Congestion Game Theory and Applications

In a Congestion game we define players and resources, where the payoff of each player depends on the resources it chooses and the number of players choosing the same resource. But such externalities effects may appear in different direction. Some times by making more congestion, our utility decreases and such cases, we say that the congestion game admits negative externalities. Here we have applied congestion game theory in probabilistic model in graph. In graph every user need to reach from source to destination. Here each user randomly selects one edge at each time and this process will continue until both have reach to destination. But if here any congestion happens we have to remove that and see any alternate path without these congestions, but after this also congestions may again happen. So this process will continue until all congestions have removed . And finally we will get edge disjoint paths for both the users after removal of all congestions. Here we have shown how congestion game theory has affected their cost in way of choosing the edges randomly.