a) Briefly explain whether CableNorth has a dominant strategy. b) Briefly explai
ID: 2590711 • Letter: A
Question
a) Briefly explain whether CableNorth has a dominant strategy. b) Briefly explain whether CableSouth has a dominant strategy. c) Briefly explain whether there is a Nash equilibrium in this game.
Figure: Pricing Strategy in Cable TV Market 1 CableNorth Advertising No Advertising CableNorth earns $100,000 CableNorth earns $70,000 Advertising CableSouth earms S100,000eams S130,000 CableSouth CableNorth earns $130,000 CableNorth earns $150,000 C0 No AdvertisingCableSouth CableSouth eams $70,000eams $150,000Explanation / Answer
A strategy is dominant if, regardless of what any other players do, the strategy earns a player a larger payoff than any other. Hence, a strategy is dominant if it is always better than any other strategy, for any profile of other players' actions. Depending on whether "better" is defined with weak or strict inequalities, the strategy is termed strictly dominant or weakly dominant. If one strategy is dominant, than all others are dominated. For example, in the prisoner's dilemma, each player has a dominant strategy.In the prisoner’s dilemma, the dominant strategy for both players is to confess, which means that confess-confess is the dominant strategy equilibrium (underlined in red), even if this equilibrium is not a Pareto optimal equilibrium (underlined in green).It must be noted that any dominant strategy equilibrium is always a Nash equilibrium. However, not all Nash equilibria are dominant strategy equilibria.
(a) Cable north does not have a dominant strategy since a strategy is dominant only if it is always better than any other strategy, for any profile of other players' actions.The above game is a dominant strategy equilibrium.
(b) Cable south does not enjoy dominant strategy as it would have been dominant only if it is better than other strategy for any profile of other player's actions.The above game is a dominant strategy equilibrium.
(c)The Nash Equilibrium is a concept of game theory where the optimal outcome of a game is one where no player has an incentive to deviate from his chosen strategy after considering an opponent's choice. Overall, an individual can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies.
It is the solution to a game in which two or more players have a strategy, and with each participant considering an opponent’s choice, he has no incentive, nothing to gain, by switching his strategy. In the Nash Equilibrium, each player's strategy is optimal when considering the decisions of other players. Every player wins because everyone gets the outcome they desire. To quickly test if the Nash equilibrium exists, reveal each player's strategy to the other players. If no one changes his strategy, then the Nash Equilibrium is proven.
In the above strategy both cable north and cable south can choose advertising strategy and opt to earn $100,000 or no advertising strategy to earn $150,000 each. Hence, there is nash equilibrium in this game and no advertising strategy results in better outcome for both north and south cable.
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