Abstract
In this paper we introduce games with optimistic aspirations and identify attractive allocation rules for such games through axiomatizations. A game with optimistic aspirations specifies two values for each coalition of players: the first value is the worth that the players in the coalition can guarantee for themselves in the event that they coordinate their actions (where the word guarantee implies a very conservative attitude), and the second value is the amount that the players in the coalition aspire to get under reasonable but very optimistic assumptions about the demands of the players who are not included in the coalition. We explain games with optimistic aspirations as well as our motivation for introducing such games by means of an example.
Highlights
The two allocation rules that we define on the class of games with optimistic aspirations in this paper, the Midpoint Shapley Value and the Equal Division Rule, are found by extending the axioms that were used in Shapley [1] to define the Shapley Value and augmenting them with stronger versions of the null player property—the strong null player property, the nullifying player property, and the destroyer player property
In this paper we introduced games with optimistic aspirations in order to be able to capture more of the possible asymmetries between participants in various situations than is possible using existing cooperative game formulations
We identified two allocation rules for games with optimistic aspirations by first extending the axioms efficiency, additivity, symmetry, and the null player property to the setting of games with optimistic aspirations and, after having shown that the four axioms EFF, ADD, SYM, and Null Player Property (NPP) do not identify a unique allocation rule, considering three possible alternatives of NPP, namely, the strong null player property, the nullifying player property, and the destroyer player property
Summary
In this paper we introduce games with optimistic aspirations, and we identify two allocation rules for such games—the Midpoint Shapley Value and the Equal Division Rule. The two allocation rules that we define on the class of games with optimistic aspirations in this paper, the Midpoint Shapley Value and the Equal Division Rule, are found by extending the axioms that were used in Shapley [1] to define the Shapley Value and augmenting them with stronger versions of the null player property—the strong null player property, the nullifying player property, and the destroyer player property. Games with optimistic aspirations are inspired much in the same way in which von Neumann and Morgenstern [2] already introduced cooperative games, namely, as descriptions of situations that are devoid of a specific structure of negotiations but that capture the potential of coalitions of players when they cooperate.
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