A Game Theoretical Approach for Solving Winner Determination Problems

Algorithm 2

The procedure 𝑓𝑖𝑛𝑑𝑁𝐸(𝑠).

Data:  𝑠: the base solution

Result:  𝑠^′: the NE solution

(1) begin

(2)  for each good 𝑔_𝑗 in 𝑠  do

(3)   𝑠^′←𝑠

(4)   remove the winner of 𝑔_𝑗 in 𝑠^′

(5)   add feasible bids to 𝑠^′ except for 𝑔_𝑗 based on a

    given ranking function

(6)   if  𝑟(𝑠^′)>𝑟(𝑠)  then

(7)     update gvc

(8)     return  𝑓𝑖𝑛𝑑𝑁𝐸(𝑠^′)

(9)   end

(10)  end

(11)  return  𝑠

(12) end