Economic applications of potential games
Chan, Tak Lun Lester
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This dissertation studies three economic problems plagued by multiple equilibria. Indeterminacy of equilibrium outcome often poses a challenge in deriving robust predictions and policy guidance. The dissertation shows how the utilization of potential game theory can better deal with this challenge. Chapter 1 studies a general contracting problem between one principal and multiple agents. The interdependence of agents’ actions and payoffs creates a coordination problem among them, leading to multiple equilibria. In general, the principal’s optimal contracting scheme varies with how one selects among equilibria. Nevertheless, for a large class of contracting models where agents’ payoffs constitute a weighted potential game, I show that one contracting scheme is optimal for a large class of equilibrium selection criteria. This scheme ranks agents in increasing weight in the weighted potential game and induces them to accept their offers in a dominance-solvable way, starting from the first agent. I also apply the general results to networks and pure/impure public goods/bads. Chapter 2 studies two-sided markets, where two groups of agents interact via platforms. These markets exhibit network effects, i.e., the value of joining a platform increases with the number of users, which in turn lead to multiple equilibria. I show that many two-sided market models are weighted potential games, enabling the selection among equilibria by potential maximization—a refinement of Nash equilibrium justified by many theoretical and experimental studies. Under potential maximization, platforms often charge the side deriving more network benefits and subsidize the other side. Therefore, profit-maximizing platforms are often designed to favor the money side much more than the subsidy side. Chapter 3 studies markets with strong network effects. In these markets, firms compete for the adoption of all consumers rather than the marginal consumer. Therefore, the Spence distortion—a quality distortion driven by competition for the marginal consumer—should be absent, contradicting the findings in the network economics literature. This inconsistency stems from the choice of equilibrium selection criterion. I show that all popular selection criteria in that literature lead to Spence distortions, whereas potential maximization does not. Therefore, network market regulations based on Spence distortion arguments may be misguided.
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