A model of best choice under incomplete information

This paper suggests two approaches to the construction of a two-player game of best choice under incomplete information with the choice priority of one player and the equal weights of both players. We consider a sequence of independent identically distributed random variables (<em class="EmphasisTypeItalic ">x</em> _{<em class="EmphasisTypeItalic ">i</em>}, <em class="EmphasisTypeItalic ">y</em> _{<em class="EmphasisTypeItalic ">i</em>}), <em class="EmphasisTypeItalic ">i</em> = 1..., <em class="EmphasisTypeItalic ">n</em>, which represent the quality of incoming objects. The first component is announced to the players and the second component is hidden. Each player chooses an object based on the information available. The winner is the player whose object has a greater sum of the quality components than the opponent’s object. We derive the optimal threshold strategies and compare them for both approaches.