An agent is said to control the situation if its acts matter to
others to the extent that at least one of them is forced to alter at
least one vector (Strategy).
The Consequence to the agent is the value of a function that assigns
real numbers to each of the outcomes. The consequence represents a list
of outcomes, prioritized, ranked. It is also known as an ordinal
utility function. If the function includes relative numerical
importance measures (not only real numbers) - we call it a Cardinal
Utility Function.
Games, naturally, can consist of one player, two players and more than
two players (n-players). They can be zero (or fixed) - sum (the sum of
benefits is fixed and whatever gains made by one of the players are
lost by the others). They can be nonzero-sum (the amount of benefits to
all players can increase or decrease). Games can be cooperative (where
some of the players or all of them form coalitions) - or
non-cooperative (competitive). For some of the games, the solutions are
called Nash equilibria. They are sets of strategies constructed so that
an agent which adopts them (and, as a result, secures a certain
outcome) will have no incentive to switch over to other strategies
(given the strategies of all other players).
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