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2. Game theory - Wikipedia

   en.wikipedia.org/wiki/Game_theory

   Separately, game theory has played a role in online algorithms; in particular, the k-server problem, which has in the past been referred to as games with moving costs and request-answer games. [125] Yao's principle is a game-theoretic technique for proving lower bounds on the computational complexity of randomized algorithms , especially online ...

3. Sprague–Grundy theorem - Wikipedia

   en.wikipedia.org/wiki/Sprague–Grundy_theorem

   An impartial game is one in which at any given point in the game, each player is allowed exactly the same set of moves. Normal-play nim is an example of an impartial game. In nim, there are one or more heaps of objects, and two players (we'll call them Alice and Bob), take turns choosing a heap and removing 1 or more objects from it.

4. Strategy (game theory) - Wikipedia

   en.wikipedia.org/wiki/Strategy_(game_theory)

   In a dynamic game, games that are played over a series of time, the strategy set consists of the possible rules a player could give to a robot or agent on how to play the game. For instance, in the ultimatum game , the strategy set for the second player would consist of every possible rule for which offers to accept and which to reject.

5. Perfect recall (game theory) - Wikipedia

   en.wikipedia.org/wiki/Perfect_recall_(game_theory)

   It is a core component of how game theorists analyze extensive-form games. The formal definition of perfect recall involves the concept of information sets in extensive-form games. It ensures that if a player reaches a certain information set, the player's past actions and information are consistent with all the nodes within that information set.

6. Kuhn's theorem - Wikipedia

   en.wikipedia.org/wiki/Kuhn's_theorem

   In game theory, Kuhn's theorem relates perfect recall, mixed and unmixed strategies and their expected payoffs. It was formalized by Harold W. Kuhn in 1953. [1]The theorem states that in a game where players may remember all of their previous moves/states of the game available to them, for every mixed strategy there is a behavioral strategy that has an equivalent payoff (i.e. the strategies ...

7. Information set (game theory) - Wikipedia

   en.wikipedia.org/wiki/Information_set_(game_theory)

   Below, the normal form for both of these games is shown as well. The first game is simply sequential―when player 2 makes a choice, both parties are already aware of whether player 1 has chosen O(pera) or F(ootball). The second game is also sequential, but the dotted line shows player 2's information set. This is the common way to show that ...