On Game Theory (2000-)

"An equilibrium is not always an optimum; it might not even be good. This may be the most important discovery of game theory." (Ivar Ekeland, "Le meilleur des mondes possibles" ["The Best of All Possible Worlds"], 2000)

"Game theory is about how people cooperate as much as how they compete... Game theory is about the emergence, transformation, diffusion and stabilization of forms of behavior." (Herbert Gintis, "Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction", 2000)

"Game theory is logically demanding, but on a practical level, it requires surprisingly few mathematical techniques. Algebra, calculus, and basic probability theory suffice. [...] the stress placed on game-theoretic rigor in recent years is misplaced. Theorists could worry more about the empirical relevance of their models and take less solace in mathematical elegance." (Herbert Gintis, "Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction", 2000)

"Game theory is a formal approach to analysing social situations employing highly stylized and parsimo-nious descriptions." (David Robinson & David Goforth, "The Topology of the 2×2 Games: A New Periodic Table". 2005)

"I think game theory creates ideas that are important in solving and approaching conflict in general." (Robert Aumann, 2005)

"An equilibrium is not always an optimum; it might not even be good. This may be the most important discovery of game theory." (Ivar Ekeland, "The Best of All Possible Worlds", 2006)

"Good decisions require that each decision-maker anticipate the decisions of the others. Game theory offers a systematic way of analysing strategic decision-making in interactive situations. [...] Game theory is not about 'playing' as usually understood. It is about conflict among rational but distrusting beings." (Geraldine Ryan & Seamus Coffey, "Games of Strategy", 2008)

"Game theory proposes a method called minimization-maximization (minimax) that determines the best possibility that is available to a player by following a decision tree that minimizes the opponent’s gain and maximizes the player’s own. This important algorithm is the basis for generating algorithms for chess programs." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)

"Game theory postulates rational behavior for each participant. Each player is conscious of the rules and behaves in accordance with them, each player has sufficient knowledge of the situation in which he or she is involved to be able to evaluate what the best option is when it comes to taking action (a move), and each player takes into account the decisions that might be made by other participants and their repercussions with respect to his or her own decision. Game theory about zero-sum games with two participants is relevant for chess. In this type of situation, each action that is favorable to one participant" (player) is proportionally unfavorable for the opponent. Thus, the gain of one represents the loss of the other." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)

"Game theory covers an incredibly broad spectrum of scenarios of cooperation and competition, but the field began with those resembling heads-up poker: two-person contests where one player’s gain is another player’s loss. Mathematicians analyzing these games seek to identify a so-called equilibrium: that is, a set of strategies that both players can follow such that neither player would want to change their own play, given the play of their opponent. It’s called an equilibrium because it’s stable - no amount of further reflection by either player will bring them to different choices. I’m content with my strategy, given yours, and you’re content with your strategy, given mine." (Brian Christian & Thomas L Griffiths, "Algorithms to Live By: The Computer Science of Human Decisions", 2016)