Learning Engagement Prisoners Dilemma Paper

Description

In a finitely repeated prisoner’s dilemma what is the optimal strategy for each player?
PROFESSOR’S GUIDANCE FOR THIS WEEK’S LE:
Prisoners’ dilemma is one of the most celebrated topics in whole game theory. In that two agents engage in a game with payoffs that has a Nash equilibrium that shuns cooperation. Here we want to investigate the possible outcome if these agents play with each other again and again.

Maysaa Al Mashaykhi on Tuesday, November 30, 2021, 10:04 PM

Prisoner’s dilemma is a strange but exciting thought experiment/game that can teach us why some cooperation strategies are better than others. The game is interesting because there’s a slight advantage longer term when you cooperate with others, even though there’s a slight disadvantage in the short term. You don’t benefit as much immediately, but the entire month’s reduction increases faster if you stick to cooperation over time. That is how some people believe partnership evolved — a group of cooperators becomes more substantial over the long haul.
Each player chooses a strategy of two moves (Cooperate and Defect). The logic describes when they want to cooperate with others and when they don’t. All you must go on is your past communications with that player.
The definition of a strategy in a repeated game determines the player’s choice for each history, particularly for histories that cannot be outcomes of the repeated game (Bravetti & Padilla,2018). As a result, the joint strategy from the item (i) is not a unique Nash equilibrium of G(k) when players have two or more strategies in the stage game.
Below are the strategies with their pros and cons.

Always Cooperate

Strategy: Cooperate with every move. That is the strategy that exemplifies “why can’t we all just get along?”
Pros: Always Cooperate is the most generous strategy available. It’s a viable strategy in environments of highly high trust, like high-functioning teams.
Cons: Cooperation without confidence is an invitation for a lot of abuse.

Always Defect

Strategy: Defect every move. This strategy explains the lost faith in cooperation. It’s the ultimate protective strategy because nobody can turn you into a victim.
Pros: You will always win or tie against any candidate because they never have an opening to take points from you.
Cons: Though you win or tie every round, you do so at a lower point threshold than cooperation would have reached.

Tit for Tat

Strategy: Start by cooperating. Copy whatever the other player made the last move. The punishment matches the crime. If someone defects against you, then immediate fault against them. If they begin cooperating again, then you start collaborating again too. It’s the incarnation of strict fairness.
Pros: Because Tit for Tat starts by cooperating and then copies the other player’s last move, it acts like Always Cooperate when interacting with it.
Cons: This strategy plays to tie, not to win.

A. Bravetti & P. Padilla. (2018). An optimal strategy to solve the Prisoner’s Dilemma.

https://www.nature.com/articles/s41598-018-20426-w

Mo’ath Awawdeh on Wednesday, December 1, 2021, 10:59 PM

Game theory is the study of interactions between players. Players can be you versus a company targeting you to buy its products, countries at war, or companies competing for markets. Game theory studies making decisions with consideration of opponents and their movements. (Harsanyi, 2013)
This theory takes a certain strategy similar to the game of chess in which you do not know what your opponent is thinking but you will choose the best thing for your benefit and to defeat him. And any decision taken affects the future of the game, either harm or benefit. (Dixit, 2005)
The most common (dominant) strategy is the strategy that gives satisfactory results regardless of the opponent’s move, and this, in turn, constitutes a Nash equilibrium, a strategy that is formed when each fork chooses the interest of the strongest and his right choice and forms his dominance, each of the dominant strategies constitutes a Nash equilibrium, which is a mathematical analysis of situations of conflict of interest. (Crawford, 1979)
Example: This concept helped the British government increase its financial returns, as it used Nash Balance to design the auction for the sale of 3G operating licenses to the telecom company and relied on its ploy to consider the auction as a game and adapted its rules to become the best strategy for bidders is to bid through bidding at prices.
Nash’s policy makes all parties to the game win, without any of them losing to gain the other, and each party moves into the equation from the reality of conviction for an average gain and not greed for the maximum possible gain. (Neti, 2012)
Because the odds of losing without Nash’s theory are greater than the odds of losing with the theory, on the contrary, it would be better for the company to choose options and competitions within reason and neglect requests that are greedy. The chances of success with a reasonable investment are much greater than the chance of success with others. (Crawford, 1979)
References:
Harsanyi, J. C. (2013). Papers in game theory (Vol. 28). Springer Science & Business Media.
Dixit, A. (2005). Restoring fun to game theory. The Journal of Economic Education, 36(3), 205-219.
Crawford, V. P., & Varian, H. R. (1979). Distortion of preferences and the Nash theory of bargaining. Economics Letters, 3(3), 203-206.
Neti Maruti Ramanarayana, S. (2012). Towards a theory of software diversity for security (Doctoral dissertation, Carleton University).

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economics

Game Theory

Prisoner’s Dilemma

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