Players select sets of resources, and each resource's cost depends on its total number of users. Each player's cost is the sum of the costs of their selected resources. A unilateral deviation changes resource loads, so a finite-player Nash equilibrium compares costs after that change, not at the old loads. For cost functions , the potential changes by exactly the deviator's cost change. A minimizer of this potential in a finite game is therefore a pure Nash equilibrium.
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A **congestion game** is a type of game in game theory that models scenarios where multiple players (or agents) choose from a set of shared resources, which can become congested as more players use them. In these games, players do not have direct control over resources, but their choices affect the availability and efficiency of those resources. ### Key Characteristics of Congestion Games: 1. **Players**: A finite set of players who independently choose resources.