Greetings,
I am trying to calculate the Shapley Value to obtain the fair distribution of value in a two player cooperative game. All the examples I have found describe three or more players. Can I calculate a Shapley value for two players?
The form I have is a little different. In my situation I have player A providing an improved service at a cost to them of $50. Player B benefits from this service to the value of $350. I wish to know what would be the Shapley (fair) value in this situation to each of the players A and B. There are two outcomes to the game:
Further clarification if required: player A provides a tool at $50 hire rate per day to player B at player B's facility, Player B pays $300 per day to rent their facility. Therefore if player A can reduce the duration of the job by one day player B will save one days tool hire and one days facility rental ($50 + $300 = $350). However Player A will be hiring their tool for one day less than normal and therefore suffer a loss of $50.
Appreciate any guidance on the above.
Scott
Assume N = {1,2}. Give each player i its stand-alone payoff v({i}} and then share what remains (v({1,2}) - v({1}) -v({2})) equally between both players. Hence, player i receives v({i}) + (v({1,2}) - v({1}) - v({2}))/2.
The Shapley value is the average of all marginal payoffs over all the permutations of the players.
With N = {1,2} there are just two permutations. In the permutation (1,2) player 1 receives v{1} and player 2 receives v(N) - v{1}. In the permutation (2,1) player 1 receives v(N)-v{2} and player 2 receives v{2}. Average each player's payoffs to obtain the Shapley value for that player.
- Badges
- Science topic
- Similar topics
- Automotive Engineering
- Machines