Florian Scheuer

A Game Theoretic Foundation of Competitive Equilibria with Adverse Selection

We construct a fully specified extensive form game that captures competitive markets with adverse selection. In particular, it allows firms to offer any finite set of contracts, so that cross-subsidization is not ruled out. Moreover, firms can withdraw from the market after initial contract offers have been observed. We show that a subgame perfect equilibrium always exists and that, in fact, when withdrawal is costless, the set of subgame perfect equilibrium outcomes may correspond to the entire set of feasible contracts. We then focus on robust equilibria that exist both when withdrawal costs are zero and when they are arbitrarily small but strictly positive. We show that the Miyazaki-Wilson contracts are the unique robust equilibrium outcome of our game. This outcome is always constrained efficient and involves cross-subsidization from low to high risk agents that is increasing in the share of low risks in the population under weak conditions on risk preferences.

Competitive Markets without Commitment

In the presence of a time-inconsistency problem with agency contracts, we show that competitive markets can implement allocations that Pareto-dominate those achieved by a benevolent government, and they induce more effort. We analyze a model with moral hazard and a two-sided lack of commitment. After agents have chosen their work, firms can modify contracts and agents can switch firms. If the ex post market outcome satisfies a weak notion of competitiveness and sufficiently separates individuals, it is Pareto superior to a government’s allocation with a complete breakdown of incentives. Moreover, competitive markets without commitment implement more effort in equilibrium under general conditions.