One may define a concept of an n-person reading this text in which each reader has a finite set of pure reading strategies and in which a definite set of interpretations to the n readers corresponds to each n-tuple of pure strategies, one strategy being taken for each reader.
Any n-tuple of reading strategies, one for each reader, may be regarded as a point in the product space obtained by multiplying the- n method spaces of the players.
One such n-tuple counters another if the strategy of each reader in the countering n-tuple yields the highest obtainable expectation for its player against, the n - 1 strategies of the other players in the countered n-tuple. A self-countering n-tuple is called an equilibrium point.
The correspondence of each n-tuple with its set of countering n-tuples gives a one-to-many mapping of the product space into itself. From the definition of countering we see that the set of countering points of a point is convex. By using the continuity of the pay-off functions we see that the graph of the mapping is closed. The closedness is equivalent to saying: if Pi, P2, ... and Qi, Q2, .... Qn, ... are sequences of points in the product space where Q. -n Q, P n P and Q,, counters P,, then Q counters P.
Any two equilibrium points lead to the same expectations for the readers, but this need not occur in general.
(Adapted from Nash, John (1950) "Equilibrium points in n-person games" Proceedings of the National Academy of Sciences 36(1):48-49.)
Any n-tuple of reading strategies, one for each reader, may be regarded as a point in the product space obtained by multiplying the- n method spaces of the players.
One such n-tuple counters another if the strategy of each reader in the countering n-tuple yields the highest obtainable expectation for its player against, the n - 1 strategies of the other players in the countered n-tuple. A self-countering n-tuple is called an equilibrium point.
The correspondence of each n-tuple with its set of countering n-tuples gives a one-to-many mapping of the product space into itself. From the definition of countering we see that the set of countering points of a point is convex. By using the continuity of the pay-off functions we see that the graph of the mapping is closed. The closedness is equivalent to saying: if Pi, P2, ... and Qi, Q2, .... Qn, ... are sequences of points in the product space where Q. -n Q, P n P and Q,, counters P,, then Q counters P.
Any two equilibrium points lead to the same expectations for the readers, but this need not occur in general.
(Adapted from Nash, John (1950) "Equilibrium points in n-person games" Proceedings of the National Academy of Sciences 36(1):48-49.)
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