In the ultimatum game, the basic theory of utility would suggest that the optimal distribution of $100 is, for you and the stranger, respectively:

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The basic theory of utility in economics suggests that individuals aim to maximize their own utility. In the context of the ultimatum game, where one player proposes how to divide a sum of money and the other player can accept or reject the proposal (with both getting nothing if the proposal is rejected), the proposer, acting purely on self-interest and assuming rationality in the responder (accepting any amount greater than $0), would theoretically propose keeping $99 for themselves and offering $1 to the stranger. This maximizes the proposer's utility under the assumption that the responder acts rationally and accepts any non-zero amount.

In the Ultimatum Game, the Basic Theory of Utility Would