Let's say there is some scarce resource and several agents compete to access this resource. Each agent is able to convert the resources into products that are beneficial to society, but each agent has a different efficiency with which it does so. Therefore, society would like to see the most efficient agent get the resource. However, the agent that pays more gets the resource.
Is it possible to model this scenario in a Price of Anarchy calculation? What would the model look like?
In the introductory examples of Price of Anarchy, I've come across Braess's Paradox and Pigou's example, but these are situations where the cost is incurred by the selfish agents themselves. In my example given above, the cost is incurred by society. That's why I'm not sure how to go about it.