Single-parameter utility: Difference between revisions

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Revision as of 14:26, 28 February 2020

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In general, each agent can assign a different and unrelated value to every outcome in <math>X</math>.

In the special case of '''single-parameter utility''', each agent <math>i</math> has a publicly- known outcome subset <math>W_i \subset X</math> which are the "winning outcomes" for agent <math>i</math> (e.g., in a single-item auction, <math>W_i</math> contains the outcome in which agent <math>i</math> wins the item).

For every agent, there is a number <math>v_i</math> which represents the "winning-value" of <math>i</math>. The agent's valuation of the outcomes in <math>X</math> can take one of two values:<ref name=agt07>{{Cite Algorithmic Game Theory 2007}}</ref>{{rp|228}}