Changing the Classic Game Prisoner's Dilemma

Your Name Mrs. Trevino English 1-1 Date The Most Dangerous Game Introduction Hook; summary; thesis (topic (who is the better hunter) + opinion) Reason 1 Opinion, reason, evidence (author last name page#), opinion Reason 2 Transition word+opinion, evidence (author last name page#), opinion

cooperate or compete. In reality, it defined that defection will have a better trade off than the

The optimal strategy for player one to pursue would be to defect under any circumstance. If player one were to cooperate, that minimum and maximum return would be one and three respectively. Whereas if player one were to defect the minimum points he or she would earn is two, and the maximum could potentially be four.

The first thing that comes to mind at the mention of Nuclear Warfare is the Cold War between the U.S. and the U.S.S.R. These two major global powers fought for dominance on the global stage for what purpose? They fought to ensure that neither side’s values and structures could dominate the world at the cost of the other’s destruction. At its peak, in the 1950s and 1960s, the Cold War represented a way of life for many Americans and Russians. The constant fear and belief that we could be bombed at any second seriously impacted the standards of living in both nations. Comparable to the fear of terrorism in the in the 21st Century, the Cold War dominates the history books during this period of time. At the same time, during the 50’s, in a different field of study, the concept of the prisoner’s dilemma and game theory were being developed. That reason, may explain why this particular dilemma is associated with nuclear decisions.

The purpose of this discussion is to give a brief explanation of the Prisoner’s Dilemma

What this means is that for both players, strategy 2 dominates strategy 1 (A2 dominates A1 for the row player and B2 dominates 31 for the column player). However, the choice (A2, B2) results in a payoff (x4) to each player smaller than

While the game has many variations, the core concept is most simply represented as a symmetric 2x2 game with ordinal payoffs. Below is an illustration of perhaps the most well known example; two suspects (Dave and Henry) are each facing the choice of whether to plead guilty or innocent. However, neither individual can be certain of what the other will decide. While the optimum outcome for the players would be to both plead innocent and receive two years each, either one of them could improve their payoff by pleading guilty. In fact, the only outcome where neither has an incentive to change their plea is the least optimal overall, where both have ‘defected’. This point is commonly referred to as the Nash equilibrium. In general, while the payoffs themselves may vary, the prisoner’s dilemma is characterised by a single dominant strategy for both players to defect, leading to an inefficient outcome.

Joseph Heller’s Catch 22 is a story of World War II bombardier John Yossarian who is stationed in Europe during the conflict. Yossarian begins in the hospital, faking an injury to avoid going on a combat missions. While in the hospital, Yossarian encounters a few interesting characters including a bigoted Texan, and a man wrapped completely in bandages. When the man in white dies, Yossarian and the other patients blame the Texan for killing the man because of his race. The texan defends his tolerance by saying he appreciates all people and then names them off by stereotypical and slurred names. At this point in the book the confusion begins to set in, from this point on the satirical paradox that is Catch-22 begins to take full effect. The book shows how war can turn everything we know on its head and make even the most sure or obvious scenarios confusing and foreign. Catch-22 provides healthy confusion throughout the story by making things the opposite of how they normally would be, making people behave in manners that would seem otherwise unethical or weird, and creating paradoxes through words and rules of the land.

The prisoner 's dilemma is mainly a decision analysis puzzle where two people are performing with their interest take actions that do not finally develop in best outcome. The

Prisoners’ Dilemma • Note that even if we start at the cooperative outcome, that outcome is not stable • Each player can improve his/her position by adopting a different strategy Temptation to defect > Rewards of Cooperation Rewards > Punishment for Not Cooperating Punishment > Sucker’s Payoff Don’t Cooperate Don’t Cooperate 3,3 Prisoners’ Dilemma Cooperate 1,4 • But since both players have changed strategy we end up at the non-cooperative outcome, where both players are worse off than if they had chosen to cooperate

Some of the best memories I have with my family is game night. Shockingly, my family will sit down and play board games together every now and again. These aren’t just a regular store bought board game like Monopoly or Sorry, we have a collection of grand master board games. Large, extensive and expensive adventures to array on a table. There has been a whole array of people to play at our table, from siblings, and other family members, to random strangers, I had only met for the first time sitting at the table. It seems like some days, the best bonds are made playing at The Game Table.

In algorithmic game theory, it is easy to find the Nash equilibrium if one can derive the default strategies of each player from the instructions/parameters of the algorithm. It is also not particularly hard to find the optimal solution to an algorithm either. In algorithmic mechanism design, it would be the goal of the algorithm designer to fashion the algorithm in such a way that causes the Nash equilibrium to be the same as the Pareto optimal (or at least close to optimal) result. This would mean that it would be impossible to make any player better off in the game without hurting another player at the same time (optimal), while it also being impossible for any one player to improve their situation by altering only their strategy (Nash equilibrium). It is the goal to make these two circumstances exist simultaneously.

Therefore it can be verified that, for the choices above, the expected return from defending A is 0.5625 × (−10) + (1 − 0.5625) × (−110) = −53.75 and the expected return from defending B is 0.5625 × (−80) + (1 − 0.5625) × (−20) = −53.75 so the mixed-strategy Nash equilibrium condition of equal expected payoffs does satisfy for the defender. Alike calculation can be made for the attacker. Normally, for the general payoff matrix in Table 2 below, the optimal mixed strategy is:

b) Find the probability of type II error for this procedure when M equals 3.

Without conflict stories would be pretty dull. In “The Most Dangerous Game” by Richard Connell there are three major types of conflicts, Man versus Man, Man versus Nature, and Man versus Himself. Rainsford’s deadly encounter with General Zaroff displays these conflicts. In “Most Dangerous Game” Man