Final answer:
The student's question relates to applying game theory to analyze strategies within given scenarios, such as the prisoner's dilemma and the ultimatum game. The dominant strategy often leads to non-cooperative outcomes, which is illustrated by the prisoner's dilemma where both players confess. More fair strategies in the ultimatum game may yield long-term benefits and depend on multiple factors including the relationship between the players and knowledge of past behaviors.
Step-by-step explanation:
The student's question involves strategies within the context of game theory, which is a branch of mathematics used to study strategic interactions with formalized incentive structures. We're dealing with certain classic game theory scenarios, including the prisoner's dilemma and strategic decision-making. The specifics of the prisoner's dilemma illustrate how individual self-interest can lead to a suboptimal outcome, and that the dominant strategy in this case is for both prisoners to confess, resulting in a total of 10 years of jail time between them.
An important insight offered by these game theory examples is that despite the temptation to act in one's own interest, cooperation or more equitable strategies can be beneficial. For instance, in the ultimatum game, a fairer offer might be the best strategy as it increases the chance of acceptance and could lead to better results over the long term.
Player 1's optimal response to Player 2 playing strategy C, the existence of a dominated strategy for Player 1, and the determination of Nash Equilibria all require specific payoff matrices or additional context that wasn't provided.