July 16, 2017

Download Automated Deduction - CADE-14: 14th International Conference by William McCune PDF

By William McCune

Court cases of the 14th foreign convention on computerized Deduction, held in Townsville, Australia, in July 1997. Paper.

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Additional info for Automated Deduction - CADE-14: 14th International Conference on Automated Deduction, Townsville, North Queensland, Australia, July 13 - 17, 1997, Proceedings

Example text

In contrast to Pareto equilibria, Nash equilibria is a strictly selfish concept, hence is not amenable to cooperative play. But an individually rational player would have no incentive to agree to a Pareto equilibrium if that solution did not assure at least as much satisfaction as the player could be guaranteed of receiving were it to ignore completely the interests of the other players. 12 The minimum guaranteed benefit that a player can be assured of achieving is its security level. Furthermore, a subgroup of players would have no incentive to agree to a joint solution unless the total benefit to the subgroup were at least as great as the minimum that could be guaranteed to the subgroup – its security level – if it acted as a unit (assuming transferable utilities which may be be reapportioned via side payments).

A-1 Adequacy: satisficing, or being “good enough,” is the fundamental desideratum of rational decision makers. We cannot rationally choose an option, even when we do not know of anything better, unless we know that it is good enough. Insisting on the best and nothing but the best, however, can be an unachievable luxury. A-2 Sociality: rationality must be defined for groups as well as for individuals in a consistent and coherent way, such that both group and individual preferences are accommodated.

If the members disagree on fundamentals (here, on probabilities and on utilities) they ought to thrash these out independently, arrive at a compromise probability distribution and a compromise utility function, and use these in the usual Bayesian manner. (Raiffa, 1968, p. 233, emphasis in original) Adopting this latter view would require the group to behave as a superplayer, or, as Raiffa puts it, the “organization incarnate,” who functions as a higher-level decision maker. Shubik refers to the practice of ascribing preferences to a group as a subtle “anthropomorphic trap” of making a shaky analogy between individual and group psychology.

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