I do not understand how to solve missing values for a prisoner's dilemma matrix.
Im not sure what you mean by "missing values". Is it the case you given a matrix of possible outcomes, where some of the cells are missing and that you are told that a particular outcome in a non-missing cell is a stable (equilibrium) outcome, and you need to infer what must have been the outcomes of missing cells?
btw, its been many moons since I have studied Nash Equilibriums and prisoner dilemma games.
No problem! I can help you understand how to solve missing values in a prisoner's dilemma matrix. In a prisoner's dilemma game, players make decisions based on their own self-interest, without communication or coordination with each other.
When some values are missing in the matrix, it means that the payoffs or outcomes for certain combinations of strategies have not been provided. However, you may still be able to solve for the missing values using the concept of equilibrium in a prisoner's dilemma.
To solve for the missing values, you need to consider the concept of Nash equilibrium. A Nash equilibrium is a situation where no player can improve their outcome by unilaterally changing their strategy, assuming the other player's strategies remain unchanged.
Here's a step-by-step approach to solve for missing values in a prisoner's dilemma matrix:
1. Identify the given outcomes: Look for cells in the matrix where values are provided and mark them as given outcomes.
2. Determine the strategy choices: Identify the available strategy choices for each player. In a prisoner's dilemma, typically each player has two choices, often labeled as "cooperate" and "defect."
3. Analyze the given outcomes: Start by considering the given outcomes. Look for any stable outcomes where neither player has an incentive to switch their strategy. These stable outcomes are potential equilibrium points.
4. Apply the concept of equilibrium: With the stable outcome(s) identified, think about what would happen if any player deviated from that outcome. Would they have an incentive to switch strategies to gain a higher payoff? If not, then the stable outcome is an equilibrium.
5. Infer missing values: After identifying equilibrium points, you can infer the missing values based on the equilibrium concept. Consider what payoffs would make each player choose their strategy in equilibrium. If a missing cell is part of an equilibrium point, you can assign a value to it that satisfies the equilibrium condition.
By following these steps, you should be able to solve for missing values in a prisoner's dilemma matrix and obtain a complete payoff matrix for the game.
Please note that solving for missing values may require some assumptions and reasoning based on the given information and the principles of the game.