Games, Theory and Applications by L. C. Thomas

Author:L. C. Thomas
Language: eng
Format: epub, azw3
Publisher: Dover Publications, Inc.
Published: 1984-06-26T16:00:00+00:00

On adding k1 to the title of the game, what happens to the sets? If k1 has appeared before in the title, then because of Theorem 6.2 will remain metarational. If not and k1 = {i}, then because of the definition of Fi there will be no change since k2,k3,...,kr remain in Fi Thus, (6.35) is the condition for to be metarational for k1k2...krG as well as k2...krG. Lastly, if k1 was in Ui originally it now enters Pi, and since

if satisfies (6.35), it also satisfies the equivalent condition for it to be metarational for i in k1k2...krG.

This result implies that we need only look at the games 123... nG, or nn — 1...21G and all such permutations of l,2,...,n, to find the metaequilibria. These games, where the title is some permutation of 1,2,...,n, are called complete games.

Definition 6.4. An outcome is a symmetric metaequilibrium if it is a metaequilibrium in all complete games.

If G has two players the symmetric metaequilibria are Ê(12G) ∩ Ê(21G), and for the Prisoners’ Dilemma, the Falklands War, and the Cuban missile crisis all the metaequilibria are symmetric. This need not always be the case—look at the following example.

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