s Decision Large Budget Small Budget Dynaco’s Decision Large Budget $30 million, $20 billion $70 million, $0 Small Budget $0, $30 million $50 million, $40 million If Synergy believes Dynaco will go with a large budget, it will choose a budget. If Synergy believes Dynaco will go with a small budget, it will choose a budget. Therefore, Synergy have a dominant strategy. If Dynaco believes Synergy will go with a large budget, it will choose a budget. If Dynaco believes Synergy will go with a small budget, it will choose a budget. Therefore, Dynaco have a dominant strategy. True or False: There is a Nash equilibrium for this scenario. (Hint: Look closely at the definition of Nash equilibrium.) True False

Answer 1

If Synergy believes Dynaco will go with a large budget then choosing large budget will provide a pay-off of $20 million to synergy while choosing small budget will provide a pay-off of $0 million to synergy. As pay-off is greater in case of large budget, it will choose a large budget.

If Synergy believes Dynaco will go with a small budget then choosing large budget will provide a pay-off of $30 million to synergy while choosing small budget will provide a pay-off of $40 million to synergy. As pay-off is greater in case of small budget, it will choose a small budget.

As Synergy's choice of budget changes with the choice of budget made by Dynaco, Synergy does not have dominant startegy. Thus, given statement is false.

If Dynaco believes Synergy will go with large budget then choosing large budget will provide a pay-off of $30 million to Dynaco while choosing small budget will provide a pay-off of $0 million to Dynaco. As pay-off is greater in case of large budget, it will choose large budget.

If Dynaco believes Synergy will go with small budget then choosing large budget will provide a pay-off of $70 million to Dynaco while choosing small budget will provide a pay-off of $50 million to Dynaco. As pay-off is greater in case of large budget, it will choose large budget.

Dominant strategy is that starategy which the player chooses irrespective of the strategy adopted by rival. As it can be seen that irrespective of strategy choosen by Synergy, Dynaco is choosing the strategy of large budget. So, Dynaco has dominant strategy. Thus, given statement is True.

Since, Dynaco has dominant strategy (large budget), it will choose it. When Dynaco chooses the strategy of large budget then Synergy also choose the strategy of large budget as it can earn higher pay-off by choosing such strategy. Once the firm choose the strategy of large budget, they will only lose if they try to individually change the strategy and thus they will stick to strategy of large budget. So, the nash equilibirum of this game is (large budget, large budget). Thus, there is a Nash equilibrium for this scenario. Hence, the given statement is true.