In combinatorial game theory, the strategy-stealing argument is a general argument that shows, for many two-player games, that the second player cannot...

the game. A standard strategy stealing argument from combinatorial game theory shows that in no m,n,k-game can there be a strategy that assures that the...

position whose Grundy value is zero, whenever this is possible. A strategy-stealing argument shows that the Grundy value is nonzero for every poset that has...

a standard strategy-stealing argument, one can thus conclude that if two players alternate, then the first player has a winning strategy when H is sufficiently...

(). This can be a non-constructive proof (possibly involving a strategy-stealing argument) that need not actually determine any details of the perfect play...

An evolutionarily stable strategy (ESS) is a strategy (or set of strategies) that is impermeable when adopted by a population in adaptation to a specific...

with finitely many strategies, there exists a value V and a mixed strategy for each player, such that (a) Given Player 2's strategy, the best payoff possible...

Nine men's morris is a strategy board game for two players, dating back to at least the Roman Empire. The game is also known as nine-man morris, mill,...

always be a winning strategy for player X. There will never be a winning strategy for player O because of the Strategy-stealing argument since an nd game...

situation where no player could gain by changing their own strategy (holding all other players' strategies fixed). The idea of Nash equilibrium dates back to...

(White), a second player win (Black), or a forced draw. Solved game Strategy-stealing argument Zugzwang Determinacy Combinatorial game theory First-move advantage...

the level of rational argument, but begin by denouncing all argument; they may forbid their followers to listen to rational argument, because it is deceptive...

impossible for Player 2 to form an I-tromino before Player 1 does: the strategy-stealing argument applies.) Harary defines the unqualified terms "winner" and "loser":...

probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit-for-tat strategy written as P = { 1 , 0 ,...

situation. A player's strategy determines the action the player will take at any stage of the game. However, the idea of a strategy is often confused or...

In game theory, a strategy A dominates another strategy B if A will always produce a better result than B, regardless of how any other player plays. Some...

In game theory, grim trigger (also called the grim strategy or just grim) is a trigger strategy for a repeated game. Initially, a player using grim trigger...

argument about the game-theoretic value of chess: he proposes allowing the move of “pass”. In this variant, it is provable with a strategy stealing argument...

often played by young children who may not have discovered the optimal strategy. Because of the simplicity of tic-tac-toe, it is often used as a pedagogical...

game complexity and the existence of optimal strategies through methods like the strategy-stealing argument. Combinatorial game theory arose in relation...

the standard assumptions, the switching strategy has a ⁠2/3⁠ probability of winning the car, while the strategy of keeping the initial choice has only...

cannot end in a draw, then one of the two players must have a winning strategy (i.e. can force a win). An alternate statement is that for a game meeting...

g(f(r)) ∈ U. We now claim that neither player has a winning strategy, using a strategy-stealing argument. Denote the current game state by a finite sequence of...

have one value per argument, and many reaction correspondences will be undefined, i.e., a vertical line, for some opponent strategy choice. One constructs...

the other player). The game has a mixed-strategy Nash equilibrium; when both players play equilibrium strategies, the first player should expect to lose...

theory, a trigger strategy is any of a class of strategies employed in a repeated non-cooperative game. A player using a trigger strategy initially cooperates...

strategy profile s' such that ui (s') ≥ ui (s) for every player i and uj (s') > uj (s) for some player j. In this equation s represents the strategy profile...

point-loss independent of the opponent's strategy. This leads to a linear programming problem with the optimal strategies for each player. This minimax method...

game Misère Partisan game Solved game Sprague–Grundy theorem Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush...

played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The...