A Game Theoretical Approach for Solving Winner Determination Problems

Algorithm 3

The procedure 𝑙𝑜𝑛𝑔𝐽𝑢𝑚𝑝(𝑠).

Data: 𝑠: the base solution

Result: 𝑠^′: the diversity increased solution

(1) begin

(2)  𝑠^′←𝑠

(3)  foreach bid 𝑔_𝑏 in 𝑠^′  do

(4)   if  the random value > gvr(𝑔_𝑏)  then

(5)    remove 𝑔_𝑏 in 𝑠^′

(6)   end

(7)  end

(8)  add feasible bids to 𝑠^′ except for 𝑔_𝑏 with trembling at

   random based on a given ranking function

(9)  if  𝑟(𝑠^′)>𝑟(𝑠)  then

(10)   update gvc

(11)   return  𝑠^′

(12)  else if  𝑡𝑟𝑒𝑚𝑏𝑙𝑖𝑛𝑔  then

(13)   return  𝑠^′

(14)  else

(15)   return  𝑠

(16)  end

(17) end