Network Formation and Potential Games
In this chapter we revisit the network-formation model in strategic form that we saw in chapter 7. We study the conditions under which these strategic-form games satisfy the property that all the information that is necessary to determine Nash equilibria can be captured in a single function on the set of all strategy profiles. If such a function exists, it is called a potential function or just a potential, and a strategic-form game that has a potential is called a potential game. For potential games, the set of strategy profiles that maximize the potential constitute a refinement of Nash equilibrium. For network-formation games that are potential games, we study the network structures that are formed in potential-maximizing Nash equilibria.
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