Prisoner’s Dilemma – Game Theory
A game is basically a structured form of engagement, normally undertaken for fun or entertainment, and occasionally used as an educational instrument. Games are very different from work, which traditionally is performed for remuneration, and unlike art, which is generally more of an expression of visual or aesthetic themes. Game creation can involve the creation of games as simple as card games to as complex as financial simulations. While a game of chance may involve investing some money, a game of skill involves the application of knowledge. While one can play any game of any kind without any goal in mind, most people will engage with certain types of games as hobbies or activities that help them develop skills or focus on particular aspects of their environment.
A game can have many components, including a set of rules, a goal, a sequence of actions to be taken, a medium to manipulate the aspects of the game, strategies used to acquire the goals, etc. The rules of a game to determine how the game is to be played, and a simple example is bingo, where the game rules determine the number of cards that must be dealt out, the number of cards that must be played with, the way the action cards are selected, the bingo points (e.g., number of coins that must be flipped over), and the game results. A game is said to be “fair” when the result of the game follows objectively predictable results, i.e., when no forces beyond the game rules decide the outcome. “Unfair” game results are usually considered to occur when a participant receives an unfair advantage, or if the participant is deprived of information or opportunities to make an effective attempt to attain a goal.
One of the most important concepts in game theory is what is called the prisoner’s dilemma. In this classic psychological game, two agents are set up in a room with a desk, a pen, a paper, a bowl of food, a bottle of wine, a glass of milk, a bottle of vinegar, etc. To get the other agent to answer all questions without the knowledge of the first agent, the latter must move all the objects from their place on the table to the glass of vinegar, keeping only the items which the first agent has already touched. Thus, the player who knows that his opponent is planning to make a move, yet does not know whether or not the other agent will do so, falls into the “dilemma” of learning the fact that his opponent has plans in advance, but choosing to carry out his plans anyway.
Another version of the prisoner’s dilemma is called the Dilemma of the Cogmate. Here, two agents are set up in a situation where one is planning to execute a risky maneuver, while the other agent plans to withhold this move. If this move is carried out, the player who withheld the move from his opponent will ultimately lose the game. Here also, it is possible for a player to get away with the disadvantage of being the “cogmate,” if he holds a higher skill than the opponent, as when a higher number of other players are present. Thus, to avoid this dangerous situation, a player may safely withhold his move and wait for the perfect timing to strike at his opponent.
Nash equilibrium is based on the game theory of matching methods. According to this, two agents can be considered to be at a zero equilibrium if there exists an acceptable strategic plan between them. The game, in this case, assumes that each player is to carry out certain strategic moves, hence creating the Nash equilibrium where every possible move of one agent is compatible with that of the other agent. This equilibrium is often referred to as being the state of equilibrium, since in the long run, it evolves in an optimal way.
The prisoner’s dilemma is more complicated because it involves the introduction of probabilities. When describing how the equilibrium is reached, it is important to note that the equilibrium described above is not necessarily the only potential for equilibrium. In the prisoner’s dilemma, it is possible for the group to reach a zero equilibrium but because of a tendency for each member of the group to defect, the other members are drawn into the game. This could result in a game referred to as the prisoner’s paradox, where a group is represented by a colored ball and each member of the group represents a color.