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A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly.This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance; solving such a game may use combinatorial game theory or computer assistance.
In Game A, you lose $1 every time you play. In Game B, you count how much money you have left — if it is an even number you win $3, otherwise you lose $5. Say you begin with $100 in your pocket. If you start playing Game A exclusively, you will obviously lose all your money in 100 rounds.
A Nash equilibrium is a strategy profile (a strategy profile specifies a strategy for every player, e.g. in the above prisoners' dilemma game (cooperate, defect) specifies that prisoner 1 plays cooperate and prisoner 2 plays defect) in which every strategy played by every agent (agent i) is a best response to every other strategy played by all the other opponents (agents j for every j≠i) .
Mean field game theory is the study of strategic decision making in very large populations of small interacting agents. This class of problems was considered in the economics literature by Boyan Jovanovic and Robert W. Rosenthal, in the engineering literature by Peter E. Caines, and by mathematicians Pierre-Louis Lions and Jean-Michel Lasry.
The Trent Tucker Rule is a basketball rule that disallows any regular shot to be taken on the court if the ball is put into play with under 0.3 seconds left in game or shot clock. The rule was adopted in the 1990–91 NBA season and named after New York Knicks player Trent Tucker , and officially adopted in FIBA play starting in 2010.
A backboard assembly displaying the shot clock in red (8 seconds) and game clock in white (11.8 seconds) In basketball games, the clock stops when the ball is dead and runs when it is live. Running out the clock was a major problem in the early days of the National Basketball Association (NBA). Often, once a team grabbed the lead, they would ...
When player 2 plays left, then the payoff for player 1 playing the mixed strategy of up and down is 1, when player 2 plays right, the payoff for player 1 playing the mixed strategy is 0.5. Thus regardless of whether player 2 chooses left or right, player 1 gets more from playing this mixed strategy between up and down than if the player were to ...
Determined game (or Strictly determined game) In game theory, a strictly determined game is a two-player zero-sum game that has at least one Nash equilibrium with both players using pure strategies. [2] [3] Dictator A player is a strong dictator if he can guarantee any outcome regardless of the other players.