Watch This Video And Answer In The Video

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1. Watch this video and answer: In the video, they played the game about 200 times. That is long enough that people may treat it as infinite. However, imagine if you played this just TWO times. Now, try to think ahead: in the second period, would you expect the players to defect or cooperate? And given that answer, how would that impact the first period?

2. Watch this video and answer: What is the key difference between a simultaneous game and a sequential game, i.e., why is one a matrix and the other a tree? Each question just needs several sentences, I need it in 12 hours.

Paper For Above instruction

The questions referenced involve fundamental concepts in game theory, which models strategic interactions among rational decision-makers. The first question explores how the game evolves over repeated plays, particularly contrasting scenarios of many repetitions versus a limited number of plays. The second question seeks to distinguish the structural differences between two primary types of strategic games: simultaneous and sequential.

Regarding the first question, when a game like the Prisoner’s Dilemma is played repeatedly many times—approaching an infinite horizon—players tend to develop strategies based on long-term relationships, reputation, and potential future punishments or rewards. The theory of the iterated prisoner's dilemma suggests that cooperation can emerge as a stable strategy over many rounds, as players learn to trust one another or reciprocate cooperation (Nowak & Sigmund, 1993). However, if only two rounds are played, the game resembles a finite one with a backward induction structure. In this finite setting, players anticipate that the other will defect in the last round since there is no future punishment, which in turn leads to defection in the second round as well—known as the "endgame effect" (Axelrod, 1984). This backward reasoning influences initial actions, leading players to defect early because they do not perceive benefits from cooperation when only a few rounds are left.

On the second question, the key difference between a simultaneous game and a sequential game lies in the timing and information structure. A simultaneous game is represented as a matrix because all players choose their strategies at the same time without knowing the others' choices. This structure reflects a one-shot interaction where players must decide without insight into opponents' actions (Fudenberg & Tirole, 1991). Conversely, a sequential game models decisions made in sequence, where players observe previous moves before acting, creating a decision tree that illustrates the order of moves and possible contingencies. The tree structure explicitly captures the information set and the dynamic nature of sequential decision-making, facilitating the analysis of subgame perfect equilibria (Selten, 1975). This fundamental difference illustrates how information and timing shape strategic behavior, with matrices suitable for simultaneous plays and trees for sequential interactions.

References

• Axelrod, R. (1984). The Evolution of Cooperation. Basic Books.
• Fudenberg, D., & Tirole, J. (1991). Game Theory. MIT Press.
• Nowak, M. A., & Sigmund, K. (1993). A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner’s Dilemma game. Nature, 364(6432), 56-58.
• Selten, R. (1975). Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory, 4, 25-55.
• Sober, E., & Wilson, D. S. (1998). Unto Others: The Evolution and Psychology of Unselfish Behavior. Harvard University Press.
• Rapoport, A., & Chammah, A. M. (1965). Prisoner’s Dilemma: A Study in Conflict and Cooperation. University of Michigan Press.
• Gibbons, R. (1992). Game Theory for Applied Economists. Princeton University Press.
• Osborne, M. J. (2004). An Introduction to Game Theory. Oxford University Press.
• Myerson, R. B. (1991). Game Theory: Analysis of Conflict. Harvard University Press.
• Binmore, K. (2005). Game Theory: A Very Short Introduction. Oxford University Press.