A Game Theoretical Approach for Solving Winner Determination Problems

Algorithm 1

The main algorithm of NESA.

Result: the winner set 𝑠

(1) begin

(2)  generate a solution 𝑠 at random

(3)  while  not meet stop condition  do

(4)   𝑠^′←𝑓𝑖𝑛𝑑𝑁𝐸(𝑠)

(5)   if  𝑟(𝑠^′)>𝑟(𝑠)  then

(6)    update gvc

(7)    𝑠←𝑠^′

(8)   end

(9)   𝑠←𝑙𝑜𝑛𝑔𝐽𝑢𝑚𝑝(𝑠)

(10)  end

(11)  return 𝑠

(12) end