Topic 2 Key concepts Flashcards
A game
A game is any situation in which two or more decision-makers are aware that the result or payoff they obtain in the situation depends not only on his/her/their own decision but also on the decisions of the rest of decision-makers. (A game is any situation of strategic interaction)
A simultaneous game
A simultaneous game is a game in which all players make their decisions at the same time OR without knowledge of what their rivals have chosen to do. (figure out what your opponent is going to do right now (knowing that, in making his own calculation, the opponent is also trying to figure out what you will do))
A game with complete information
the strategy sets, the payoff functions and the rationality (the motivation) of all players are common knowledge.
A Pareto efficient outcome of a game
An outcome of a game is called Pareto efficient if, when comparing players’ payoffs with every other feasible outcome of the game, there is no alternative where one player can improve without making the other player(s) worse off.
(In every alternative, either for one player to improve the other one must be worse off, OR they are both worse off. If there exists at least one outcome where one player can improve without the other player being worse off, the outcome is Pareto inefficient).
A Social Welfare efficient outcome of a game
A combination of actions that yields an efficient outcome is the one that maximises the aggregate utility.(efficiency in terms of Social Welfare) (every socially efficient outcome is also Pareto efficient, but not all Pareto efficient outcomes are socially efficient outcomes)
A dominated action/strategy of a player in a game
An action (strategy) of a player is dominated if it yields lower payoffs than at least another action, for any possible combination of actions of her rivals. (No matter what the others might be doing, the player will always prefer not to play that action)
Dominated action=Dominated strategy
A dominant action/strategy of a player in a game
An action (strategy) of a player is dominant if it yields higher payoffs than any other action, for any possible combination of actions of her rivals. (No matter what the others might be doing, the player will always prefer to play the same action)
Dominant action=Dominant strategy
A weakly dominant action/strategy of a player in a game
If a player has an action that is always a best response (although not necessarily unique), then it is her weakly dominant action.
The best-response function of a player in a game
A best-response function indicates the strategy (or strategies) that maximise your payoff for each of the combination of strategies of the rest of players. (It tells you the best choice (or choices) of this player, for each of the choices that the other players might be making.)
Successive elimination of dominated actions/strategies
A rational player will never play a dominated strategy.
But if the game has complete information, then all players’ rationality and payoffs are common knowledge among them. Players will use this information to mutually anticipate that dominated strategies will not be played and will remove them from consideration.
Removing dominated strategies reduces the size of the game and then the “new” game may have another dominated strategies. If this process keeps working until a unique outcome is reached, then the game is said to be dominance solvable.
A game with a Prisoners’ Dilemma structure
- Each player has a cooperative action, such that if everybody plays it, an efficient outcome is achieved. It is dominated.
- Each player has a non-cooperative action such that if everybody plays it, an inefficient outcome is achieved. It is dominant.
Strategy
A strategy is a complete plan of action contingent on each possible scenario.
(In a simultaneous game that is only played once, a strategy indicates what to do for each possible action of the other player).
