Mathematical Modeling: Game Theory and Decision Making

In a zero-sum game, the gains of one player are exactly balanced by the losses of the other players, resulting in a total gain of zero.

The Prisoner's Dilemma is a classic example of a non-cooperative game, where each player's best strategy depends on the strategy of the other player.

In a Nash Equilibrium, no player can improve their outcome by unilaterally changing their strategy, given the strategies of the other players.

A Coalitional Game is a type of cooperative game where players can form coalitions to achieve a common goal.

The Shapley Value is a solution concept used in cooperative games to fairly distribute the gains from cooperation among the players.

Expected Value, Minimax Regret, and Hurwicz Criterion are all types of decision-making under uncertainty, where the decision-maker is faced with multiple possible outcomes and must choose a strategy based on their beliefs about the likelihood of each outcome.

The Expected Value of a random variable is the weighted average of all possible outcomes, where the weights are the probabilities of each outcome.

The Minimax Regret criterion is used to make decisions under uncertainty, where the decision-maker chooses the strategy that minimizes their maximum possible regret.

The Hurwicz Criterion is a decision-making criterion that combines optimism and pessimism by weighting the best and worst possible outcomes.

Expected Value is a type of decision-making under risk, where the decision-maker knows the probabilities of all possible outcomes.

In a decision tree, each node represents a possible outcome, a decision point, or a chance event.

Expected Value, Minimax Regret, and Hurwicz Criterion are all types of decision-making under uncertainty, not certainty.

The Prisoner's Dilemma is a classic example of a cooperative game, where players can cooperate to achieve a mutually beneficial outcome.

The Nash Equilibrium is a classic example of a non-cooperative game, where each player's best strategy depends on the strategy of the other player.

Cournot Competition is a classic example of a cooperative game, where players can cooperate to achieve a mutually beneficial outcome.