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Game theory, John Nash: Nash Equilibrium is named after the American…
Game theory
What is Game theory?
Game theory is a mathematical framework used to analyze strategic interactions between rational decision-makers. It studies how individuals or entities make choices when their outcomes depend on the choices of others.
Form of game
The form of a game in game theory refers to the structure and rules defining players, strategies, and payoffs. It categorizes games based on elements such as the number of players, information availability, and types of strategies.
Extensive Form
It includes nodes, branches, and information sets to depict the order of moves and information available to players.
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Normal Form
Normal form represents a game using a matrix where players' strategies and corresponding payoffs are listed.
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The matrix includes all possible strategy combinations and their outcomes, making it easier to identify Nash Equilibria.
Nash Equilibrium:
Nash Equilibrium is a concept in game theory where each player's strategy is optimal given the strategies of others. In Nash Equilibrium, no player has an incentive to unilaterally deviate from their chosen strategy.
It doesn't necessarily guarantee the best possible outcome for all players, only that no player can improve their position by changing strategies.
Games can have multiple Nash Equilibria, and not all may be optimal.
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Application
Game theory finds applications in various fields such as economics, political science, biology, and computer science.
Applied to study voting behavior, negotiations, and conflict resolution.
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Used to analyze market behavior, auction strategies, and pricing decisions.
The Monty Hall problem
The Monty Hall problem is a probability puzzle based on a game show scenario where a contestant must choose one of three doors, one of which hides a prize, and then is offered the chance to switch doors after one of the other doors is revealed to be empty.
Pareto
Pareto optimality is a state in which no individual or entity can be made better off without making someone else worse off. It's a concept used to assess the efficiency of resource allocation or distribution within a system.
2-finger morra
2-finger morra is a hand game where players simultaneously display a number of fingers, and the winner is determined based on a set of rules which assign values to different finger combinations.
Rock paper scissor
Rock paper scissors is a hand game usually played between two people, where each player simultaneously forms one of three shapes with an outstretched hand. The possible shapes are rock, paper, and scissors.
The 2/3 game
The 2/3 game is a strategic game where two players must simultaneously choose a number between 0 and 1. The player whose chosen number is closest to 2/3 of the average of the two numbers wins.
Stag Hunt
Stag Hunt is a game used in game theory to illustrate the trade-off between cooperation and individual payoff. In the game, players must choose between hunting a stag (which yields a high payoff if both cooperate) or hunting a hare (which yields a low payoff but doesn't require cooperation).
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John Nash: Nash Equilibrium is named after the American mathematician John Nash, who introduced the concept in his doctoral thesis "Non-Cooperative Games" in 1950 at Princeton University.